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Statistical Process Control: No Hits, No Runs, No Errors?

Vetter, Thomas R. MD, MPH*; Morrice, Douglas PhD

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doi: 10.1213/ANE.0000000000003977
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In God we trust; all others bring data.

Without data, you’re just another person with an opinion.

—W. Edwards Deming (1900–1993), American engineer, statistician, professor, author, lecturer, and management consultant

Increasing emphasis is being placed on delivering value-based health care, in which value can be defined as health outcomes achieved per dollar spent.1 In this value-based health care quotient, the numerator of achieved health outcomes encompasses quality and safety as well as patient and provider satisfaction.2–4

Significant changes in population demographics and health policy are mandating these new value-based models of health care delivery—including for surgical patient care.5,6 Anesthesiologists are well positioned to assume a broader yet continued highly collaborative role in the perioperative care of surgical patients.7

Furthermore, anesthesiologists have considerable experience and demonstrated expertise in the fields of performance improvement and quality improvement. They can thus serve as leaders in this new perioperative care environment,5,7 including in perioperative population health management.8–11

A novel intervention or new clinical program must achieve and sustain its operational and clinical goals.12 To demonstrate successfully optimizing health care value, providers and other stakeholders must longitudinally measure and report these tracked relevant associated outcomes.13 This includes anesthesiologists and perioperative health services researchers who chose to participate in these process improvement and quality improvement efforts (“play in this space”).14–16

Previous tutorials in this ongoing series in Anesthesia & Analgesia dealt with types of clinical study design17,18 and data analysis.19–23 The present basic statistical tutorial focuses on the related and equally germane topic of statistical process control. It is not intended to provide in-depth coverage24–26 but instead to familiarize the reader with these specific concepts and techniques:

  • Random (common) causes of variation versus assignable (special) causes of variation
  • Six Sigma versus Lean versus Lean Six Sigma
  • Levels of quality management
  • Run chart
  • Control charts
  • Selecting the applicable type of control chart
  • Analyzing a control chart


As noted in 2 previous tutorials, depending on the circumstances, there are various study designs that are appropriate to apply in conducting clinical or health services research, including process improvement and quality improvement efforts.17,18

Figure 1.:
Research study design classification system or taxonomy.17 , 18

These various study designs are conventionally classified as experimental, quasi-experimental, or observational, with observational studies being further divided into descriptive and analytic subcategories (Figure 1).17,18,27–30 In this current tutorial, specific attention is focused on quasi-experimental study designs, which are particularly applicable to process improvement and quality improvement efforts.


A quasi-experimental study is typically performed when there are practical and/or ethical barriers to conducting a randomized controlled trial.17,31 A quasi-experimental study design can be applied in practice-based research on the performance improvement or quality improvement with a new intervention or health care delivery program.17,31–33 The reader is referred to the work of Shadish et al34 for an in-depth coverage of quasi-experimental study designs.

Uncontrolled Before and After Study

An uncontrolled before and after study simply measures ≥1 performance or quality variables before and after the introduction of an intervention in the same study population and at the same care delivery site(s). Any observed before versus after difference in the quality metric or key performance indicator is assumed to be due to the intervention.12,17,31,32,34,35

The findings of an uncontrolled before and after study, which focuses on performance or quality improvement, are often presented graphically using statistical process control methods, including a single Shewhart-style, statistical process control chart for the pre- and postintervention time periods with their respective sequential time points and measurements.17,36–40

Controlled Before and After Study

In a controlled before and after study, a control population with similar demographics is identified. This control population is expected to demonstrate an underlying temporal trend in other performance or behavior that is also similar to the active study population.12,17,31,32,34,41

A sample of performance or quality data is collected simultaneously from both populations before and after the intervention or a new health care delivery program is introduced into the active study population. These performance or quality data are compared, and any observed differences are assumed to be due to the process change.31,32,34,41

The findings of an controlled before and after study, which focuses on performance or quality improvement, can also be presented graphically using statistical process control methods, including 2 Shewhart-style, statistical process control charts for the pre- and postintervention time periods and their respective sequential time points and measurements—1 chart for the active intervention group and the other chart for the control group.17,36–40

