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• Volume 16, Issue 5
• Application of statistical process control in healthcare improvement: systematic review
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• Johan Thor ,
• Jonas Lundberg ,
• Jakob Ask ,
• Jesper Olsson ,
• Cheryl Carli ,
• Karin Pukk Härenstam ,
• Mats Brommels
• Medical Management Centre, Karolinska Institutet, Stockholm, Sweden
• Correspondence to:
 Dr Johan Thor
 Medical Management Centre, Berzelius väg 3, 5th floor, Karolinska Institutet, S-171 77 Stockholm, Sweden; johan.thor{at}ki.se

Objective: To systematically review the literature regarding how statistical process control—with control charts as a core tool—has been applied to healthcare quality improvement, and to examine the benefits, limitations, barriers and facilitating factors related to such application.

Data sources: Original articles found in relevant databases, including Web of Science and Medline, covering the period 1966 to June 2004.

Study selection: From 311 articles, 57 empirical studies, published between 1990 and 2004, met the inclusion criteria.

Methods: A standardised data abstraction form was used for extracting data relevant to the review questions, and the data were analysed thematically.

Results: Statistical process control was applied in a wide range of settings and specialties, at diverse levels of organisation and directly by patients, using 97 different variables. The review revealed 12 categories of benefits, 6 categories of limitations, 10 categories of barriers, and 23 factors that facilitate its application and all are fully referenced in this report. Statistical process control helped different actors manage change and improve healthcare processes. It also enabled patients with, for example asthma or diabetes mellitus, to manage their own health, and thus has therapeutic qualities. Its power hinges on correct and smart application, which is not necessarily a trivial task. This review catalogues 11 approaches to such smart application, including risk adjustment and data stratification.

Conclusion: Statistical process control is a versatile tool which can help diverse stakeholders to manage change in healthcare and improve patients’ health.

• MRSA, methicillin resistant Staphylococcus aureus
• PEFR, peak expiratory flow rate
• QI, quality improvement
• RCT, randomised controlled trial
• SPC, statistical process control

https://doi.org/10.1136/qshc.2006.022194

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Quality improvement (QI) practices represent a leading approach to the essential, and often challenging, task of managing organisational change. 1 Statistical process control (SPC) is, in turn, a key approach to QI. 2 SPC was developed in the 1920s by the physicist Walter Shewhart to improve industrial manufacturing. It migrated to healthcare, first in laboratory settings (eg, Fisher and Humphries 3 ) and then into direct patient care applications, along with other approaches to QI. Before we report on our systematic review of the literature on how SPC has been applied to QI in healthcare, there is a need to define SPC and its role in QI.


 “Statistical process control (SPC) is a philosophy, a strategy, and a set of methods for ongoing improvement of systems, processes, and outcomes. The SPC approach is based on learning through data and has its foundation in the theory of variation (understanding common and special causes). The SPC strategy incorporates the concepts of an analytic study, process thinking, prevention, stratification, stability, capability, and prediction. SPC incorporates measurement, data collection methods, and planned experimentation. Graphical methods, such as Shewhart charts (more commonly called ‘control charts’), run charts, frequency plots, histograms, Pareto analysis, scatter diagrams, and flow diagrams are the primary tools used in SPC.” (Carey 4 , p xviii)

The terms “statistical process control” and “statistical quality control” are often used interchangeably, 5 although sometimes the latter is used to describe a broader organisational approach to quality management that evolved into the concept of total quality management. 6

One of the tenets of QI is that to improve healthcare performance we must change our way of working. 7 But change does not always mean improvement. To discriminate between changes that yield improvement and those that do not, relevant aspects of performance need to be measured. In addition, measurement guides decisions about where improvement efforts should be focused in the first place. SPC may facilitate such decision making. Control charts, central to SPC, are used to visualise and analyse the performance of a process—including biological processes such as blood pressure homoeostasis or organisational processes such as patient care in a hospital—over time, sometimes in real time. Statistically derived decision rules help users to determine whether the performance of a process is stable and predictable or whether there is variation in the performance that makes the process unstable and unpredictable. One source of such variation can be a successful intervention aimed at improvement that changes performance for the better. If the improvement is maintained, the process will stabilise again at its new level of performance. All of this can be easily determined by using SPC. 4

Although there are theoretical propositions that SPC can facilitate decision making and QI in healthcare (eg, Berwick, 8 Benneyan et al , 9 Plsek 10 ) it is not clear what empirical support there is in the literature for such a position 11 :


 “The techniques of statistical process control, which have proved to be invaluable in other settings, appear not to have realised their potential in health care. ... Is this because they are, as yet, rarely used in this way in health care? Is it because they are unsuccessful when used in this way and thus not published (publication bias)? Or is it that they are being successfully used but not by people who have the inclination to share their experience in academic journals?” (p 200)

The present systematic review aimed to answer these questions. We examined the literature for how and where SPC has been applied in QI of clinical/patient care processes and the benefits, limitations, barriers and facilitating factors related to such application.

MATERIALS AND METHODS

Drawing on the principles and procedures for systematic review of QI interventions 12 we searched for articles on the application of SPC in healthcare QI published between 1966 and June 2004 (see appendix A) in the following databases: Web of Science, Ovid Medline(R), EMBASE, CINAHL (Cumulative Index to Nursing and Allied Health Literature), PsycInfo, and the Centre for Reviews and Dissemination databases. We also included articles found by searching reference lists or from elsewhere which we were aware of, if they met our inclusion criteria: original empirical studies of SPC application in improvement of clinical/patient care processes in healthcare organisations, published in English. We excluded articles dealing with application of SPC in laboratory or technical processes (eg, film processing) and in surveillance/monitoring (unless they also contained empirical data about improvement efforts), as well as tutorials (unless they contained empirical case studies), letters, book reviews and dissertations.

We reviewed abstracts, when available, or else other information about the publication provided in the database (eg, publication type such as letters, book reviews or original articles). Articles that did not meet the inclusion criterion were excluded. We retrieved and read the full text of the remaining articles, again excluding the articles that did not meet the inclusion criterion.

We developed, pilot tested and modified a data abstraction form which we then used to consistently capture information of relevance to our review questions on reading the full text articles. The information recorded was: whether and how the article met the inclusion criterion; study objective(s); study design; whether the study empirically compared application of SPC with any other method for process data display and analysis; reported benefits, limitations, barriers and facilitating factors related to SPC; organisational setting; country where study was conducted; clinical specialty; unit of analysis; variables for SPC analysis; and other observations. Some questions in the form required a yes/no or brief response (eg, country where study was conducted) and others required answers in the form of direct quotes from the article or the a summary of the article written by the reviewer. Each article was read and data abstracted by one member of the review team (the coauthors of this review). Following this, all the data abstraction forms were reviewed by the first author, who solicited clarification and checked for any missing or incomplete data to ensure consistency in reporting across all articles reviewed. He also conducted the initial data synthesis, which was then reviewed by the entire team.

We determined the study design for each article and whether the investigators intended to test the utility of SPC application, alone or in combination with other interventions. In several articles, the study design or study objectives were not explicitly stated. Our determination of such intention in such cases was based on our reading of the full text papers.

Simple descriptive statistics—for example, the number of publications per year of publication or per country—were used to characterise the included studies. The qualitative nature of our research questions and of the abstracted data shaped our analysis and synthesis of findings regarding benefits, limitations, SPC variables, etc. 13 The abstracted data was reviewed one question at a time and data from each article was classified into one or more thematic categories, each with a descriptive heading. Informed by our present understanding of QI and healthcare, we developed these categories as we reviewed the data, rather than using categories derived a priori from theory. For data that did not fit into an existing category, we developed a new one. Thus the categories emerged as we synthesised the data. We report the categorised data in tabular form, illustrated with examples, and give the references of all the source studies.

To strengthen our review through investigator triangulation, 14 we sought feedback on an earlier version of this manuscript from two SPC experts: one was the most frequent coauthor in the included studies and the other was an expert on SPC application also in settings other than healthcare. Their comments helped us refine our data synthesis and distil our findings.

