A Production Model and Continuous Sampling Plan
A production model is considered where the quality of output decreases until corrective action is taken and then the cycle is repeated. For this model, the sampling plan of examining each Fth item and taking corrective action whenever a defective is found, is evaluated. Illustrations are presented of the production model and choice of sampling plan, F. The relationship of this model and plan to earlier ones is discussed. Specifically, the probability of producing a good item after t units of production is assumed to be PRzt), where z(t) is the value of a Poisson process and represents the change (from good to bad) in the production process since "trouble-shooting." P and R are "quality" parameters satisfying 0 <P _1 and 0<R <1. Costs, such as that of looking for and removing trouble, and of inspection, are introduced. The average income is maximized by the choice of F.