The Economic Design of -Charts When There is a Multiplicity of Assignable Causes

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Abstract
An earlier article by the author [4] studied the economic design of -charts used to maintain current control of a process when there is a single assignable cause occurring randomly, but with known effect. The present article extends the study to allow for the occurrence of several assignable causes the probability distribution of which is known. The initial model studied reveals the existence of readily acceptable (local minimum) solutions that are relatively stable with respect to model changes, including marked changes in the distribution of assignable causes. There were also found in some cases economically better solutions that would not be as readily acceptable as those offered by the local minima (e.g., the limits might fall at ± 6σ). The article argues that as extensions of the model approach reality, only the local-minimum solutions will remain. It then goes on to show that these can be well approximated by solutions of single-cause models. Thus in practice it may be sufficient to use single-cause models.

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