Statistical Process Control Chart X-bar Chart Example

This Statistical Process Control Chart  x bar and r chart example describes an effective way to create a high-level performance tracking system that includes a process capability report-out in one report-out.  The described 30,000-foot-level reporting first assesses process stability from a high-level vantage point and then if the process is stable provides a capability statement, using terminology that everyone can easily understand.  This 30,000-foot-level report-out methodology can also be used to enhance Key Performance Indicators (KPIs) reporting.

Additional insight for this x bar and r chart example is described in the published article (PDF available below) titled “Performance Metric Reporting at the 30,000-Foot-Level: Resolving Issues with x-bar and R Control Chart and Process Capability Indices Reporting.”  This article was written by Forrest Breyfogle.

Statistical Process Control charts and process capability statements need to lead to the most appropriate action or non-action for a given set of data.  This document uses an x bar and r chart example to describe a 30,000-foot-level report-out approach that is in alignment with this desired.

To accomplish this x bar and r chart example objective, this writing addresses how to:

  • Create control charts so that the chart-creation mathematics is consistent with a team’s belief as to what fundamentally should be considered the source of common-cause variability and special-cause occurrence(s).
  • Determine and report-out a process prediction statement whenever a process is stable when viewed from the 30,000-foot-level. This prediction statement is then written so that everyone can easily interpret its meaning, even when there are no specifications.
  • Provide in one visual report-out the process stability assessment along with a prediction statement, when appropriate.

Statistical Process Control Chart X-bar Chart Example: Separation of Special-cause from Common-cause Variability

For a given process, one would think that everyone (when creating a control chart) would make a similar conclusion relative process stability and its capability/performance, where the only difference is from sampling probability (i.e., samples will differ by “luck of the draw”). However, this is not necessarily true. With a traditional approach, process statements are not only a function of process characteristics and sampling-chance differences but can also be dependent upon sampling approach.

This sampling-difference issue can have dramatic implications:

  • One person could describe a process as not being in control, which would lead to activities that are to immediately address process perturbations as abnormalities, while another person could describe the process as being stable. For this second interpretation, the described perturbations would be perceived as fluctuations typically expected within the process. Any long-lasting improvement effort for this second type of process response involves looking at the whole process to determine what might be done differently to enhance the process’ performance.
  • One person could describe a process as not predictable, while another person could describe output response as predictable.

To illustrate how different interpretations can occur, let’s consider the process time series data

statistical process control chart x bar chart

This set of data would typically lead to an x-bar and R control chart.  However, someone could have taken only one sample (e.g., sample number 5) and that would have received a very different conclusion relative to process stability.

The question is what can be done to resolve this x bar and r chart example inconsistency.

For more information on x bar and r chart example and process capability reporting, download the ASQ June 2017 Statistics Division Newsletter Vol. 36, No. 2, 2017 article titled Performance Metric Reporting at the 30,000-Foot-Level: Resolving Issues with x-bar and R Control Chart and Process Capability Indices Reporting″. This article was written by Forrest Breyfogle.

Download