Spichiger Table Forgot Metropolitan Section
Reading “60 Years and Still Going Strong” (James O. Spichiger, May 2006, p. 42) was a trip down memory lane for me.
I probably joined ASQ in 1955 as part of the requirement to pass Ellis Ott’s class at Rutgers. So I wasn’t there at the founding of ASQC. However, I knew a number of the founding members and am familiar with the works of many more.
I wasn’t there so I can’t be sure, but I was taken aback not to see the Metropolitan Section listed in Table 2 as the current section next to the Newark Society for Statistical Quality Control.
This really surprises me, particularly since Spichiger was a great regional director for region 3, which includes the Metropolitan Section and its offshoots—North Jersey, Long Island, Tappan Zee and maybe even Princeton.
Editor’s Note: After some research, ASQ has found records showing the Society for Statistical Quality Control became the Metropolitan New York Section. It was renamed and now is called the NY/NJ Metropolitan Section.
AIAG Team Member Responds to Columns
I would like to thank Donald Ermer for his two Measure for Measure columns (“Improved Gage R&R Measurement Studies,” March 2006, p. 77, and “Appraiser Variation in Gage R&R Measurement,” May 2006, p. 75). Despite some minor computational errors on p. 76 of the May column (2.45% and 3.09% should be 2.37% and 3.17%, respectively), the work was very insightful.
His geometrical approach, although comprehended in the current Automotive Industry Action Group (AIAG) Measurement Systems Analysis manual, is refreshing as well as reinforcing. As a member of the original AIAG team that published the Measurement System Analysis manual, I would like to provide further insight into three of the key issues addressed by Ermer. The first two were raised in the March column and the third in the May column.
In the March column, Ermer finds two errors in the AIAG reproducibility and repeatability (R&R) study:
- No adjustment for gage (equipment) variation in computing part variation (PV), as was properly done for appraiser variation (AV).
- The use of standard deviation, instead of variance, in computing component percentage variation numbers.
In both cases, the term “error” might be misleading. Our team members fully understood both points; however, we made conscious decisions in both cases to present the material as released. Of course, these types of decisions are subject to challenge and discussion, but we based them on full consideration of the mind-set of the manual’s primary customers—personnel of automotive parts and assembly plants and automotive suppliers.
For the first issue, adjustment for gage variation, the primary focus of the AIAG form is on gage and operator variation assessment, not part variation assessment. Accordingly, we deemed the gage variation correction factor (which derives from a function of the expected mean squares in the analysis of variance table) appropriate for the operator (appraiser) variation, because the operator should not be penalized for gage variation.
But, given the additional complexity that would be needed on the form for compensating PV for gage (equipment) variation, we made a conscious decision, despite possibly double counting gage (equipment) variation as part of total variation, not to further complicate the form with gage corrections when computing PV.
We made this decision taking into account an environment and time (1990) in which computations probably would be made manually on a shop floor, along with the probable insignificance of the difference it would make relative to PV.
We appreciate Ermer’s recognition that PV also should not be penalized for gage (equipment) variation. If the decision were otherwise, the team certainly knew how to properly adjust for the gage variation, as Ermer shows on p. 76 of the May column.
As for the second issue, using variance instead of standard deviation, the AIAG team again fully understood the matter. In fact, we listed the variance percentage contributions, which total 100%, along with the standard deviation percentage contributions, for the example we used in the manual to specifically highlight the difference between the two.
When considering the manual’s customers, who draw heavily on the standard deviation mind-set (+/-3 sigma, Six Sigma, design for Six Sigma) and who often interpret the word variance as the difference from a goal, standard or target—as opposed to its statistical meaning—we developed calculations and targets based on standard deviation rather than variance. Again, we understand the point of additivity of variances.
The final issue may have simply been an
oversight, or lack of familiarity with the AIAG form’s
Ki factors, by Ermer.
He points out, in the first paragraph of p. 76 of the May column,
“In the AIAG study, the constants d2,
d2, m, and d2, o are all assumed equal to d2 for the different sample sizes in the subgroup.”
The three factors referenced apply to the gage, parts and operators, respectively. In the AIAG manual’s summary form, we in fact did apply the proper d2* values for both AV and PV, through the Ki factors in Table 1 in the March column. In the AIAG manual, we used d2 instead of d2* for EV, because its k-value, or number of subgroups, is large (≥30).
It can (and should) be verified, from Table 3 in the March column, that Ki = 5.15/d2* for K2 and K3, in which d2* = 1.91 (k = 1, n = 3) and 3.18 (k = 1, n = 10, not shown in Table 3), for operators and parts, respectively. The 5.15 factor simply represents the number of standard deviations, which accounts for approximately 99% of the area under the normal curve, centered at 0 (+/-2.575 sigma).
Again, for equipment variation, K1 = 5.15/d2 (not d2*), in which d2 is taken to be 1.128. We used d2 for cases in which the k-value was ≥30, because the difference between d2 and d2* is virtually negligible for that range of k-values, particularly as subgroup size (n) increases.
General Motors Corp.
In “Fighting Back” (Debbie Phillips-Donaldson, Up Front, May 2006, p. 6), U.S. manufacturers’ warranty costs for 2004 were stated as $25 million dollars. The correct figure is $25 billion.