A clear goal

In reading the One Good Idea column, "Find the Answers You Seek," (August 2008, p. 80) I agree with Ray Harkins in one area: Product engineers often prefer to minimize the tolerance guidelines they provide for manufacturing. This can happen for a couple of reasons.

First, the resulting sum of part tolerances may have an impact on the final assembly, making it cheaper to tighten the part tolerances rather than lose expensive assembled products. Second, it might be that the product engineer has no idea what to expect from the process.

I am very worried, however, about promoting the idea of "back calculating" the capability indexes from the sample inspection data for the following reasons:

  1. During the initial submission of tolerance guidelines, the data is often very limited. As a result, the capability indexes’ confidence intervals will be wide.
  2. By taking the samples from the incoming material lots, the time sequence of manufacturing will not be known. This will result in incorrect plotting of control charts and incorrect interpretation of process stability. Hence, Cp and Cpk calculations will not make sense.
  3. It is better to stick with process performance indexes, such as Pp and Ppk. These calculations use the sigma from accumulated data and are independent of process stability.
  4. By encouraging back calculating of Cp and Cpk (or Pp and Ppk for that matter), there is a danger that engineering personnel will not work on continuous improvements to reduce variation. Instead, they might choose to take this shortcut to create satisfactory indexes artificially.

Product engineers who are too conservative establishing their tolerances for no valid reason should be educated about the cost of manufacturing tight tolerances and trained in the application of tolerance design and quality engineering tools.

This approach of back calculating the specification to desired capability should only be used in very extreme cases in which the technology maturity or cost prohibits any variation reduction, or in which the customer is hung up on a specific Cpk target and is not willing to budge.

Govind Ramu
Quality manager, JDS Uniphase Corp.
Milpitas, CA

Author’s response

In writing this article, I was trying to outline a quality-related application for Excel’s Goal Seek tool. The same tool could be used in other applications, such as Gage Selection Guide, where Goal Seek calculates a characteristic’s minimum tolerance range necessary for an established gage to achieve 20% repeatability and reproducibility. I’ve used this tool to determine the most expensive house an individual could afford, working backward from a budgeted monthly payment. Its uses are endless.

I was not trying to say designers should base the tolerance guidelines on the supplier’s process capability. Looking back at this column and Ramu’s comments, I should have clarified this point further. It is common in my production parts approval process (PPAP) work, which has taken me to most of the appliance manufacturers in the United States, for the product engineer or the supplier quality engineer to insist that all dimensions be within the print specification before approving the part for use in production. One way of accomplishing this task is to change the blueprint to match the part layout.

I used the phrase "incidental differences" in the second paragraph of the column to highlight that Goal Seek is not a means of specifying function-critical dimensions, nor is it—in reference to Ramu’s fourth point—a means of eliminating the need for continuous improvement. In practice, the method I described in the column has served our customers well in terms of offering recommendations for tolerance changes.

Regarding Ramu’s second and third points, he is absolutely correct. Cp and Cpk are calculated using an estimated sigma typically derived from the range portion of a statistical process control chart and deal with variation only within the subgroups. Pp and Ppk use a calculated sigma and deal with the total variation of the parts measured.

I struggled over which term to use because of the confusion between Cpk and Ppk I’ve seen regularly. I went with Cpk because it is the more familiar of the two, and I added the phrase "from the appropriate subgroups" to suggest time-based measurements.

In retrospect, maybe I should have gone with Ppk. But I didn’t want to distract the reader from the Goal Seek tool by focusing on the problem of choosing the correct index for the job. In fact, I am nearly finished writing an article detailing the similarities and differences between these two indexes.

I also agree with Ramu’s first point. Data is limited at the onset of a project. But if an engineer were simply trying to establish a print tolerance to accommodate the full range of expected values, he could set the Ppk in the Goal Seek tool to a level that would mitigate concerns about a low confidence level in his sample data.

In my example, I selected 1.33 as a target because it suggests the expected process range is at least 25% smaller than the print specification. A better choice in some cases would be 1.5 or 2.0. Ramu might prefer to design a Goal Seek tool that sets the low end of the confidence interval of a Ppk calculation to a certain value, and then adjust the tolerance range to achieve that. Again, the possibilities are endless.

Ray Harkins
Quality manager, Mercury Plastics Inc.
Middlefield, OH

Completely flat

In the Expert Answers department of the August 2008 issue (p. 8) you published a question about statistical process control applied to flatness measurement. The expert, Shin Ta Liu, provided an answer, but not a complete one.

Liu suggests that when using a mean control chart for flatness, it is good if the control chart shows values that are below the lower control limit. The practitioner should then search for an assignable cause and, if found, adopt the improved process. I have three concerns with this answer:

  1. Reducing flatness might not be desirable, as it might lead to stiction problems. So defining "goodness" or "badness" really depends on the physical properties of the characteristic you are trying to improve and their relationship to what is desirable.
  2. Even if the assignable causes are found, this does not mean they can always be adopted. There can be physical, technical or economic reasons that make adoption impractical.
  3. Having the control chart show values that are below the lower control limit does not necessary imply process improvement. In fact, it can imply that the measurement system has become unstable or failed. The term "measurement system" used in this context can be any combination of mechanical, electrical or manpower used in the measurement of the quality characteristic.

My recommendation is that if the control chart signals a possible process improvement (either above or below the control limits), check the measurement system first. If the measurement system is stable, then proceed to search for assignable causes and, if found, adopt them if it is practical to do so.

John J. Flaig
Managing director, Applied Technology
San Jose, CA

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