The use of three probability distributions to model the time to failure in an economic model of a multivariate quality control procedure is investigated. A discrete-time Markov (geometric) model is developed, as well as two non-Markovian (Poisson and logarithmic series) models. Numerical examples are presented which indicate that both the Markov assumption and the shape of the distribution of time to failure are of considerable importance in determining the optimal test parameters.
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Heikes et al. (1974) studied this question.
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