Interrupted Time Series

Interrupted time series is considered the strongest, quasi-experimental research design for evaluating the longitudinal effects of an intervention.17,34,42–47 An interrupted time series design assesses whether an intervention had a significantly greater effect than the underlying temporal or background trend.12,17,31,32,34,41,44,46,47 This design can be appropriate for evaluating the effects of a wide-scale, system-wide guideline implementation or care delivery process change—situations in which it is difficult to identify a valid control group or randomize study participants.17,31,32,34,41,44,45

Outcomes data are consistently collected at ≥20 nearly equal time points before and then at ≥20 nearly equal time points after the intervention. The multiple time points before implementing the intervention allow the underlying trend to be estimated, whereas the multiple time points after implementing the intervention allow the effect of the intervention to be estimated, potentially accounting for any continued underlying or background trend in the outcome.12,17,31,34,41,46–48

The key distinction is that the results of an interrupted time series are reported as 2 sequential, graphically adjacent, yet distinct scatter plots with their respective trend lines shown—not simply with a conventional Shewhart-style, statistical process control chart for the pre- and postintervention time periods.46,47,49

However, an interrupted time series design may still not adequately compensate for the effects of other known or unknown interventions or events occurring concurrently with the study intervention, which might also affect the performance or quality outcome measure(s).31,32,34 Segmented (also known as hockey stick, piecewise, or broken stick) regression can mitigate this internal validity risk, and its use with an interrupted time series design has become strongly recommended as to make it essentially a prerequisite.41–43,50,51


Statistical process control is a branch of statistics that combines rigorous sequential, time-based analysis methods with graphical presentation of performance and quality data. Statistical process control and its primary tool—the control chart—provide researchers and practitioners with a method of better understanding and communicating data from health care performance and quality improvement efforts.39

The basic theory of statistical process control was developed in the late 1920s by Walter Shewhart, a statistician at the AT&T Bell Laboratories in the United States.52,53 It was then applied in post-World War II Japan and eventually disseminated worldwide by W. Edwards Deming.53,54

Shewhart and Deming originally worked with manufacturing processes, but both recognized that their methodology could be applied to any sort of process.39 In its broader sense, statistical process control is concerned with repeated measurements of a process exhibiting variation. In this broader context, statistical process control has greater and major applicability in clinical care and health care–related quality improvement.


Statistical process control (1) presents performance and quality data in a format that is typically more understandable to practicing clinicians, administrators, and health care decision makers; and (2) often more readily generates actionable insights and conclusions.39

Health care quality improvement is predicated on statistical process control.24,25,55 Undertaking, achieving, and reporting continuous quality improvement in anesthesiology, critical care, perioperative medicine, and acute and chronic pain management all fundamentally rely on applying statistical process control methods and tools.


The notion of random or common causes of variation versus assignable or special causes of variation has its roots in the earliest, seminal work by Shewhart on quality control.56 All processes display variation. The distinction between 2 types of variation is fundamental to statistical process control.

Random or common causes of variation refer to the random variation or noise inherent in any process, which yields unpredictable outcomes. This means that the outputs of any process, whether in health care, manufacturing, or some other application, are not identically repeatable due to naturally occurring variation in, for example, materials or operating conditions.

Assignable or special causes of variation refer to process variation identifiable and assignable to specific causes. Furthermore, this type of variation can be corrected and controlled. Examples include human error due to lack of training or absence of standard operating procedures and malfunctioning equipment that needs adjustment or repair. Once detected, appropriate corrective actions eliminate these sources of variation and restore the process to control. Essentially, statistical process control accounts for common causes of variation and then detects and corrects assignable causes of variation.

Statistical process control relies on the statistical theory of hypothesis testing.57 The null hypothesis assumes in-control process displays’ common causes of variation according to a specific probability distribution. Typically, process observations are sample averages that rely on the Central Limit Theorem, resulting in a normal or Gaussian (“bell shaped”) probability distribution.58

If sampling of the process yields variation with a low probability of being explained by common causes of variation, one rejects the null hypothesis and considers the process out of control. This rejection of the null hypothesis represents the detection step of assignable causes of variation.