The database searches yielded 311 references. The initial review (abstracts etc.) yielded 100 articles which we read in full text form. Of these, 57 articles met the inclusion criteria and have been included in the review. 15– 71 To characterise the body of liferature, figure 1 shows the year of publication and whether the studies were conducted in USA or elsewhere (further specified below); table 1 gives the study designs and objectives—whether or not to test SPC utility.

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 Study design and objectives of the studies included in the systematic review*

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 The number of included articles by year of publication. (A total of 55 articles were published in 1990–2003; the two articles from 2004 are not included in this graph since the database searches were conducted in June 2004.) Black bars: studies conducted in the USA; grey bars: studies conducted outside the USA.

Most of the articles (45/57) concerned application of SPC in healthcare improvement in the USA. 15– 35, 37– 40, 42, 43, 45, 47, 49– 56, 59, 60, 63, 67– 71 While the first US-based article was published in 1990, the non-US articles were published between 1998 and 2003: three articles were from the UK, 61, 62, 66 three were from Switzerland, 36, 41, 46 and one each were from Australia, 58 Finland, 65 France, 57 Indonesia, 44 Norway 64 and Spain. 48 The intention to test the utility of SPC is exemplified by a study aiming to reduce the rate of acquisition of methicillin-resistant Staphylococcus aureus (MRSA) on wards and units at Glasgow Royal Infirmary hospitals. 61 Annotated control charts displaying data on MRSA acquisition were fed back monthly to medical staff, managers and hotel services. Sustained reductions in the rate of acquisition from the baseline, which could not otherwise be accounted for, started 2 months later. In contrast, investigators at a paediatric emergency department used SPC to demonstrate a decline in the rate of contamination following the introduction of a new approach to drawing blood for culture specimens, 68 but the study had no intention to test the utility of SPC per se.

To characterise the content of the articles, we first present how and where SPC has been applied to healthcare QI. Tables 2–4 present the study settings (ie, hospital etc. where SPC was applied; table 2), the field of healthcare (ie, specialties or forms of care; table 3), and the units of analysis (table 4). Table 5 enlists the 97 distinct SPC variables that have been reported. Tables 6–9 convey our synthesis of the reported benefits, limitations, barriers and facilitating factors related to SPC application. For each category, we have given explanations or examples and references to the source articles.

 How and where SPC was applied: study settings*

 How and where SPC was applied: fields of healthcare*

 How and where SPC was applied: units of analysis*

 SPC variables*

 Benefits of using SPC to improve clinical processes*

SPC has been applied to healthcare improvement in a wide range of settings and specialties, at diverse levels of organisations and directly by patients, using many types of variables (fig 1, tables 2–5). We found reports of substantial benefits of SPC application, as well as important limitations of, barriers to and factors that facilitate SPC application (tables 6–9). These findings indicate that SPC can indeed be a powerful and versatile tool for managing changes in healthcare through QI. Besides helping diverse stakeholders manage and improve healthcare processes, SPC can also help clinicians and patients understand and improve patients’ health when applied directly to health indicators such as PEFR in asthma or blood sugar concentrations in diabetes. In healthcare, the “study subject” can thus also be an active agent in the process, as when patients apply SPC to their own health. Several studies indicated the empowering effects this may have on patients. 35, 38, 40, 50 SPC application thus has therapeutic potential as it can help patients manage their own health. We agree with Alemi and Neuhauser 70 that this potential merits further investigation.

Most of the included articles concerned application of SPC in healthcare improvement in the USA. Articles from other countries appeared only towards the end of the study period (fig 1). We have no explanation for this finding, but we speculate that it is related to differences between US and other healthcare systems with regard to QI awareness and implementation. 73

Only 22 studies included in the review were intended to test the utility of SPC (table 1). Of the four controlled studies, only one included a control chart in the intervention (as a minor component which did not fully exploit the features of SPC). In 35 articles we did not find an intention to test the utility of SPC application. In those cases, SPC was applied for other reasons (ie, to evaluate the impact of other interventions). Even though many articles thus did not address the utility of SPC, all studies offered information—to varying degrees—relevant to our review’s question of how SPC has been applied to healthcare. The utility of SPC is reflected in benefits reported regarding SPC application (table 6).

SPC has been applied in over 20 specialties or fields of healthcare, at a wide range of levels (tables 3 and 4), suggesting that SPC has broad applicability in healthcare. The dominance of anaesthesia and intensive care can be explained in large part by the fact that many studies included their services in conjunction with other specialties. This reflects the way in which anaesthesia has a vital supporting role in many clinical care processes. The 97 SPC variables reported (table 5) demonstrate a diversity of situations in which SPC has been applied, ranging from process indicators of patients’ health to health outcomes and many aspects of healthcare processes and organisational performance. This indicates that SPC is a versatile QI tool.

The benefits of SPC application (table 6) mirror those given in books and tutorials on SPC (exemplified by the quote in the Introduction to this review). As noted in a report from a top-ranked healthcare system which has applied SPC widely:


 “Among the most powerful quality management tools that IHC [Intermountain Health Care, USA] has applied is statistical process control, SPC. Most notable among those tools are control charts. Under optimal conditions, these graphical depictions of process performance allow participants to know what is happening within their processes as ‘real time’ data enable them to make appropriate decisions. The capability of truly understanding processes and variation in a timely manner has resulted in the most dramatic, immediate, and ongoing improvements of any management technique applied at IHC.” (Shaha, 26 p 22)

The limitations of SPC application (table 7) identified by this review are important, and yet perhaps less emphasised than the benefits in books and tutorials on SPC. SPC cannot solve all problems and must be applied wisely. There are many opportunities to “go wrong”, as illustrated by the case where incorrect application was highlighted by other authors (limitation number 5 in table 7). In several cases, our own understanding of SPC suggested that investigators had not used it correctly or fully (eg, standard decision rules to detect special causes were not applied to identify process changes). In the worst case scenario, incorrect application of SPC could lead to erroneous conclusions about process performance and waste time, effort and spirit and even contribute to patient harm. In the more authoritative studies we reviewed, co-investigators included experts in industrial engineering or statistics or authors who otherwise had developed considerable expertise in SPC methodology. On the basis of these observations, we conclude that although SPC charts may be easy to use even for patients, clinicians or managers without extensive SPC training, they may not be equally simple to construct correctly. To apply SPC is, paradoxically, both simple and difficult at the same time. Its power hinges on correct and smart application, which is not necessarily a trivial task. The key, then, is to develop or recruit the expertise necessary to use SPC correctly and fully and to make SPC easy for non-experts to use, before using it widely.

 Limitations of SPC application in improvement of clinical processes*

Autocorrelation is another limitation of SPC highlighted by this review. Our review, and published books, offer limited advice on how to manage it:


 “There is no single acceptable way of dealing with autocorrelation. Some would say simply to ignore it. [Others] would disagree and suggest various measures to deal with the phenomenon. One way is to avoid the autocorrelation by sampling less frequently. ... Others argue against plotting autocorrelated data on control charts and recommend that the data be plotted on a line chart (without any centerline or control limits).” (Carey, 4 p 68)

Just over a quarter of the articles reported barriers to SPC application (table 8). The three broad divisions of barriers—people, data and chart construction, and IT—indicate where extra care should be taken when introducing SPC in a healthcare organisation. Ideas on how to manage the limitations of and barriers to SPC application can be found among the factors reported to facilitate SPC application (table 9). They deal with, and go beyond, the areas of barriers we found. We noted the prominence of learning and also of focusing on topics of interest to clinicians and patients. The 11 categories under the heading “Smart application of SPC can be helpful” contain valuable approaches that can be used to improve SPC application. Examples include risk adjustment 51, 52, 71 and stratification 30, 37, 59 to enable correct SPC analysis of data from heterogeneous populations of patients (or organisational units). Basic understanding of SPC must be taught to stakeholders and substantial skill and experience is required to set up successful SPC application. Experts, or facilitators, in healthcare organisations can help, as indicated in table 9, and as we have described for other QI methods. 74

