Summary This paper proposes a production model for quality surveillance, which is based on a cusum chart using the decision interval criterion. An algorithm for determining the economically optimum control parameters is presented. Some criticisms of the conventional ad hoc design of a cusum chart are made, and it is suggested that the average run lengths (ARL) at the rejectable quality level should be less than 2 when this model is applicable. A simplified version of the algorithm is also devised which gives control plans which are close to optimum. This scheme is suitable for application at the factory level. Also included is a table of ARL for some neglected, but useful, values of the decision interval and the process deviate.

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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.