Economic Design of np Charts for Processes Subject to a Multiplicity of Assignable Causes

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Abstract
A model is developed for production processes which have an in-control state and may jump to one of several out-of-control states in course of time, each such state being associated with an assignable cause. The quality characteristic is an attribute so that an np-chart control scheme is applied. Various cost and time elements are included in the derivation of the loss-cost function. By minimizing this function with respect to the three control variables, namely, the sampling interval, the sample size and the acceptance number, the economically optimal control plan can be obtained. A numerical example is given using a new prior distribution. The results compare favourably with those derived from a matched single cause model.

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