fms95032 wrote:Hi Stan,

Thanks - I'll take a closer look and see how to create the plans according to your direction.

Do you know of any reference or source for this approach?

cheers,

Fred

I do not know of another example because the approach might be unique. But it is based on the laws of probability.

You multiply two probabilities together when you want to know the probability that both events will occur. For example, that the lot will be accepted by both the sampling plan for droplet size and the sampling plan for flow rate.

The acceptabilities of the two variables -- droplet size and flow rate --are correlated. So the applicable probability rule for the lot Pa is the rule for the probability of non-independent events. That rule calls for using conditional probabilities.

Link to Rules of ProbabilityThe conditional probability requirement is met in this case because the Pa's of the oc curves are conditional probabilities -- the condition being the lot percent nonconforming for that variable -- on the horizontal axis of the oc curve.

The probabilities of acceptance of the two variables plans are forced to be dependent by the way your specification limits define the effect of the variables on lot percent nonconforming.

So in my prior example when I took the square root and when I multiplied two equal Pa's, I assumed that the two variables made equal contributions to acceptability or rejectability of a lot. -- this is in terms of the variable's contribution to percent nonconforming. The relationships can be further visualized by showing the corresponding lot means next to % nonconforming on the horizontal axes of the oc curves. My program TP414 can generate oc curves for the mean.