A Better Picture

Description: All processes have variation. When you collect data on these processes, you can get a better understanding of the magnitude of that variation and what efforts are needed to reduce the variation to improve product quality.…

Keywords: Statistics,Stability index,Variation

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As one of the co-authors of the paper, I would like to add some additional thoughts in response to the comments of Vladimir.

We absolutely agree with Vladimir that the stability index (SI) is just a single number and has its limitations, which we have noted in the article. As Vladimir notes, it is a way to assess past performance. However, in many modern manufacturing environments with hundreds of variables to monitor, it is impossible to track all of the control charts on a regular basis, hence the need for a screening method to quickly get to the most critical variables to consider more closely. So the SI can be used as a screening approach before using the most effective stability assessment tool, the control chart. If you have just a few charts to monitor, then the need for the SI is less. In terms of the arbitrariness of using 1.33 of a value, we believe there is more value in considering SI values along a spectrum, as we show in Figure 5. Using the SI along a spectrum helps one to focus on the most important quality issues, whether they are related to stability or capability, or both. In our collective work with many engineers and quality professionals for our respective employers, we have found that they appreciate the simplicity and value of the Stability Index. Based on our experiences, we believe it to be very useful for practitioners.
--Willis Jensen, 01-24-2020

Do see the value in pairing these indices with OTS SPC.
--Jayet Moon, 01-16-2020

In response to “A Better Picture” (QP, Jan. 2020, pp.41-49): I found this article interesting but I am not sure whether it brings practitioners more benefit or more harm. No single index can answer the question if the process is stable or not – only control chart can do. The reason: all single metrics are based on some statistical assumptions (e.g., normality, and/or i.i.d. condition, and/or something similar) that in most cases can’t be checked up in practice. Only simple Shewhart control chart does not require these statistical assumptions. The authors know this so they suggest using the stability index (SI) “in conjunction with control charts”. But if I have already constructed control chart I am not interested in any SI – I simply see if my process is stable or not. Moreover, if one looks, for example, at fig.4 she/he will see that calculating standard deviation by all data is useless: the data are not homogeneous. Additionally it is worth noting that the SI in the example shown was calculated by six months data: in practice nobody will reveal the cause of the lack of stability after several days – so this information over months or weeks is almost always useless. Obviously, the SI will always be “post-mortem” metric. And my last comment concerns the fact that most of practitioners are trying to use the specific values of capability indices (CI) as quality criteria about their processes. The same will be the future of SI. And the value of 1,25 for SI is as arbitrary as 1,33 for CI or 3,4 ppm for Six Sigma approach. Finally I consider the paper useful for statisticians and not useful for practitioners
--Vladimir Shper, 01-11-2020

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