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Scott A. Hindle


Process Capability: What It Is and How It Helps, Part 2

Seeing the data differently

Published: Tuesday, August 30, 2016 - 12:36

In part one of this four-part series, we considered the basics of process capability, as witnessed through the learning curve of Alan in his quest to determine the product characteristics of the powder, Product 874. We pick up with Alan here as he prepares for his second meeting with his colleague Sarah, to discuss his preliminary results.

The second article Sarah had given Alan was titled “Individual Charts Done Right and Wrong,” by Donald J. Wheeler. It helped him to move in a different direction with the data he received to assess process capability. He recalled having been briefly exposed to Shewhart-type control charts, the subject of the paper, during a training class some time back, but he didn’t remember much about them.

As he read through the article, he was intrigued by the following comment from Wheeler about data that had been analyzed:
“...This is sufficient evidence to say that this process is changing,” Wheeler wrote. “When this happens the important questions are no longer questions about the process location or the process dispersion [which are used to calculate Cpk], but rather questions about what is causing this process to change. Estimation is moot. Discovery of the assignable cause is paramount.”

Alan found the definition of moot to be “not important or not relevant, therefore not worth discussing.” If estimation—i.e., calculation of statistics—were moot for his data set, then all his work so far was for nothing. This left Alan anxious. His next meeting with Sarah was still a couple of hours away, so he decided to use this time to prepare as best he could.

A chart of Product 874 data

In Wheeler’s article under the section “The chart for individual values done right,” Alan saw that something called “moving ranges” were used. Wheeler used the shortened term XmR chart, meaning a chart for both the individual data values, X; and for the calculated moving range values, mR. Hence, there were two actual charts. Two options were discussed to compute the process limits for the charts: the average moving range and the median moving range. Wheeler argued against the median moving range as the default approach, so Alan proceeded to use the average moving range. His computations are in figure 1, with the graphical result in figure 2 (both done in Microsoft Excel).

Figure 1: Original data and computed mR values to create an XmR chart for Product 874 data. Click here for larger image.

Figure 2: XmR chart for Product 874 data. Click here for larger image.

Alan’s interpretation of the XmR chart

Alan observed that points—the red lines—were out of the limits on both the X chart and the mR chart. Guided by Wheeler’s article, he interpreted Product 874 data to represent a changing process. He thought the following comment made by Wheeler ought to apply directly to the production process that generated Product 874’s capability data:

“When this happens [i.e., evidence of the process changing], the important questions are no longer questions about the process location or the process dispersion, but rather questions about what is causing this process to change.”

Alan updated figure 2 by highlighting the points outside the limits and adding some comments (see figure 3). He was quite aware that he didn’t know what was causing the process to change because he didn’t know anything about the process or the data. He didn’t even have a contact at the plant making Product 874. What should he do if Wheeler was right in his assertion that estimation is moot? How could he give his boss a report saying that process capability is moot?

Figure 3: XmR chart from figure 2 with points outside the limits highlighted and comments provided. Click here for larger image.

A ‘wrong’ X chart

Toward the end of Wheeler’s article was the section “The chart for individual values done wrong.” The first paragraph, concerned with the moving range method, ended with the statement, “The use of any other measure of dispersion is wrong.” This impled that only limits based on the moving ranges are “right.” Curious, Alan decided to create an X chart using the value for SDprocess of 0.4206 he had calculated to determine Cp and Cpk. (He realized that the “wrong” X chart would no longer come with an mR chart.) Alan also recognized that his SDprocess value of 0.4206 is what Wheeler referred to as a “global standard deviation statistic.”

Figure 4 shows the X chart with the “wrong” limits as well as the “right” limits. The “wrong” limits are:
• Upper limit (in red): 11.061
• Central line (in green): 9.7995
• Lower limit (in red): 8.538

Figure 4: X chart with both “right” and “wrong” limits included. (The “right” limits of 8.653 and 10.946 are shown computed in figure 1.) Click here for larger image.

Alan’s findings seemed to be in reasonable agreement with Wheeler’s comments:
• The “wrong” limits (from the global standard deviation statistic) were inflated in the presence of signals of process changes.
• Data value two, which is comfortably out of the “right” upper limit, is just inside the “wrong” upper limit (so this signal would escape detection).

Two other points struck Alan:
• Wheeler’s comment in reference to the “wrong” limits: “While this may paint a pretty picture of your process, it is simply nothing more than another way to lie with statistics.”
• He also asked himself if the moving range method might have something to do with Cp and C.”pk, but he didn’t know because process capability was not mentioned in Wheeler’s article.

Finishing his preparation

With the clock now ticking, Alan did a quick internet search using “process capability xmr chart.” He printed the first result, which was an article titled “A Guide to Control Charts,” by Carl Berardinelli. On page three of his printout, Alan’s attention was caught by the statement, “A process should be stable and in control before process capability is assessed.”

Alan realized that his process data represented an unstable or not-in-control process. Figure 3 provided him with enough evidence to make this conclusion. But Berardinelli’s statement only compounded his confusion. Being asked to assess process capability when process capability couldn’t be assessed was a hard one for him to get his head around. Alan decided to go for a coffee to avoid confusing himself further.

Part three continues with Alan meeting Sarah for a second time.


About The Author

Scott A. Hindle’s picture

Scott A. Hindle

Scott Hindle supports R&D and factory operations on process capability studies for new products and processes, statistical process control (SPC) for use in routine production, and the use of on-line measurement devices as a part of both SPC and engineering process control.