Abstract
This paper investigates the design of accelerated life test (ALT) sampling plans under progressive Type II interval censoring with random removals. For ALT sampling plans with two over-stress levels, the optimal stress levels and the allocation proportions to them are obtained by minimizing the asymptotic generalized variance of the maximum likelihood estimation of model parameters. The required sample size and the acceptability constant which satisfy given levels of producer’s risk and consumer’s risk are found. ALT sampling plans with three over-stress levels are also considered under some specific settings. The properties of the derived ALT sampling plans under different parameter values are investigated by a numerical study. Some interesting patterns, which can provide useful insight to practitioners in related areas, are found. The true acceptance probabilities are computed using a Monte Carlo simulation and the results show that the accuracy of the derived ALT sampling plans is satisfactory. A numerical example is also provided for illustrative purpose.
Highlights
The design of reliability sampling plans under Type II censoring schemes has been studied by many researchers (Fertig & Mann, 1980; Hosono, Ohta, & Kase, 1981; Kocherlakota & Balakrishnan, 1986; Schneider, 1989; Balasooriya, 1995; Wu, Hung, & Tsai, 2003)
This paper investigates the design of accelerated life test (ALT) sampling plans under progressive Type II interval censoring with random removals
More information on the lifetime distribution is collected and the required sample size n is decreased. Taking these two kinds of effect into consideration, shorter inspection interval doesn’t always yield smaller required sample size for ALT sampling plans under progressive Type II interval censoring with random removals
Summary
The design of reliability sampling plans under Type II censoring schemes has been studied by many researchers (Fertig & Mann, 1980; Hosono, Ohta, & Kase, 1981; Kocherlakota & Balakrishnan, 1986; Schneider, 1989; Balasooriya, 1995; Wu, Hung, & Tsai, 2003). Tse and Yang (2003) discussed the design of reliability sampling plans for the Weibull distribution under progressive Type II censoring with random removals, where the number of units removed at each failure was assumed to follow a binomial distribution. This study can be noted as an extension to the work of Ding and Tse (2013) along three directions: (i) the research topic is extended from the design of optimal ALT plans to the design of optimal ALT reliability sampling plans, in which both the consumer’s risk and the producer’s risk are satisfied In this sense this paper resolves a more practical problem; (ii) instead of minimizing the asymptotic variance of an estimated quantile of units’ lifetime distribution, this paper minimizes the asymptotic generalized variance of the maximum likelihood estimation of model parameters.
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