Optimal acceptance sampling plans for log-location-scale lifetime models using average risks

Assuming that the probability of obtaining a defective unit in a production process, p, is not constant, a versatile methodology is presented for determining optimal failure-censored reliability sampling plans for log-location-scale lifetime models. The optimization procedure to decide the acceptability of a product is usually sufficiently accurate for the most widely used parametric lifetime models, such as the Weibull and lognormal distributions, and fairly robust to small deviations in the prior knowledge. Moreover, lower and upper bounds on the optimal sample size, and the corresponding acceptance constants, are derived in closed-forms. The proposed approach extends the traditional sampling plans to those cases in which appreciable prior information on p exists, and also allows the analyst the flexibility to delimitate the range of p and to incorporate into the reliability analysis prior impartiality between the producer and the consumer. In addition, the practitioners may achieve substantial savings in sample size, better information on the production process and better assessment of the true producer and consumer risks. An example related to the acceptability of a certain kind of gyroscope is included for illustrative purposes. Various practical prior distributions are considered to describe the random fluctuations in the proportion defective.