Ppk study, using pooled standard deviation or not?

[Miner]

Minitab has the Multi-Vari chart and a variant of that called the Variability chart.

If you don't have an ASQ membership, isixsigma has a decent article on Multi-Vari charts. However, I would add a 4th source of variation that is often omitted. The article states: The three sources of variation represented on the chart are:

• Positional, or within-unit variation
• Cyclical, or between-unit variation
• Temporal, or the variation due to change over time

I would add the following source to the three above:

• Structural variation, or variation between process streams (e.g., machines, lines and facilities, etc.)

 

[Bev D]

I’ve found that too many ‘current’ references to multi-vari change the components/families of variation from teh original names/categories (just for the sake of change?) and it dilutes the power of the multi-vari. I guess that since there is no math involved it freaks these people out.

The original components are:
Within piece
Piece to piece
Lot to lot (or set-up to set-up)
Supplier or material lot to lot or batch to batch
Time to time (hour to hour, day to day, month to month, season to season if necessary)
Operator to operator
Shift to shift
Machine to machine
Cycle to cycle. (Shot to shot within a cavity for multi-cavity equipment)
Cavity to to cavity
Operation to operation
Use to use (for multi use products)

…and any others that apply to the specific situation.

I also prefer the original articles by Leonard Seder (I think an ASQ member can request these for free from ASQ - at least I’ve had success this way for ‘pre-quality progress’ articles)

Leonard A. Seder, “Diagnosis With Diagrams – Part I”, Industrial Quality Control, January 1950, pp. 11-19
Leonard A. Seder, “Diagnosis With Diagrams – Part II”, Industrial Quality Control, March 1950, pp. 7-11

As Ellis Ott said: “plot your data and THINK about your data”.
Raw data plotted in multi-variate, time series format is the best statistical analysis ever…

 

[Semoi]

If you want to study the critical input parameters, multi vari charts are great. Nevertheless, before I plunge into a variational analysis I usually make sure that it is the most urgent topic. Maybe your time is better spend on some other topic. Thus, I suggest you first calculate the Ppk value for each subgroup, and report the minimal Ppk value (and its 95% confidence interval). If this is not meaningful -- e.g. because the sample size is "too small" and the uncertainty "too large" -- you could report the pooled Ppk value instead. Use the reported Ppk value to check if this process deserves your attention.

Why the pooled Ppk could make sense:
If we assume that the mean values of the three groups are not equal, the between-group variance inflated the total variance. Therefore, it is probable that the pooled Ppk is smaller than the weighted average of the three individual Ppk values. Thus, the pooled Ppk value is more conservative than the weighted averaged Ppk -- but less conservative than the minimal Ppk. However, as the others already stated: A pooled Ppk only makes sense if the different groups are somewhat comparable. E.g. if you drill holes with the same tolerance into different products and you measure the position accuracy of these holes on three different products, the pooled data could make sense.

 

[John Predmore]

Just make up a number to tell your manager

I had to share this Dilbert cartoon - one of my all-time favorites. Credit to Scott Adams.

 

[Bev D]

One of my all time favorites. Use it in a lot of training…

 

[Jim Wynne]

This seems like a be-careful-what-you-ask-for moment for the OP . I think that his best option (from this vantage point) is to explain to his boss that what he's asking for makes no sense, and that under the most appropriate circumstances, Ppk is a useless statistic. Well, perhaps not useless, as it does serve to fill a void that should be left empty.

 

[Bev D]

There is value in trying to understand why Ppk is silly. Understanding process performance does have value. If the OP can learn how to plot their data in multi-vari, time series, SPC chart and understand the role of homogeneity they’ll have taken a huge step forward and may even find it useful in convincing his bass.

@KitchenAlbatros you might want to read my paper “statistical alchemy” particularly the section of process capability indices. It has the arguments against the indices and provides ideas on alternatives

 

[Jim Wynne]

There is value in trying to understand why Ppk is silly.

Undoubtedly. There is also value in knowing when to use a rocket launcher and when to use a fly swatter.

 

[KitchenAlbatros]

Thanks everyone for your input. @Bev D , I already read the paper and it does make a lot of sense. I have a call planned with some bosses over this topic because I feel that they also don't really understand what they are asking. So I hope that they are open to any input I give them.