 Barriers to SPC application*

 Factors or conditions facilitating application of SPC*

We found more information on SPC benefits and facilitating factors than on limitations and barriers, and this may represent a form of publication bias, as indicated by the quote in the Introduction. 11 We did not find any study that reported failed SPC application. We can speculate that there have been situations when SPC application failed, just as there must be many cases of successful SPC application that have not been reported in the literature. Studies of failed SPC application efforts, as well as studies designed to identify successful ways to apply SPC to manage change, would help inform future SPC application efforts. On the basis of this review, we agree with the argument that “medical quality improvement will not reach its full potential unless accurate and transparent reports of improvement work are published frequently and widely (p 319),” 75 and also that the way forward is to strengthen QI research rather than to lower the bar for publication. 76

Methodological considerations regarding the included studies

None of the studies we found was designed to evaluate the effectiveness quantitatively—that is, the magnitude of benefits—of SPC application. This would have required other study designs such as cluster randomised trials or quasi-experimental studies. 12 Although the “methods of evaluating complex interventions such as quality improvement interventions are less well described [than those to evaluate less complex interventions such as drugs]”, Eccles et al argue that the “general principle underlying the choice of evaluative design is ... simple—those conducting such evaluations should use the most robust design possible to minimise bias and maximise generalisability. [The] design and conduct of quantitative evaluative studies should build upon the findings of other quality improvement research (p 47).” 77 This review can provide such a foundation for future evaluative studies.

An important distinction is warranted here: we believe that SPC rests on a solid theoretical, statistical foundation and is a highly robust method for analysing process performance. The designs of the studies included in this systematic review were, however, not particularly robust with regard to evaluating the effectiveness of SPC application, and that was not their objective. This does not mean that SPC is not a useful tool for QI in healthcare, only that the studies reviewed here were more vulnerable to bias than more robust study designs, even if they do indicate many clear benefits of SPC application (table 6). Despite the studies not being designed to evaluate the effectiveness of SPC, many used SPC to effectively show the impact of QI or other change initiatives. In this way, SPC analysis can be just as powerful and robust as study designs often deemed superior, such as randomised controlled trials (RCTs). 77 The key to this power is the statistical and practical ability to detect significant changes over time in process performance when applying SPC. 9 On the basis of a theoretical comparison between control charts and RCTs, Solodky et al 38 argue that control charts can complement RCTs, and sometimes even be preferable to RCTs, since they are so robust and enable replication—“the gold standard” for research quality—at much lower cost than do RCTs. These points have been further elaborated in subsequent work. 78, 79

A curious methodological wrinkle in our review is: can you evaluate the application of a method (eg, SPC) using that same method for the evaluation? Several of the included studies used SPC both as (part of) an intervention and as a method to evaluate the impact of that intervention. For example, Curran et al used annotated control charts to feed information on MRSA acquisition rates back to stakeholders and used these same control charts to show the effectiveness of the feedback programme. 61

Relationship between monitoring and improvement

When SPC is applied for monitoring, rather than for managing change, the aims are different—for example, to detect even small but clinically important deviations in performance—as are the methodological challenges. 80, 81 This review focused on the latter. Thus although studies on SPC application for monitoring healthcare performance were excluded from this review, we recognise the importance of such monitoring. The demarcation between monitoring and improvement is not absolute. Indeed, there are important connections between measurement, monitoring and improvement, even if improvement does not follow automatically from indications of dissatisfactory performance. “To improve performance, organizations and individuals need the capability to control, improve, and design processes, and then to monitor the effects of this improvement work on the results. Measurement alone will not suffice (pp 1–35).” 82

Monitoring performance by way of control charts has been suggested as a better approach to clinical governance in the British National Health Service. Through six case studies, Mohammed et al demonstrate how control chart monitoring of performance can distinguish normal performance from performance that is either substandard or better than usual care. “These case studies illustrate an important role for Shewhart’s approach to understanding and reducing variation. They demonstrate the simplicity and power of control charts at guiding their users towards appropriate action for improvement (p 466).” 83

Comments on the review methodology

No search strategy is perfect, and we may well have missed some studies where SPC was applied to healthcare QI. There are no SPC specific keywords (eg, Medical Subject Headings, MeSH) so we had to rely on text words. Studies not containing our search terms in the title or abstract could still be of potential interest although presumably we found most of the articles where SPC application was a central element. We believe the risk that we systematically missed relevant studies to be small. Therefore, our findings would probably not have changed much due to such studies that we might have missed.

The review draws on our reading, interpretation and selection of predominantly qualitative data—in the form of text and figures—in the included articles to answer the questions in our data abstraction form. The questions we addressed, the answers we derived from the studies, and the ways we synthesised the findings are not the only ways to approach this dataset. Furthermore, each member of the review team brought different knowledge and experiences of relevance to the review, potentially challenging the reliability of our analysis. An attempt was made to reduce that risk by having one investigator read all data abstraction forms, and obtain clarifications or additional data from the original articles when needed. That investigator also conducted the initial data synthesis, which was then reviewed by the entire team and the two outside experts. Although other interpretations and syntheses of these data are possible, we believe that ours are plausible and hope they are useful.

The methods for reviewing studies based primarily on qualitative data in healthcare are less well developed than the more established methods for quantitative systematic reviews, and they are in a phase of development and diversification. 13, 84, 85 Among the different methods for synthesising evidence, our approach is best characterised as an interpretive (rather than integrative) review applying thematic analysis—it “involves the identification of prominent or recurrent themes in the literature, and summarising the findings of different studies under thematic headings”. 86 There is no gold standard for how to conduct reviews of primarily qualitative studies. Our response to this uncertainty has been to use the best ideas we could find, and to be explicit about our approach to allow readers to assess the findings and their provenance.

The main limitation of this review is the uncertainty regarding the methodological quality of many of the primary studies. Assessment of quality of qualitative studies is still under debate, and there is no consensus on whether at all, or, if so, how to conduct such assessments. 84 We reviewed all the studies that satisfied our inclusion criteria and made no further quality assessment. Therefore our findings should be considered as tentative indications of benefits, limitations, etc to be corroborated, or rejected, by future research. The main strength of this review is our systematic and explicit approach to searching and including studies for review, and to data abstraction using a standardised form. It has helped generate an overview of how SPC has been applied to healthcare QI with both breadth and depth—similar to the benefits of thematic analysis reported by investigators reviewing young people’s views on health and health behaviour. 87

In conclusion, this review indicates how SPC has been applied to healthcare QI with substantial benefits to diverse stakeholders. Although there are important limitations and barriers regarding its application, when applied correctly SPC is a versatile tool which can enable stakeholders to manage change in healthcare and improve patients’ health.

Database search strategy

Web of Science (1986 – 11 June 2004)

TS [topic search]  =  ((statistical process control or statistical quality control or control chart* or (design of experiment and doe)) and (medical or nurs* or patient* or clinic* or healthcare or health care))

We limited the search to articles in English only which reduced the number of hits from 167 to 159. We saved these 159 titles with abstracts in an EndNote library. Using a similar strategy, we searched the following databases through Ovid:

Ovid MEDLINE(R) (1966 to week 1, June 2004)

EMBASE (1988 to week 24, 2004)

CINAHL (1982 to week 1, June 2004)

PsycINFO (1985 to week 5, May 2004)

This yielded 287 hits, including many duplicates, which we saved in the same EndNote library as above.

Centre for Reviews and Dissemination (CRD)

We searched all CRD databases and found two articles which we also added to our EndNote library.

Acknowledgments

We thank Ms Christine Wickman, Information Specialist at the Karolinska Institutet Library, for expert assistance in conducting the database searches. We also acknowledge the pilot work conducted by Ms Miia Maunuaho as a student project at Helsinki University, supervised by Professor Brommels, which provided a starting point for this study. We thank Professor Duncan Neuhauser, Case Western Reserve University, Cleveland, Ohio, USA, and Professor Bo Bergman, Chalmers University of Technology, Gothenburg, Sweden, for their helpful comments on an earlier version of this manuscript. We thank Dr Rebecca Popenoe for her editorial assistance.

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Funding: No dedicated funding was received for this study. All coauthors were supported by their respective employers in conducting this research as part of their work.

Competing interests: None.

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The Contribution of Variable Control Charts to Quality Improvement in Healthcare: A Literature Review

Line slyngstad.

