00426 190c45644d0b0a239e28db52d020e7

430

Pignatiello & Ramberg

Thus, we have three different ‘Variances” here. A procedurę, called analysis of variance (ANOKA), can be used to estimate these components of variation. We notę, however, it is not a procedurę that is considered in the proposed standard. Whenever a components of variance model is employed, verification of the underlying statistical assumptions, such as normality, should be applied to the residuals from the predictive or fitted model rather than to the original data. For this model, the predicted values of individual observations are simply the rational sample averages.

The obvious ąuestion that remains is: what should be used to represent process capability? When the rational sample size is greater than one, an X -chart is used in conjunction with a R- or .S’-chart for monitoring the process and collecting the data.

Here, the two procedures from the proposed standard, both of which use the “edited” data from control charts on X and either R or S, are:

•Procedurę 1: Estimate the process mean, p, by the grand average. Estimate the process standard deviation, ct, with R/d₂ or S/c_A .

•Procedurę 2: Estimate the process mean, p, by the grand average. Estimate the process standard deviation, o, by the overall standard deviation of all of the (edited) data, effectively ignoring which observations came from which samples. That is, treat each observation as if it were from just one very large ‘lampie” (which should be sufficiently large to skip the division by the c₄).

Once again, a comparison of the two process standard deviation estimates allows assessment of the model. If the procedurę 2 estimate is substantially larger than the procedurę 1 estimate, then there are at least two components of variation. The procedurę 1 estimate indicates the potentially achievable capability while the procedurę 2 estimate indicates that other sources of variability could be evaluated.

Again, a decision on reporting this information must be madę. At this writing both methods appear to be acceptable according to the proposed standard for representing capability and the choice should be madę in the context of application.

Other Process Studies

Although the recent literaturę on process capability indices is profuse, very little appears on data collection schemes. The design of a statistically