Abstract
In this paper, we have considered the problem of optimal inspection times for the progressive interval type-I censoring scheme where uncertainty in the process is governed by the two-parameter Rayleigh distribution. Here, we also introduced some optimality criterion and determined the optimum inspection times, accordingly. The effect of the number of inspections and choice of optimally spaced inspection times based on the asymptotic relative efficiencies of the maximum likelihood estimates of the parameters are also investigated. Further, we have discussed the optimal progressive type-I interval censoring plan when the inspection times and the expected proportions of total failures in the experiment are under control.
Highlights
The Rayleigh distribution is recognized to be a very useful distribution in the lifetime analysis and operations research for its mathematical simplicity and statistical flexibility
We have contemplated the problem of planning progressive interval type-I (PITI) censoring scheme for Rayleigh distribution
It is noted that the inspection times using optimality criterion that minimize Shannon entropy has either highest asymptotic relative efficiencies (AREs) or close to that relative efficiency which is the highest among all the considered criterion
Summary
The Rayleigh distribution is recognized to be a very useful distribution in the lifetime analysis and operations research for its mathematical simplicity and statistical flexibility. In the PITI censored situations, a natural problem that may arise is to determine the associated inspection times appropriately before conducting the experiment to assess the parameter(s) of interest with the least possible reduction in efficiency as compared to the exactly observed situation. In this context, Lin, Chou, and Balakrishnan (2013) have developed some optimum inspection plan for log-normal distribution. A discussion on optimal grouping or monitoring times can be found in the works of Kulldorf (1961) based on the criterion of minimizing the asymptotic variance or maximizing the determinant of the expected Fisher information matrix of the maximum likelihood estimates (MLEs) of the parameters under the interval type-I censoring scheme.
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