1 Molde University College, Molde, 6410, Norway

To conduct a literature review to determine where and how variable control charts have contributed to quality improvement in healthcare.

A targeted literature search of the ABI/INFORM Global, Science Direct, Medline and Google Scholar databases was conducted, which yielded 6875 papers. Screening articles on the basis of title and abstract resulted in references to 163 articles, leading to the identification of 29 articles published between 1992 and 2019 that met the inclusion criteria. Common themes, variables and units of analysis were then analyzed.

Variable control charts have been applied in 11 different healthcare contexts, using 17 different variables, at various levels within healthcare organizations. The main reason for applying variable control charts is to demonstrate a process change, usually following a specific change or quality intervention. The study identified various limitations and benefits of applying variable control charts. The charts are visually easy to understand for both management and employees, but they are limited by their requirement for potentially complex and resource-intensive data collection.

Variable control charts contribute to quality improvement in healthcare by enabling visualization and monitoring of variations and changes in healthcare processes. The methodology has been most frequently used to demonstrate process shifts after quality interventions. There still is a great potential for more studies applying variable control charts.

Introduction

Quality of care can be defined as the

degree to which health services for individuals and population increase the likelihood of desired health outcomes and care consistent with professional knowledge. 1

Quality of care can be measured through dimensions, most commonly effectiveness, safety, responsiveness, accessibility, equity and efficiency. 2

In recent decades, quality improvement (QI) strategies and methods from industry have been applied more commonly to healthcare. Quality improvement involves concerted and continuous efforts to make changes that will improve patient outcomes, system performance and professional development. 3 With rapid developments in technology and more complex healthcare systems, it is becoming increasingly important to apply methods to monitor whether changes lead to better quality and patient outcomes.

One of the most challenging tasks for healthcare leadership, is to control the processes leading to the desired quality. Over the last decade, researchers have demonstrated how control charts can be an efficient tool for monitoring processes and quality.

Statistical process control (SPC) methods are management tool for measuring and visualizing stability and monitoring QI from one point in time to another. These methods provide a powerful statistical tool for QI that distinguishes between special-cause variation and common variation. The literature on SPC in healthcare is growing, including literature reviews, tutorials and practitioners note, focusing on everything from general use of SPC in healthcare, 4 , 5 to more specified topics, such as surgery 6 or pressure ulcer prevention. 7 Tutorials do also cover a wide range of areas such as detecting and monitoring hospital acquired infections, 8 charts for data involving very large sample sizes, 9 or the application of risk-adjusted control charts in health care. 10

In addition, SPC is a practical tool that benefits different organizational levels, at the management level and front-line staff levels. Management refers to the leaders of healthcare organizations, and front-line staff is the employees dealing with the patients.

For the service quality to meet patients’ expectations, the process delivery must be stable and repeatable. 11 Quality is sometimes best expressed through numerical measurements, such as the waiting time, 12 length of stay 13 or door-to-needle-time, 14 where it is feasible to use variable control charts. 11 These are SPC charts that use variables as a quality indicator. However, there appears to have been no previous review of the use of variable control charts in the context of health care.

The main objective of this literature review is to examine where and how variable control charts have contributed to QI in healthcare, including their objectives, outcomes, limitations, and benefits, for both management and front-line staff.

Materials and Methods

A targeted literature search in relevant databases was conducted by the author, to identify studies that meets the inclusion criteria. There was one reviewer of this article. Following sections describe the process of selecting articles included in the review.

Eligibility Criteria

Inclusion criteria.

The criteria for inclusion in the literature review were that the research should apply variable control charts in healthcare, and should be conducted in organizations providing care, such as hospitals, nursing homes and home healthcare.

Exclusion Criteria

Articles concerning pharmacies, laboratories and organizations providing mental health care, such as psychiatric hospitals, were excluded from the study, as were studies of random samples of patients across different institutions. Articles examining all levels of institutions were included, from organization to individual performance level. Only empirical articles were included, while tutorials, letters, reviews and books were excluded. All articles reviewed were written in English and published in peer-reviewed journals.

Study Identification

A search of the ABI/INFORM Global, Science Direct, Medline and Google Scholar databases was performed to identify research articles that applied SPC in healthcare for all years to date (2021). The search terms used were: control chart healthcare, statistical process control healthcare, variable control chart application healthcare, Shewhart control chart healthcare, process improvement healthcare, process analysis healthcare, six sigma healthcare, LSS healthcare and total quality management (TQM) healthcare. Relevant articles found in reference lists was included further in the review. When the searches were conducted, title and abstract were crucial if the article was included further in the review. It was often from the title or abstract which charts were used, since the type of variable determines what charts are appropriate to use.

Study Selection and Data Extraction

The title and abstract were reviewed to understand the content and ascertain whether the article met the inclusion criteria. If the inclusion criteria were not met, the article was excluded. Included articles were read in full, and information relevant to this review was extracted and organized in an Excel sheet, including title, authors, year of publication, country, criteria for inclusion, study objective, study outcome, output variable, journal, unit of analysis, study context and level of analysis, and length of period for the data used in the SPC charts. It was also noted whether variable control charts were used with additional methods of analysis, such as regression analysis or interviews. Visual statistics in the form of graphs were used to present relevant information from the data, such as country and year of publication. The review also extracted qualitative information on the objectives of the studies, their outcomes, and the limitations and benefits of applying SPC in healthcare.

Results of the Search

The database search resulted in references to 6875 articles (see Figure 1 ). Screening articles on the basis of title and abstract resulted in references to 163 articles, of which 120 of the records were excluded. A reading of the abstracts suggested that 43 articles might meet the inclusion criteria. 15 of these articles were excluded; 7 applied run chart, 6 used attributes in their control chart, and 4 were was tutorial notes, and 26 of the articles met the inclusion criteria. 13–40 The articles reference list were checked for possible articles, found 3 more. Thus, a total of 29 articles met the inclusion criteria.

Flow diagram.

Characteristics of the Studies

First, the articles were sorted by year of publication and the country in which the research was conducted (see Figure 2 ). The earliest study was published in 1992 41 and the latest in 2019. 38 Both of these were conducted in the USA. Between 1992 and 2006, there were long gaps between publications, but from 2006 they became more frequent. The highest numbers of studies were published in 2014 and 2016, with four in 2014 15 , 24 , 26 , 33 and five in 2016. 16 , 23 , 29–31

Year of publication and country.

Research for 11 of the articles was conducted in the USA, 13 , 18 , 21 , 24 , 28 , 32 , 35–37 , 39 , 42 and one comparative study of the USA and Turkey 38 was also categorized as USA. Three articles each were published in the UK, 19 , 33 , 34 Sweden 23 , 25 , 26 and India, 15–17 and two each in Italy 30 , 31 and Taiwan. 20 , 40 Single studies were conducted in Brazil, 29 Switzerland, 14 Australia 27 and Israel. 20 Because the majority of articles were based on research in the USA, the others were classified into a single “other countries” category.

With regard to content, Table 1 summarizes the research contexts, output variables and units of analysis. Twelve studies were conducted in surgery departments, 13 , 20 , 21 , 24 , 28–32 , 35 , 36 , 39 five in emergency departments 19 , 25–27 , 33 and two in intensive care 14 , 22 and health information departments. 15 , 17 Single studies were conducted in a urology department, 23 internal medicine, 38 a medical record department, 16 a registration department, 37 a women, infants and children clinic 18 and a general practice. 34 One study focused on an entire hospital. 41

Content of Articles

The output variables used varied considerably. The most frequent was waiting time, which was used in six studies. 13 , 18 , 25 , 26 , 34 , 37 Turnaround time was used in four studies, 16 , 17 , 30 , 31 operative time in three 20 , 24 , 32 and non-operative time in two. 32 , 39 The remaining variables were used only once. The most frequent unit of analysis was department level, used in 15 articles, with the remainder conducted at individual patient, individual surgeon, individual observation and organizational levels. The follow up period in the papers, varied from 4 days to 34 months.

