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Scott A. Hindle


Process Capability: What It Is and How It Helps, Part 4

Getting to the current capability of the process

Published: Thursday, September 1, 2016 - 16:45

A t the end of part three of this four-part series on process capability, Alan was ready to identify a contact at the factory who could assist in providing some context around the collected data and the overall production process.

Discussion with Joe

Joe, working on the production team, was the person Alan found. Joe was told he needed to provide more context about Product 874 data and give insight into the production process. To facilitate the discussion with Joe, Alan added some questions to Sarah’s X chart (as seen in figure 1).

Figure 1: X chart of Product 874 data with focus on the process changes detected by the software. Click here for larger image.

Their discussion soon got down to the production process making Product 874 and the need to get more context around the data Alan had been given to assess process capability. Joe agreed to discuss Alan’s questions internally in the hope of finding some answers. He said he’d get back to Alan and Sarah in a few days.

Joe’s feedback

Joe put his findings in an email as seen in figure 2 in preparation for the discussion with Alan and Sarah.

Figure 2: Summary of Joe’s feedback.

Alan wrote down the key points coming from their discussion:

Mixing time
• Inconsistencies in the choice of mixing time could be the assignable cause behind the two points outside the limits (production runs 1 and 2)
• Introducing a new, standardized mixing time is an important process “fix;” more consistency in quality should be expected from production run 4 onwards
• All production operators have been trained

Material 1748
• A problem with Material 1748 could also explain the second point outside the lower limit (production run 2)
• Purchasing department had confirmed that the issue with the non-approved source had been resolved with the supplier; they wouldn’t use this source for future deliveries

Measurement of samples
• The laboratory technician in charge of the regularly used rapid measurement method had detected a problem with a positive bias via a monitoring sample, explaining the run above the central line
• Between March 10 and March 21 the calibration was updated and found to be free of bias
• Monitoring of this measurement method since March 21 has indicated consistent precision with no evidence of bias

Changes since production run 6
• Joe confirmed that no changes of note had been made to the production process since production run 6

• Joe’s findings made sense as viable explanations of the detected process changes (assignable causes)
• Action had been taken on all the identified assignable causes to better control them in routine production
• Because production runs 6–17 displayed no signals of process change in figure 1, it adds greater weight to the belief that the assignable causes have been correctly identified and effectively controlled

The call concluded with Joe thanked for his great work. Joe, knowing that Alan had to write a report, said he was looking forward to receiving it.

A new analysis of process capability

Sarah asked Alan if this learning changed the way he viewed process capability for Product 874 data. Alan asked Sarah to be a bit more explicit. She asked if the original 56 data values should be used in the analysis of capability. Alan looked pensive but didn’t respond. Sarah, trying to help, asked if all 56 data values combined represent a mixture of different processes, each with a different story to tell.

Alan then said he got it. Referring to figure 2, and given the context of the data, he said that data from production runs 1 to 5 (values 1 to 16) should not be included in a new assessment of process capability because only values 17 to 56 represent the “current” process, which no longer needs to contain the story of:
• Potential issues due to inconsistencies in mixing time
• Material 1748 coming from a non-approved source
• Bias in measurement

Alan proceeded to assess process capability using values 17 to 56. He first updated his table of values as seen in figure 3, and then created an XmR chart of the data, using Sarah’s software to again customize the x-axis to be based on production run number (as seen in figure 4).

Figure 3: Representation of Product 874 data based on the learnings from the XmR chart analysis and feedback from Joe

Figure 4: XmR chart for data values 17 to 56

As figure 4 indicates a predictable process, Alan decided he was in a safe position to assess the capability of the process. He also knew to use the standard deviation coming from the moving ranges, giving him the following inputs to estimate capability:
• Average: 9.731 (see the central line on the X chart)
• Standard deviation: 0.357 ÷ 1.128 = 0.316 (the central line on the mR chart is the average moving range value)
• Specifications of 8.30 to 11.30

Alan’s first reaction was one of relief. He was now looking at capability statistics that satisfied the standard expectation of minimum capability 1.33.

Knowing that Cp and Cpk don’t take the process target into account, Alan decided to check if the process was on-target using a one-sample t-test. With a 95% confidence interval of 9.6379 to 9.8241, and p-value of 0.142, he found no evidence of the process being off-target. This also meant that his Cp and Cpk statistics were estimates of the same thing, i.e., a capability best estimated as 1.5-1.6. The conclusion Alan took was that the process is:
a) predictable (or stable or in control)
b) capable, and
c) on-target

He put this into a simple picture, using a histogram, as Sarah had recommended (and as seen in figure 5).

Figure 5: Representation of the current process capability for Product 874.

Alan computed a theoretical PPM value of 3.47 (using the average of 9.731, a standard deviation of 0.316, and the specification limits). He realized that this was, in many ways, an estimate of zero so long as the process remains predictable. No probability model is needed to reach this conclusion.

Back to the report

Alan completed his report, happy that he had not only completed the work successfully but also that the conclusion was positive: a predictable, capable, and on-target process. Alan also included in his report the extended quote found below, taken from a discussion he’d had with Sarah:

“To sustain the achieved capability, data from future production runs should be placed on the XmR chart in a timely, sequential manner. Signals of process changes on the chart would:
• Represent a deterioration in performance
• Reduce confidence in prediction until successful action on the assignable causes is taken
• Give an opportunity to develop process knowledge if the signals are investigated
• Return process performance to either its level of capability or improve performance to a new level of capability given successful action on the identified assignable causes”

Summary of Alan’s findings

Alan said he’d learned a lot, adding that XmR charts can help teach a lot about a process. His learning, he said, could be understood as the differences between the two flowcharts seen in figures 6 and 7.

Figure 6: Flowchart of Alan’s approach to his process capability task before learning

Figure 7: Flowchart of Alan’s approach to his process capability task after learning

Last word

Sarah commended Alan on a job well done, joking that his use of the XmR chart had made him an effective industrial statistician. She commented that his after flowchart didn’t include a data-collection plan step, which is often very important. Nor had this situation exposed him to the challenge of improving the capability of a predictable process or the question of rational subgrouping when using an average and range chart.

Sarah added that she was most pleasantly surprised at how quick Joe’s investigation of the assignable causes had been. She cautioned Alan that it might be trickier next time. Control charts, she said, are most often successfully integrated into manufacturing when assignable causes are investigated as close to real time as possible, because this increases the likelihood of successfully finding the cause.

Finally, she asked Alan how process capability helps. He said that speaking about process predictability, or stability, is needed to make capability useful and reliable. Alan gave four points:
• It helps to develop process knowledge by pushing you to ask more questions, and answer them
• It enables rational or more trustworthy predictions about future process performance
• It helps to decide if, and how urgently, improvement efforts should be directed towards a process
• It provides a basis for action to sustain and also further improve a process’s capability


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 online measurement devices as a part of both SPC and engineering process control.