The subsequent correction step requires further investigation to understand the specific causes (eg, personnel make errors on a task for which they have not been adequately trained) and if corrective action occurs (eg, personnel receive proper training and management institutes standard operating procedures in order to eliminate these errors).

The distinction between common and assignable causes of variation may be one of degrees. As quality management matures, organizations seek to improve their processes by adopting continuous improvement approaches. Under continuous improvement, these organizations take rigorous steps to make more of the variation in the process assignable rather than simply categorizing it as random and unpredictable.59 In the next section, we discuss specific approaches for continuous improvement.


Six Sigma and Lean represent 2 continuous quality improvement approaches. These processes have been applied and to varying degrees validated in complex health care environments to eliminate error and affect change.16,60–65

Developed by Motorola and championed by General Electric, Six Sigma exemplifies a philosophical framework and statistical methodology designed to eliminate defects in products and processes.66 We focus on the Motorola approach because it provides the statistical foundation for programs used in practice.

Six Sigma consists of repeated cycling through the following 5 steps: (1) defining the process, (2) measuring outcomes, (3) analyzing the measurements, (4) making improvements, and (5) controlling the improved process.66 For analysis and improvement, Six Sigma relies on the comparison of process variability embodied in common cause variation used to construct statistical process control chart limits and process specification limits or design tolerances set by managers or customers of the process. Defects result from process outputs that fall outside the specification limits.

Six Sigma achieves continuous improvement by reducing process variability relative to the specification limits—such that ±6 sigma units of process variation falls within these specification limits. This ideally translates to a defect rate of 2 parts per billion opportunities (eg, clinical events). It does so by persistent process improvement, shifting more and more common causes of variation to assignable causes of variation for correction and control. As a result, the probability distribution associated with common cause variation narrows relative to the specification limits occasioning fewer defects.

The Lean approach has its foundations in the Toyota Production System.67 The overarching idea of waste reduction drives the principles, organizational practices, and methods found in this comprehensive approach to quality management. The principles include a set of ideals to eliminate defects, inventories, setups, breakdowns, and nonvalue-adding activities in processes. Although aspirational, these principles help organizations know where to focus their continuous quality improvement efforts and apply the statistical techniques we discuss in this article, along with process improvement and inventory control practices from the field of operations management.67

Organizationally, the Lean approach empowers and rewards people directly involved in the processes to take responsibility for quality and its continuous improvement. Whenever possible, front-line workers detect and correct quality problems when they occur. They conduct root cause analysis, participate on cross-functional teams to address longer term quality issues, and continually look for ways to improve quality. Lean also involves the standardization of work, flexible capacity, and specialized production methods centered on the idea of “pull” or “Just-in-Time,”68 by which one produces only the required amounts when needed.

Lean Six Sigma represents the amalgamation of these 2 systems. It merges the management practices of Lean with the scientifically based, statistical rigor of Six Sigma to eliminate waste and reduce variation to improve quality in a continuous manner.69 While Lean and Six Sigma both originated in manufacturing, their scope has expanded to eliminate waste in all aspects of an enterprise along the value chain, including product development, supply chain management, and sales and maintenance.70 Additionally, Lean Six Sigma has many different applications across various industries, including health care.65,71–73


In practice, quality management programs differ in their levels of maturity, from inspection through process control and, ultimately, to continuous improvement (Figure 2).74

Figure 2.:
Maturity levels of quality management programs.74

The most rudimentary approaches involve inspection of the quality of outputs generated by a process. The inspection typically entails selecting a sample of process outputs and then determining whether a high enough percentage of the sample passes quality inspection. If the observed passing percentage exceeds a threshold, as determined by inferential statistical analysis, then the procedure deems all process outputs of sufficient quality and accepts them. Otherwise, it rejects them. Hence, the inspection approach screens for bad quality after the fact but does nothing to control or improve it. Consequently, as the old adage goes, “You cannot inspect in quality.”75

Process control involves monitoring a process using statistical process control techniques. If monitoring indicates that the process is producing poor quality (ie, the process has gone out of control), then corrective action seeks to fix the problem and bring the process back into control. This approach keeps the quality of the process outputs within an acceptable range of variation. While process control represents a major advancement beyond inspection, it maintains the quality status quo.