Reasons for Applying SPC and the Use of Additional Methods

There were different objectives for applying variable control charts in healthcare. They were generally applied to demonstrate a shift in a process, or for various reasons in retrospective studies. Fifteen studies applied variable control charts to demonstrate a change resulting from an improvement project. 14 , 16–18 , 21 , 23 , 25–27 , 29 , 33 , 35–37 , 40 Waiting time was the most frequently used performance measure, used in four articles. 18 , 25 , 26 , 37 Turnaround time was used as a measure in two articles, 16 , 17 while the other variables were represented only once.

In the remaining studies, the reasons for applying variable control charts were diverse. In some articles, the charts were used to determine steady-state behavior or benchmarks, 20 , 30 , 31 to measure variation or process performance, 15 , 34 , 38 to identify links between changes and opportunities for improvement between hospital and micro- or/macro-systems, 28 to evaluate whether nurse staffing was meeting needs, 22 or for other reasons. 19 , 24 , 39

It was noted that additional methods were often used when applying variable control charts. As illustrated in Figure 3 , variable control charts were the only method used in 12 studies, while additional methods were used in 16 cases. In nine studies that used additional methods, quantitative methods were applied, while in seven articles a mixed-methods approach was adopted.

Were methods other than variable control charts used?

Limitations of Applying Variable Control Charts

Limitations to data collection.

The most common limitation of applying variable control charts is that, for various reasons, collecting data may be resource-intensive and time-consuming. In some cases, where data are not readily available, collection may be complex and require people to collect sufficient data. 19 Examples in the literature include undertaking manual patient chart reviews, 28 collecting data on waiting times through data collection sheets, 37 and measuring turnaround time for health records preparation with a stopwatch. 17 Due to the time and resources required for collection, sample sizes may limit the results, since monitoring a process over time requires several months data. 21 The analysis may therefore be limited to a specific period, such as one day or one shift, which may be unrepresentative of day-to-day occurrences, as the day on which the data were collected may be anomalous. 19 For the similar reasons, data may be limited to one department. 23

Limitations of Data Used in the Charts

A frequently raised issue is that variable control charts must sometimes be used alongside other methods. Variable control charts visualizes the performance of the output variable and do not necessarily have a descriptive function, so they must be supplemented with methods such as semi-structured interviews, 25 , 26 descriptive statistics or value stream mapping. 15 , 16 This is also the case when the data are retrospective and links between particular causes and events in the process cannot be identified. 28 , 35 Such cases require the investigation of out-of-control points by care providers, 38 so additional methods must be used.

Furthermore, observational bias may affect the recording of data, as in the Hawthorne effect, because observing people may improve their performance. 19 In some studies this effect has been observed from the outset of the formal process analysis, but the effects are transient and should not be mistaken for definitive results. 14

Other limitations reported include the difficulty of defining a true baseline or “before” period for comparison when seasonal differences affect the variables, 27 and the fact that traditional control chart approaches make no adjustment for varying risk profiles. Medical contexts must deal with heterogeneous patient cases. Information on patient-related risk adjustment is rarely used, 38 and few articles discuss the use of risk-adjusted Shewhart charts. 20 In some cases, information on risk was unavailable, or it required information from systems to construct patient mix adjustment models, and information from a hospital-wide cost accounting system to measure total in-hospital cost. 21

Like many other statistical methods, variable control charts require the data to be normally distributed. Sometimes they require transformed data, making it more difficult to present the data to others. 21 It mayalso not involve the use of control groups, 18 making generalization more challenging. For instance, when the unit of analysis is a single surgeon, 39 the results are unlikely to be readily transposable to other surgical populations. 35

Benefits of Applying Variable Control Charts

Variable control charts are visually easy to understand.

The selected articles mention several benefits of applying variable control charts. First, charts are reported to be visually easy to understand, and may reveal otherwise unobtainable insights. 18 They may inspire the development of patient diagnosis-to-treatment routines and work process measurements, and enable the visualization of resource use. 23 They may demonstrate whether a process is stable or unstable, 34 and provide a method for assessing undisturbed or steady-state process behavior. 30 Variable control charts measure effects over time through simple statistics. 20 They provide early warning of systematic change taking place in a process, 27 , 30 , 32 , 39 and enables the nature of an identified shift in performance, whether gradual or sudden, to be determined. 39 Applying variable control charts in process analysis may significantly improve the quality of a time-sensitive process. 14

Variable Control Charts are Useful for Front-Line Staff

Some articles suggest that variable control charts are helpful for employees. Front-line staff can see what is happening, with an opportunity to stand back from daily routines to view things differently. 19 Variable control charts may also help to motivate cultural change and moves toward continuous improvement and excellence. 15 , 19

Variable Control Charts are Useful for Management

Variable control charts benefit managers, enabling them to make decisions based on science rather than intuition. 15 The charts can support public health agencies in developing service delivery processes, 18 and allow comparison of an organization with and its partners or competitors. 34 They provide insights into the processes investigated, allow the monitoring of consecutive events, 14 and improve performance quality through early detection of problems. 31 Variable control charts may be used as a monitoring tool for one-off interpretations. 27 They may also help decision makers to achieve institutional goals and objectives, 30 and to pinpoint performance shifts 39 and the direction they are taking. 34

The review findings demonstrate that variable control charts contribute to QI in various healthcare settings, with different types of output variables, at different levels within healthcare organizations. The review also reveals the reasons for applying variable control charts and using additional methods, and it highlights the limitations and benefits of their use. The amount of previous research is less than expected, with only 29 articles meeting the inclusion criteria. The current healthcare environment, involving complex systems, presents enormous potential for using such methodologies in research and practical applications.

As illustrated by Figures 1 and ​ and2, 2 , relevant research has increased since 2006. Primarily in the USA, with only nine studies in other countries. This may reflect a stronger tradition in the USA than in Europe regarding using applications from industry in healthcare.

There are several of benefits and limitations of applying variable control charts to QI in healthcare. The benefits and limitations mentioned in the articles indicate that variable control charts may be a powerful tool, especially in settings where data can easily be obtained. Several papers have noted that the charts are beneficial for both front-line staff and management because the charts are visual, and are good tools for understanding processes and supporting decision-making. Several articles have suggested that the application of variable control charts is limited by the resources required to collect data that are not readily available. Amassing data may require both time and resources that many institutions do not have, which may explain why few studies have applied variable control charts. However, technological developments in IT systems and applications are likely to make data collection easier and make the use of such methodologies more available. The studies included in this review suggest many potential research opportunities in new healthcare settings, as well environments where variable control charts have already been applied.

Variable control charts are a data-driven method. Application of variable control charts would not lead to changes but is often used to demonstrate process variation and effects of different quality interventions, for instance lean 25 or six sigma. 13 When data collection is time-consuming, and frequently used with other methods ( Figure 2 ), it requires clear and present management to apply the charts, which might be an additional reason for the limited number of studies applying variable control charts.

From the origin SPC was applied to monitor variations in manufactured products. 43 Because it sometimes difficult to provide products with equal quality from unit to unit, charts were used to monitor the variability. An example of this is the blade thickness in the production of jet turbines. 11 To date, applying variable control charts in healthcare seems to have the most gain in cases where quality interventions have been made, usually after a process change or quality intervention. In such research, there would typically be more focus on whether a shift has occurred in the process, rather than on monitoring the variation itself. This concerns 15 of the selected articles in this review. The reason for this is uncertain but might relate to the service intangibility and heterogeneity, and the difficulty in research to find feasible measures to monitor. It would typically be easier to concretize a physical product than a service.

Variable control charts have been applied in 11 different healthcare fields, although some of these have been investigated more frequently than others. Some areas and variables have a more obvious connection to the quality of care than others, but most studies have a connection to the most common quality dimensions which are effectiveness, safety, responsiveness, accessibility, and efficiency. 2 The results reveal great potential for applying variable control charts in QI in healthcare.

Twelve of the selected studies were conducted in surgery departments, of which five used operative and non-operative time as output variables. 20 , 24 , 32 , 35 , 39 In these five studies, operative and non-operative time were used to monitor cost and efficiency. In other research, operative and non-operative time are related to safety. For example they correlate the duration of surgery with complications and higher risk. 44 , 45 Longer operating times and increased use of theatres have also been shown to expose patients to greater risk of surgical site infections, 24 and faster operating times are associated with better outcomes. 46 Although variable control charts could be important for monitoring cost and efficiency, there might be potential for other measurements to be applied to SPC charts from surgery departments.

