Apply Statistical Methods to Understand Variation

Understanding variation is achieved, in part, by collecting and analyzing process and product measures so that special causes of variation can be identified and addressed to achieve predictable performance.

A special cause of process variation is characterized by an unexpected change in process performance. Special causes are also known as “assignable causes” because they can be identified, analyzed, and addressed to prevent recurrence.

The identification of special causes of variation is based on departures from the system of common causes of variation. These departures can be identified by the presence of extreme values, or other identifiable patterns in the data collected from the subprocess or associated work products. Knowledge of variation and insight about potential sources of anomalous patterns are typically needed to detect special causes of variation.

Sources of anomalous patterns of variation may include:

Lack of process compliance Undistinguished influences of multiple underlying subprocesses on the data Ordering or timing of activities within the subprocess Uncontrolled inputs to the subprocess Environmental changes during subprocess execution Schedule pressure Inappropriate sampling or grouping of data

• Establish trial natural bounds for subprocesses having suitable historical performance data. Natural bounds of an attribute are the range within which variation normally occurs. All processes will show some variation in process and product measures each time they are executed. The issue is whether this variation is due to common causes of variation in the normal performance of the process or to some special cause that can and should be identified and removed.

  When a subprocess is initially executed, suitable data for establishing trial natural bounds are sometimes available from prior instances of the subprocess or comparable subprocesses, process performance baselines, or process performance models. These data are typically contained in the organization’s measurement repository. As the subprocess is executed, data specific to that instance are collected and used to update and replace the trial natural bounds. However, if the subprocess in question has been materially tailored, or if the conditions are materially different than in previous instantiations, the data in the repository may not be relevant and should not be used.

  In some cases, there may be no historical comparable data (for example, when introducing a new subprocess, when entering a new application domain, or when significant changes have been made to the subprocess). In such cases, trial natural bounds will have to be made from early process data of this subprocess. These trial natural bounds must then be refined and updated as subprocess execution continues.

  Examples of criteria for determining whether data are comparable include:

  Product lines Application domain Work product and task attributes (e.g., size of product) Size of project
• Collect data, as defined by the selected measures, on the subprocesses as they execute.
• Calculate the natural bounds of process performance for each measured attribute. Examples of where the natural bounds are calculated include:
  Control charts Confidence intervals (for parameters of distributions) Prediction intervals (for future outcomes)
• Identify special causes of variation. An example of a criterion for detecting a special cause of process variation in a control chart is a data point that falls outside of the 3-sigma control limits.

  The criteria for detecting special causes of variation are based on statistical theory and experience and depend on economic justification. As criteria are added, special causes are more likely to be identified if present, but the likelihood of false alarms also increases.

• Analyze the special cause of process variation to determine the reasons the anomaly occurred. Examples of techniques for analyzing the reasons for special causes of variation include:
  Cause-and-effect (fishbone) diagrams Designed experiments Control charts (applied to subprocess inputs or to lower level subprocesses) Subgrouping (analyzing the same data segregated into smaller groups based on an understanding of how the subprocess was implemented facilitates isolation of special causes)
  Some anomalies may simply be extremes of the underlying distribution rather than problems. The people implementing a subprocess are usually the ones best able to analyze and understand special causes of variation.
• Determine what corrective action should be taken when special causes of variation are identified. Removing a special cause of process variation does not change the underlying subprocess. It addresses an error in the way the subprocess is being executed.
• Recalculate the natural bounds for each measured attribute of the selected subprocesses as necessary. Recalculating the (statistically estimated) natural bounds is based on measured values that signify that the subprocess has changed, not on expectations or arbitrary decisions.

  Examples of when the natural bounds may need to be recalculated include:

  There are incremental improvements to the subprocess New tools are deployed for the subprocess A new subprocess is deployed The collected measures suggest that the subprocess mean has permanently shifted or the subprocess variation has permanently changed
• Revise the measures and statistical analysis techniques as necessary.