Continuous improvement challenges the quality status quo and leads to ever-improving quality. Consequently, it is the most mature quality program applied in practice. One such approach, namely, Six Sigma, operationalizes continuous improvement by comparing the process variation to the process specifications. The latter are design tolerances set by process managers or consumers of the process outputs. Six Sigma achieves ever-improving quality by relentlessly pursuing process improvement to force more and more process variation inside the process specifications. The approach may also entail setting the standards higher by tightening the specifications to achieve even greater levels of quality.

Because of their more progressive and rigorous nature, process control and continuous improvement have greater relevance and applicability to outputs (outcomes) in health care settings.


The run chart is the simplest but also a useful chart for statistical process control. The basic run chart is a plot of the data observations of an individual variable plotted in time order. Thus, it is synonymous with a time-series plot. A run chart can detect overall trends, variation, and patterns in the time-ordered data.16,76–79 Use of a run chart has several advantages76,80:

  • It requires no statistical calculations, computer hardware, or software.
  • It can be constructed literally by hand with paper and a pen or pencil.
  • It can be used with any type of process (clinical, financial, or operational).
  • It can be used with virtually any type of data (discrete measurements, counts of events, percentages, or ratios).
  • It can be easily and thus widely understood.

Unlike a control chart, a run chart can be used for data that do not display a normal (Gaussian) distribution. A run chart usually includes a centerline, which represents the median of all the observed values.76–78

Run charts have been used to report diverse quality improvement efforts in the perioperative setting, including decreasing operating room turnover,81 improving clinician hand hygiene,82 monitoring changes in wireless hands-free communication patterns during electronic health record system implementation,83 and detecting opioid abuse among anesthesiologists.84


Both a run chart and a control chart are used to distinguish random (common) causes of variation versus assignable (special) causes of variation in the outcomes generated by and data collected about a process. However, the control chart is considered a more sensitive and powerful tool than the run chart.85

Like a run chart, a control chart is a graphic representation of data over time. To the casual observer, control charts can look similar to run charts. Data are plotted with time on the horizontal axis and the process measure on the vertical axis. Like a run chart, a control chart has a centerline, but this centerline represents the mean rather than the median of all the observed values in that time period. A control chart also includes an upper control limit and a lower control limit.16,76,78,80,86

The upper control limit and lower control limit correspond to ±3 SD or sigma units from the mean for the observed sample.78,80 However, the upper control limit and lower control limit of a control chart should not to be confused with the 99% upper and lower confidence interval limits of the sample data distribution. The control limits describe the variability in the process, whereas confidence limits describe the variability in a distribution of data.80,85

Control charts have been applied to report diverse quality improvement efforts in the perioperative setting, including intraoperative glucose monitoring to reduce surgical site infections in patients with diabetes,87 modifications to the electronic medical record to improve the administration of the second antibiotic dose,88 the use of an anesthesia medication template to reduce medication errors during anesthesia,89 and the benefits of a distraction-free pediatric induction zone.90


Control charts are conventionally divided into those applicable for continuous or variables data and those intended for discrete or attributes data. Continuous or variables data can take on different measurement values on a continuous scale. Discrete or attributes data are counts of events that can be aggregated into typically dichotomous (binary, yes/no) categories. With 1 type of discrete data, one can count both the occurrences and nonoccurrences and then calculate the percentage of “defectives.” With the other type of discrete data, one can only count the occurrences, which are regarded as “defects.”78,85


The I-chart or X-chart, where X stands for a data value, is simply a run chart with an upper control limit and a lower control limit added. The “I” in I-chart stands for “individual.” Each subgroup and its data point comprised a single observation. Like with a run chart, an I-chart displays the individual values of the process observations in a time-ordered sequence. Like a run chart, the primary use of an I-chart is to provide initial insights for a process or quality improvement project, particularly a nonrandom pattern to and thus influence on the outcome data.78,85,86,91