Concerning other measures monitored in surgery, reduced costs and increased efficiency seem to motivate the monitoring of turnaround time, first-case on-time start, and first-case tardiness. 21 , 29–31 , 36 For first-case tardiness, delays, and patient satisfaction are mentioned as important factors. 29 Days between incidences of HAPUs are considered “never events” that should be minimized. 28 In the research in the review, cost, efficiency, safety and accessibility were cited as the primary reasons for monitoring operating rooms.

Eight studies were conducted in contexts where processes were highly time-sensitive, emergency departments 19 , 25–27 , 33 and intensive care. 14 , 22 In such settings, time may have significant consequences for the quality of treatment and patient outcomes. For instance, when treating myocardial infarction, 14 , 40 door-to-needle and cycle times must be reduced, because treatments are most effective in the first hours. 47 Variable control charts could provide valuable quality information when monitoring length and variation in time in such settings. Another example where variable control charts could provide valuable information, is ambulance response time after different interventions.

Waiting time is the most frequently used output variable in the articles 13 , 18 , 25 , 26 , 34 , 37 motivated by efficiency and patient safety. Waiting time is a strong indicator of quality and patient satisfaction, 18 , 34 , 37 and may affect mortality rates and lead to inefficient use of resources. 25 , 26 It is broadly accepted in the literature that waiting times may significantly influence healthcare quality. Waiting time affect customer satisfaction, 12 where total waiting time to visit a clinician is one of the most significant predictors. 48 This variable is a strong quality predictor and should be readily available for institutions, it is surprising that it has not received greater attention in the literature on adopting a control chart approach. Unlike many other quality predictors in health care, waiting time is relatively easy to interpret, because it is desirable to minimize it in many settings.

Length of stay is used as an output variable in three articles 13 , 27 , 38 concerning monitoring quality and performance. Although the connection between length of stay and quality of care is unclear in the selected studies, it has been accepted in the literature, 49 and is often used as a metric of efficiency and effectiveness. 50–52

In some studies, the objective of improvement projects was to make processes more efficient by reducing the time spent on time-consuming activities. Time spent on the registration process and preparing medical processes and health records are examples of this. 15–17 In all these cases, variable control charts were used to monitor efficiency and reduce costs. For instance, reducing turnaround time on the preparation of health or medical record may improve department productivity and performance, 16 , 17 or improve the registration process and reduce waiting times in the system. 15

Variable control charts are a data-driven method. This review demonstrates that in health care, variable control charts have been most frequently used to demonstrate process shifts after quality interventions, such as for instance lean and Six Sigma. The review also reveals that even shown that even variable control charts are applied in various context to QI in healthcare, there still is a great potential for more studies applying variable control charts. To date, the surgery department and departments where process are highly time-sensitive, are the most frequent settings of applying variable control charts.

There are both limitations and benefits to applying variable control charts. The data for applying variable control charts often require resources to collect, and the charts are often used with other methods, which most likely explains the scarce amount of research applying variable control charts. Such research would also require clear and consistent management to apply the charts. Despite the limitations for application, the benefits of the charts` may help both employees and leaders understand the processes and monitor changes in healthcare QI.

The author reports no conflicts of interest for this work.

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The optimal control chart selection for monitoring COVID-19 phases: a case study of daily deaths in the USA

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Muhammad Waqas, Song Hua Xu, Syed Masroor Anwar, Zahid Rasheed, Javid Shabbir, The optimal control chart selection for monitoring COVID-19 phases: a case study of daily deaths in the USA, International Journal for Quality in Health Care , Volume 35, Issue 3, 2023, mzad058, https://doi.org/10.1093/intqhc/mzad058

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Epidemiologists frequently adopt statistical process control tools, like control charts, to detect changes in the incidence or prevalence of a specific disease in real time, thereby protecting against outbreaks and emergent health concerns. Control charts have proven essential in instantly identifying fluctuations in infection rates, spotting emerging patterns, and enabling timely reaction measures in the context of COVID-19 monitoring. This study aims to review and select an optimal control chart in epidemiology to monitor variations in COVID-19 deaths and understand pandemic mortality patterns. An essential aspect of the present study is selecting an appropriate monitoring technique for distinct deaths in the USA in seven phases, including pre-growth, growth, and post-growth phases. Stage-1 evaluated control chart applications in epidemiology departments of 12 countries between 2000 and 2022. The study assessed various control charts and identified the optimal one based on maximum shift detection using sample data. This study considered at Shewhart ( ⁠|$\bar X$|⁠ , |$R$|⁠ , |$C$|⁠ ) control charts and exponentially weighted moving average (EWMA) control chart with smoothing parameters λ  = 0.25, 0.5, 0.75, and 1 were all investigated in this study. In Stage-2, we applied the EWMA control chart for monitoring because of its outstanding shift detection capabilities and compatibility with the present data. Daily deaths have been monitored from March 2020 to February 2023. Control charts in epidemiology show growing use, with the USA leading at 42% applications among top countries. During the application on COVID-19 deaths, the EWMA chart accurately depicted mortality dynamics from March 2020 to February 2022, indicating six distinct stages of death. The third and fifth waves were extremely catastrophic, resulting in a considerable loss of life. Significantly, a persistent sixth wave appeared from March 2022 to February 2023. The EWMA map effectively determined the peaks associated with each wave by thoroughly examining the time and amount of deaths, providing vital insights into the pandemic’s progression. The severity of each wave was measured by the average number of deaths |$W5(1899)\,\gt\,W3(1881)\,\gt\,W4(1393)\,\gt\,W1(1036)\,\gt\,W2(853)\,\gt\,(W6(473)$|⁠ . The USA entered a seventh phase (6th wave) from March 2022 to February 2023, marked by fewer deaths. While reassuring, it remains crucial to maintain vaccinations and pandemic control measures. Control charts enable early detection of daily COVID-19 deaths, providing a systematic strategy for government and medical staff. Incorporating the EWMA chart for monitoring immunizations, cases, and deaths is recommended.

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The Complete Guide to Understanding Control Charts

Published: February 18, 2013 by Carl Berardinelli

Control charts have two general uses in an improvement project.

The most common application is as a tool to monitor process stability and control.

A less common, although some might argue more powerful, use of control charts is as an analysis tool.

The descriptions below provide an overview of the different types of control charts to help practitioners identify the best chart for any monitoring situation, followed by a description of the method for using control charts for analysis.

Identifying Variation

When a process is stable and in control, it displays common cause variation, variation that is inherent to the process. A process is in control when based on past experience it can be predicted how the process will vary (within limits) in the future. If the process is unstable, the process displays special cause variation, non-random variation from external factors.

Control charts are simple, robust tools for understanding process variability.

The Four Process States

Processes fall into one of four states: 1) the ideal, 2) the threshold, 3) the brink of chaos and 4) the state of chaos (Figure 1). 3

When a process operates in the ideal state , that process is in statistical control and produces 100 percent conformance. This process has proven stability and target performance over time. This process is predictable and its output meets customer expectations.

A process that is in the threshold state is characterized by being in statistical control but still producing the occasional nonconformance. This type of process will produce a constant level of nonconformances and exhibits low capability. Although predictable, this process does not consistently meet customer needs.

The brink of chaos state reflects a process that is not in statistical control, but also is not producing defects. In other words, the process is unpredictable, but the outputs of the process still meet customer requirements. The lack of defects leads to a false sense of security, however, as such a process can produce nonconformances at any moment. It is only a matter of time.

The fourth process state is the state of chaos . Here, the process is not in statistical control and produces unpredictable levels of nonconformance.

Every process falls into one of these states at any given time, but will not remain in that state. All processes will migrate toward the state of chaos. Companies typically begin some type of improvement effort when a process reaches the state of chaos (although arguably they would be better served to initiate improvement plans at the brink of chaos or threshold state). Control charts are robust and effective tools to use as part of the strategy used to detect this natural process degradation (Figure 2). 3

Elements of a Control Chart

There are three main elements of a control chart as shown in Figure 3.

