# Interpreting Run Charts and Shewhart Charts

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Interpreting Run Charts and Shewhart Charts

Agenda Features of Run Charts Interpreting Run Charts
A quick mention of variation Features of Shewhart Charts Interpreting Shewhart Charts

Displaying Key Measures over Time – Run Chart
Data displayed in time order Time is along X axis Result along Y axis Centre line = median One “dot” = one sample of data

Three Uses of Run Charts in Quality Work
Determine if change is an improvement Three Uses of Run Charts in Quality Work Median 429 Slide source: L. Provost, used with permission The Data Guide, p 3-18 4

Three Uses of Run Charts in Quality Work
2. Determine if improvement is sustained Median 429 Slide source: L. Provost, used with permission The Data Guide, p 3-18 5

Three Uses of Run Charts in Quality Work
3. Make process performance visible Median 429 Slide source: L. Provost, used with permission The Data Guide, p 3-18 6

How Do We Analyze a Run Chart?
Visual analysis first If pattern is not clear, then apply probability based rules Slide source: L. Provost, used with permission The Data Guide, p 3-10 7

Non-Random Signals on Run Charts
A Trend 5 or more A Shift: 6 or more Too many or too few runs An astronomical data point Slide source: L. Provost, used with permission Evidence of a non-random signal if one or more of the circumstances depicted by these four rules are on the run chart. The first three rules are violations of random patterns and are based on a probability of less than 5% chance of occurring just by chance with no change. The Data Guide, p 3-11 8

Source: Swed, Frieda S. and Eisenhart, C
Source: Swed, Frieda S. and Eisenhart, C. (1943) “Tables for Testing Randomness of Grouping in a Sequence of Alternatives.” Annals of Mathematical Statistics. Vol. XIV, pp , Tables II and III. The Data Guide, p 3-14 9

Trend? Note: 2 same values – only count one
Slide source: M. Rathgeber, MERGE consulting, used with permission

Shift? Note: values on median don’t make or break a shift
Slide source: M. Rathgeber, MERGE consulting, used with permission

Shift? Slide source: M. Rathgeber, MERGE consulting, used with permission

Interpretation? There is a signal of a non-random pattern
Slide source: M. Rathgeber, MERGE consulting, used with permission There is a signal of a non-random pattern There is less than 5 % chance that we would see this pattern if something wasn’t going on, i.e. if there wasn’t a real change

Plain Language Interpretation?
Slide source: M. Rathgeber, MERGE consulting, used with permission There is evidence of improvement – the chance we would see a “shift” like this in data if there wasn’t a real change in what we were doing is less than 5%.

Two few or too many runs? 1. bring out the table 2. how many points do we have (not on median?) 3. how many runs do we have (cross median +1) 4. what is the upper and lower limit? Slide source: M. Rathgeber, MERGE consulting, used with permission

Two few or too many runs? 1. bring out the table 2. how many points do we have how many runs do we have (cross median +1) what is the upper and lower limit? Slide source: M. Rathgeber, MERGE consulting, used with permission

Two few runs? Plain language interpretation
Slide source: M. Rathgeber, MERGE consulting, used with permission There is evidence of improvement – our data only crosses the median line twice – three runs. If it was just random variation, we would expect to see more up and down.

Two many runs? Plain language interpretation
Slide source: M. Rathgeber, MERGE consulting, used with permission There is evidence of a non-random pattern. There is a pattern to the way the data rises and falls above and below the median. Something systematically different. Should investigate and maybe plot on separate run charts.

Astronomical Data Point?
Slide source: M. Rathgeber, MERGE consulting, used with permission

Understanding Variation
Walter Shewhart (1891 – 1967) W. Edwards Deming ( ) The Pioneers of Understanding Variation

Intended and Unintended Variation
Intended variation is an important part of effective, patient-centered health care.   Unintended variation is due to changes introduced into healthcare process that are not purposeful, planned or guided. Walter Shewhart focused his work on this unintended variation. He found that reducing unintended variation in a process usually resulted in improved outcomes and lower costs. (Berwick 1991) Slide source: L. Provost, used with permission Health Care Data Guide, p. 107

Shewhart’s Theory of Variation
Common Causes—those causes inherent in the system over time, affect everyone working in the system, and affect all outcomes of the system Common cause of variation Chance cause Stable process Process in statistical control Special Causes—those causes not part of the system all the time or do not affect everyone, but arise because of specific circumstances Special cause of variation Assignable cause Unstable process Process not in statistical control Could insert “a” game Health Care Data Guide, p. 108

Health Care Data Guide, p. 113
Shewhart Charts The Shewhart chart is a statistical tool used to distinguish between variation in a measure due to common causes and variation due to special causes Slide source: L. Provost, used with permission (Most common name is a control chart, more descriptive would be learning charts or system performance charts) Health Care Data Guide, p. 113

Control Charts – what features differ from a run chart?

Control Charts/Shewhart Charts
upper and lower control limits to detect special cause variation Extend limits to predict future performance Not necessarily ordered by time advanced application of SPC – is there something different between systems 25

Example of Shewhart Chart for Unequal Subgroup Size
Health Care Data Guide, p. 114

Adapted from Health Care Data Guide, p. 151 & QI Charts Software

Slide source: L. Provost, used with permission

Health Care Data Guide, p. 116
Note: A point exactly on the centerline does not cancel or count towards a shift Health Care Data Guide, p. 116 29

Slide source: L. Provost, used with permission

Special cause: point outside the limits
Slide source: L. Provost, used with permission

Slide source: L. Provost, used with permission

2 out of 3 consecutive points in outer third of limits or beyond
Special cause 2 out of 3 consecutive points in outer third of limits or beyond Slide source: L. Provost, used with permission

Slide source: L. Provost, used with permission

Slide source: L. Provost, used with permission

Slide source: L. Provost, used with permission

Common Cause Slide source: L. Provost, used with permission

Health Care Data Guide, p. 116
Note: A point exactly on the centerline does not cancel or count towards a shift Health Care Data Guide, p. 116 38

Case Study #1a

Case Study #1b Percent of cases with urinary tract infection

Case Study #1c Percent of cases with urinary tract infection

Case Study #1d Percent of cases with urinary tract infection

Case Study #1e Percent of cases with urinary tract infection

Case Study #1f Percent of cases with urinary tract infection

Health Care Data Guide, p. 116
Note: A point exactly on the centerline does not cancel or count towards a shift Health Care Data Guide, p. 116 45

Case Study #2a Percent of patients with Death or Serious Morbidity who are >= 65 years of age

Case Study #2b Percent of patients with Death or Serious Morbidity who are >= 65 years of age

Case Study #2c Percent of patients with Death or Serious Morbidity who are >= 65 years of age

Case Study #2d Percent of patients with Death or Serious Morbidity who are >= 65 years of age

References BCPSQC Measurement Report
Langley GJ, Moen R, Nolan KM, Nolan TW, Norman CL, Provost LP (2009) The Improvement Guide (2nd ed). Provost L, Murray S (2011) The Health Care Data Guide. Berwick, Donald M, Controlling Variation in Health Care: A Consultation with Walter Shewhart, Medical Care, December, 1991, Vol. 29, No 12, page Perla R, Provost L, Murray S (2010) The run chart: a simple analytical tool for learning from variation in healthcare processes, BMJ Qual Saf : Associates in Process Improvement website