X-Bar Chart

The X-bar chart is an extension of the I-chart. X-bar stands for the mean value. With an X-bar chart, each subgroup and its corresponding data point contains >1 observation, and the outcome data are measured and their mean (average) value is thus calculated.78,85,86,92


The p-chart is considered the most easily understood and most often applied control chart. For each event, its dichotomous outcome is considered “special” or “not special,” with the special outcome being typically (but not always) adverse or unfavorable. The values are calculated by dividing the count of special outcome events (numerator) by the total event count (denominator). Hence, the “p” in p-chart stands for either “percent” or “proportion.”78,85,86,93 The np-chart is a variation of the p-chart, in which the count of “special outcomes” is plotted; however, the p-chart will reportedly always instead suffice.93


The c-chart is the simplest attribute control chart. Each plotted point is the c value or the count of occurrences of defects for each sampled period. A count cannot exist without an area of opportunity or “exposure.” This so-called area of opportunity is the subgroup size, with which a c-chart is equal and constant (fixed) for each measured time period and its subgroup. The “c” in c-chart stands for count or “constant area of opportunity.”78,85,86,94


For a u-chart, the area of opportunity or subgroup sample size does not need to be constant. If the subgroup sample sizes vary considerably, a u-chart rather than a c-chart is applicable. The “u” in u-chart stands for “unit” or “unequal area of opportunity.” The sampled subgroups must be compared “on a level playing period.” This is accomplished by dividing the subgroup defect count by the subgroup size, where this size is expressed in the most logical unit of measure. This u-chart is also called a “count per unit” chart.78,85,86,94


The Choice of a Control Chart Depends on the Process of Interest and How the Process or Quality Improvement Question Is Posed78
Figure 3.:
Algorithm for choosing a specific type of control chart. With 1 type of discrete or attributes data, one can count both the occurrences and nonoccurrences and then calculate the percentage of “defectives.” With the other type of discrete data, one can only count the occurrences, which are regarded as “defects.”78 , 85 Definitions of chart types are located in the text.

After determining the type of collected data, the next step is to examine a control chart decision algorithm (Figure 3). This algorithm can be exemplified using operating room turnaround time (“wheels out to wheels in”) (Table). Charts for continuous or variables data are more powerful in detecting assignable or special causes of variation than charts for discrete or attributes data. The X-bar chart is similarly more powerful than the I-bar chart. The c-chart or u-chart is likewise more powerful than the p-chart. Thus, whenever possible, one should seek to measure an activity rather than count events.85,95 Anesthesiologists and perioperative health services researchers undertaking process and quality improvement efforts should attempt to collect their outcomes data such that they will be able to use the better chart, not simply a correct chart.85


Both a run chart and a control chart are intended to distinguish random or common causes of variation versus assignable or special causes of variation in the outcome data produced by a process.85 As noted earlier, assignable or special causes of variation refer to process variation that can be corrected and controlled by an intervention. While beyond the intended scope of this tutorial, a series of rules and pattern recognition has been promulgated for identifying and classifying process variation in run and control charts.16,78,96–98


This statistical tutorial focuses on the basics of statistical process control. While statistical process control is principally the content expertise and ostensibly the domain of engineering, manufacturing, and management science, it is also pertinent to patient care, education, and research in anesthesiology, perioperative medicine, critical care, and pain medicine. Thus, our other goal here is to raise awareness of the importance of statistical process control in patient care and clinical research in anesthesiology, perioperative medicine, critical care, and pain medicine.

Even though we provide a conventional, simplistic algorithm for choosing a specific type of control chart (Figure 3), we do not promote a cookbook approach to statistical process control. Moreover, this tutorial is not intended to provide in-depth coverage of the rather expansive field of continuous quality improvement. The so-inclined reader is referred to one of the number of textbooks with in-depth coverage of the rationale and methodology of continuous quality improvement.24,25,99–101


Name: Thomas R. Vetter, MD, MPH.

Contribution: This author helped write and revise the manuscript.

Name: Douglas Morrice, PhD.

Contribution: This author helped write and revise the manuscript.

This manuscript was handled by: Jean-Francois Pittet, MD.


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