• A control chart begins with a time series graph.
• A central line (X) is added as a visual reference for detecting shifts or trends – this is also referred to as the process location.
• Upper and lower control limits (UCL and LCL) are computed from available data and placed equidistant from the central line. This is also referred to as process dispersion.

Control limits (CLs) ensure time is not wasted looking for unnecessary trouble – the goal of any process improvement practitioner should be to only take action when warranted. Control limits are calculated by:

• Estimating the standard deviation , σ, of the sample data
• Multiplying that number by three
• Adding (3 x σ to the average) for the UCL and subtracting (3 x σ from the average) for the LCL

Mathematically, the calculation of control limits looks like:

(Note: The hat over the sigma symbol indicates that this is an estimate of standard deviation, not the true population standard deviation.)

Because control limits are calculated from process data, they are independent of customer expectations or specification limits.

Control rules take advantage of the normal curve in which 68.26 percent of all data is within plus or minus one standard deviation from the average, 95.44 percent of all data is within plus or minus two standard deviations from the average, and 99.73 percent of data will be within plus or minus three standard deviations from the average. As such, data should be normally distributed (or transformed) when using control charts, or the chart may signal an unexpectedly high rate of false alarms.

Controlled Variation

Controlled variation is characterized by a stable and consistent pattern of variation over time, and is associated with common causes. A process operating with controlled variation has an outcome that is predictable within the bounds of the control limits.

Uncontrolled Variation

Uncontrolled variation is characterized by variation that changes over time and is associated with special causes. The outcomes of this process are unpredictable; a customer may be satisfied or unsatisfied given this unpredictability.

Please note: process control and process capability  are two different things. A process should be stable and in control before process capability is assessed.

Control Charts for Continuous Data

Individuals and Moving Range Chart

The individuals and moving range (I-MR) chart is one of the most commonly used control charts for continuous data; it is applicable when one data point is collected at each point in time. The I-MR control chart is actually two charts used in tandem (Figure 7). Together they monitor the process average as well as process variation. With x-axes that are time based, the chart shows a history of the process.

The I chart is used to detect trends and shifts in the data, and thus in the process. The individuals chart must have the data time-ordered; that is, the data must be entered in the sequence in which it was generated. If data is not correctly tracked, trends or shifts in the process may not be detected and may be incorrectly attributed to random (common cause) variation. There are advanced control chart analysis techniques that forego the detection of shifts and trends, but before applying these advanced methods, the data should be plotted and analyzed in time sequence.

The MR chart shows short-term variability in a process – an assessment of the stability of process variation. The moving range is the difference between consecutive observations. It is expected that the difference between consecutive points is predictable. Points outside the control limits indicate instability. If there are any out of control points, the special causes must be eliminated.

Once the effect of any out-of-control points is removed from the MR chart, look at the I chart. Be sure to remove the point by correcting the process – not by simply erasing the data point.

The I-MR chart is best used when:

• The natural subgroup size is unknown.
• The integrity of the data prevents a clear picture of a logical subgroup.
• The data is scarce (therefore subgrouping is not yet practical).
• The natural subgroup needing to be assessed is not yet defined.

Xbar-Range Charts

Another commonly used control chart for continuous data is the Xbar and range (Xbar-R) chart (Figure 8). Like the I-MR chart, it is comprised of two charts used in tandem. The Xbar-R chart is used when you can rationally collect measurements in subgroups of between two and 10 observations. Each subgroup is a snapshot of the process at a given point in time. The chart’s x-axes are time based, so that the chart shows a history of the process. For this reason, it is important that the data is in time-order.

The Xbar chart is used to evaluate consistency of process averages by plotting the average of each subgroup. It is efficient at detecting relatively large shifts (typically plus or minus 1.5 σ or larger) in the process average.

The R chart , on the other hand, plot the ranges of each subgroup. The R chart is used to evaluate the consistency of process variation. Look at the R chart first; if the R chart is out of control, then the control limits on the Xbar chart are meaningless.

Table 1 shows the formulas for calculating control limits. Many software packages do these calculations without much user effort. (Note: For an I-MR chart, use a sample size, n ,  of 2.) Notice that the control limits are a function of the average range (Rbar). This is the technical reason why the R chart needs to be in control before further analysis. If the range is unstable, the control limits will be inflated, which could cause an errant analysis and subsequent work in the wrong area of the process.

Can these constants be calculated? Yes, based on d 2 , where d 2 is a control chart constant that depends on subgroup size.

The I-MR and Xbar-R charts use the relationship of Rbar/ d 2 as the estimate for standard deviation. For sample sizes less than 10, that estimate is more accurate than the sum of squares estimate. The constant, d 2 , is dependent on sample size. For this reason most software packages automatically change from Xbar-R to Xbar-S charts around sample sizes of 10. The difference between these two charts is simply the estimate of standard deviation.

Control Charts for Discrete Data

Used when identifying the total count of defects per unit ( c ) that occurred during the sampling period, the c -chart allows the practitioner to assign each sample more than one defect. This chart is used when the number of samples of each sampling period is essentially the same.

Similar to a c -chart, the u -chart is used to track the total count of defects per unit ( u ) that occur during the sampling period and can track a sample having more than one defect. However, unlike a c -chart, a u -chart is used when the number of samples of each sampling period may vary significantly.

Use an np -chart when identifying the total count of defective units (the unit may have one or more defects) with a constant sampling size.

Used when each unit can be considered pass or fail – no matter the number of defects – a p -chart shows the number of tracked failures ( np ) divided by the number of total units ( n ).

Notice that no discrete control charts have corresponding range charts as with the variable charts. The standard deviation is estimated from the parameter itself ( p , u or c ); therefore, a range is not required.

How to Select a Control Chart

Although this article describes a plethora of control charts, there are simple questions a practitioner can ask to find the appropriate chart for any given use. Figure 13 walks through these questions and directs the user to the appropriate chart.

A number of points may be taken into consideration when identifying the type of control chart to use, such as:

• Variables control charts (those that measure variation on a continuous scale) are more sensitive to change than attribute control charts (those that measure variation on a discrete scale).
• Variables charts are useful for processes such as measuring tool wear.
• Use an individuals chart when few measurements are available (e.g., when they are infrequent or are particularly costly). These charts should be used when the natural subgroup is not yet known.
• A measure of defective units is found with u – and c -charts.
• In a u -chart, the defects within the unit must be independent of one another, such as with component failures on a printed circuit board or the number of defects on a billing statement.
• Use a u -chart for continuous items, such as fabric (e.g., defects per square meter of cloth).
• A c -chart is a useful alternative to a u-chart when there are a lot of possible defects on a unit, but there is only a small chance of any one defect occurring (e.g., flaws in a roll of material).
• When charting proportions, p – and np -charts are useful (e.g., compliance rates or process yields).

Subgrouping: Control Charts as a Tool for Analysis

Subgrouping is the method for using control charts as an analysis tool. The concept of subgrouping is one of the most important components of the control chart method. The technique organizes data from the process to show the greatest similarity among the data in each subgroup and the greatest difference among the data in different subgroups.

The aim of subgrouping is to include only common causes of variation within subgroups and to have all special causes of variation occur among subgroups. When the within-group and between-group variation is understood, the number of potential variables – that is, the number of potential sources of unacceptable variation – is reduced considerably, and where to expend improvement efforts can more easily be determined.

Within-subgroup Variation

For each subgroup, the within variation is represented by the range.

The R chart displays change in the within subgroup dispersion of the process and answers the question: Is the variation within subgroups consistent? If the range chart is out of control, the system is not stable. It tells you that you need to look for the source of the instability, such as poor measurement repeatability. Analytically it is important because the control limits in the X chart are a function of R-bar. If the range chart is out of control then R-bar is inflated as are the control limit. This could increase the likelihood of calling between subgroup variation within subgroup variation and send you off working on the wrong area.

Within variation is consistent when the R chart – and thus the process it represents – is in control. The R chart must be in control to draw the Xbar chart.

