Economic Design of Fraction Nonconforming Control Charts with Multiple State Changes

Abstract

A number of models for the economic design of fraction nonconforming control charts have been presented. When multiple out-of-control states exist, a common assumption has been that at most a single assignable cause may affect the state of the production process during a specified or random interval. A model which does not constrain the number of shifts is presented and the effects of the “single shift” assumption are reviewed. Results indicate that the previous models' assumptions are valid for a significant range of model parameters. However, cases are presented for which some models are shown to be weakened by their limiting assumptions. In particular, the “single shift per process investigation” assumption is shown to exhibit a misleading relationship between the sampling interval and sample acceptance policy, such that an artificial degree of stability is conferred upon the production process when the expected interval between process investigations becomes large.

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