Between Subgroup Variation

Between-subgroup variation is represented by the difference in subgroup averages.

Xbar Chart, Take Two

The Xbar chart shows any changes in the average value of the process and answers the question: Is the variation between the averages of the subgroups more than the variation within the subgroup?

If the Xbar chart is in control, the variation “between” is lower than the variation “within.” If the Xbar chart is not in control, the variation “between” is greater than the variation “within.”

This is close to being a graphical analysis of variance (ANOVA). The between and within analyses provide a helpful graphical representation while also providing the ability to assess stability that ANOVA lacks. Using this analysis along with ANOVA is a powerful combination.

Knowing which control chart to use in a given situation will assure accurate monitoring of process stability. It will eliminate erroneous results and wasted effort, focusing attention on the true opportunities for meaningful improvement.

• Quality Council of Indiana. The Certified Six Sigma Black Belt Prime r , Second Edition, Quality Council of Indiana, West Terre Haute, Ind., 2012.
• Tubiak, T.M. and Benbow, Donald W. T he Certified Six Sigma Black Belt Handbook , Second Edition, ASQ Quality Press, Milwaukee, Wisc., 2009.
• Wheeler, Donald J. and Chambers, David S. Understanding Statistical Process Control . SPC Press, Knoxville, Tenn., 1992.

About the Author

Carl Berardinelli

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A CASE STUDY OF QUALITY CONTROL CHARTS IN A MANUFACTURING INDUSTRY

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– Most of the modern industrial processes are naturally multivariate. Multivariate control charts are supplanted univariate control charts, as it takes into account the relationship between variables and identifies the real process changes, which are undetectable by univariate control charts. In practice, the basic assumption that the measurements are independently and identically distributed about a target value is not always valid. Violation of this assumption increases the False Alarm Rate (FAR) and deteriorates the separation of assignable causes from common causes. This paper presents the application of Multivariate Statistical Process Control (MSPC) charts (e. g., Hotelling , MEWMA) to monitor the flare making process in a straight fluorescent light bulb industry. Furthermore, it develops the appropriate procedure for monitoring a multivariate autocorrelated data variable (i. e., dynamic behavior) by using Autoregressive Integrated Moving Average (ARIMA) models. Univariate SPC charts and decomposition approach are used to identify the out-of-control signals that are generated from multivariate SPC charts. Software packages such as Minitab 17 and Statgraphics Centurion XVI are used to construct the control charts.

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Sweetmeats are nature&#39;s most important contribution to civilization. Khoa and chhana based sweets are the most important pleasant and charming foods to most of the people of India. The first prerequisite for producing excellent quality of sweetmeats is the availability of high quality khoa and chhana. In most of the markets of India, khoa and chhana based sweets are more or less available, but the quality of sweets varies from place to place. The present research was carried out to determine the fat and protein compositions of sweets available in market and to compare them with sweets prepared in the laboratory.

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Statistical Process Control (SPC) is an efficient methodology for monitoring, managing, analysing and recuperating process performance. Implementation of SPC in industries results in biggest benefits, as enhanced quality products and reduced process variation. While dealing with the theory of control chart we generally move with the assumption of independent process observation. But in practice usually, for most of the processes the observations are autocorrelated which degrades the ability of control chart application. The loss caused by autocorrelation can be obliterated by making modifications in the traditional control charts. The article presented here refers to a combination of EWMA and CUSUM charting techniques supplementing modifications in the control limits. The performance of the referred scheme is measured by comparing average run length (ARL) with existing control charts. Also, the referred scheme is found reasonably well for detecting particularly smaller displacements...

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Rapid assessment of surface water quality using statistical multivariate analysis approach: Oder River system case study

• Balcerowska-Czerniak, Grażyna
• Gorczyca, Beata

Many physicochemical and biological monitored parameters must be taken into consideration to fully evaluate the surface water environmental condition. However, there are situations where a simple and rapid assessment of the poor water quality situations is critically important. This work presents a universal methodology for monitoring of many parameters simultaneously and early detection out-of-control samples in a real-time mode. The approach uses multivariate statistical quality control chart based on Principal Component Analysis (PCA) model with two well-known measures of abnormal behaviour in a process or system: Hoteling's T 2 statistics and Q-statistic. The proposed TQ_PCA quality index provides on-line assessment of the water sample quality, with no specific knowledge and assumptions about control limits for monitored parameters required. A water sample is assessed through the simple control chart using the PCA model established for training/reference samples. The power of the proposed index has been tested using water quality data from the Oder River, including the time of the largest ecological disaster in recent European river history. The proposed index showed excellent analysis performance for physicochemical water quality dataset from Polish stations and physicochemical and biological water quality dataset from German/Frankfurt station, confirming earlier reports. There were consecutive number of alarms reported by the statistical index, a month prior to the disaster when there were no evident changes in the individual parameters. The method presented in this study demonstrated capability of assessment of the major water quality parameters, whose changes preempt the uncommon event. The presented TQ_PCA index could be easily extended to any research involving a large dataset of monitoring parameters from any industrial chemical process.

• Quality monitoring;
• Water quality index;
• Physicochemical parameters;
• Multivariate analysis;
• Hotelling T<SUP>2</SUP> chart;
• Principal component analysis

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POPULATION HEALTH ANALYTICS

Using control charts to measure performance, august 10th, 2021  |   emergency department classification  |   population health management & improvement.

In some of our recent posts, we’ve been taking a look at how the ACG System’s suite of tools can be used to understand emergency department (ED) visits, which helps users optimize health care utilization and reduce potential costs.

If you read our earlier posts , you know that the ACG System can reveal specific trends in ED visits for a certain population, specifically, patients who visited for non-emergent care or primary care (PCP) treatable conditions. By drilling down into this data, ACG System users can understand root causes of ED use, segment patients into actionable groups and develop an effective strategy to reduce potentially-avoidable visits.

This week, we’ll discuss a method for tracking those ED reduction strategies using control charts.

How Control Charts Work

Control charts are a user-friendly tool that differentiate true change in a metric from random variation that occurs naturally. Control charts help identify meaningful change early and are an engaging visualization for different types of stakeholders. Supplementing the control chart with markers of key intervention dates can help leaders understand the relationship of intervention timing to outcomes. These advantages make control charts the ideal tool to monitor changes in ED utilization. In fact, the ACG System’s granular ED visit export file can help develop effective control charts for internal monitoring purposes.

Using Control Charts to Monitor ED Visits

All this makes sense in theory, but let’s look at a real-world example of how control charts can be used to monitor ED usage in a population. In the below example, the user became concerned about an increasing trend in avoidable ED visits starting in Month 16. The trend was identified via overall increase in ED visits/1000, and once the analytic team drilled down into the trend, it revealed growth in avoidable ED visits as an impactable cost-driver. A suite of interventions to reduce avoidable ED visits was implemented in Month 19.

The analytic team used historic ED visit data, organized by the ACG System’s ED Classification algorithm’s category and month , to generate the control chart with historic mean and measures of variation. The horizontal blue line represents historic average monthly rate of avoidable ED visits. The two red lines represent upper and lower control limits.

Interpreting this graph, the peaks in Month 17 and 19 represent significant variation above historic means, supporting the organization’s interpretation that avoidable ED visits were increasing. Once the intervention was implemented in Month 19, utilization returned to post-intervention means in months 22 and 23. However, had the data points continued near the upper control limit, the organization would have an early-stage indicator that the intervention was not achieving the desired outcome.

Looking out to month 25, utilization of avoidable ED visits crosses the lower control limit, indicating significant variation from the historic mean – in this case, for the better.

The Value of Control Charts

The above example demonstrates how the ACG System’s unique tools and granular visit-level data can help an organization use control charts to monitor ED visits in near-time, creating a strong business-level understanding of intervention impact. Ultimately, these control chart tools give users clear, specific data to indicate whether or not a specific intervention is achieving the desired goal. The result? Users have the information and tools they need to make changes that optimize health care resources and reduce costs.

*The ACG team would like to thank Shannon Murphy, MA for concept and development of this ED monitoring application. More details on using Statistical Process Control and Control Charts to monitor health interventions can be found here .

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