Sequential D-Optimal Design for Binary Lifetime Testing on Weibull Distribution

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  • ワイブル分布からの二値観測寿命試験のための逐次D-最適試験計画
  • ワイブル ブンプ カラ ノ ニチ カンソク ジュミョウ シケン ノ タメ ノ チクジ D サイテキ シケン ケイカク

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Abstract

When products under lifetime testings need destructive investigations, the data sets consist of binary values observed only at times prespecified for each item. Iwamoto and Suzuki [6] derives a D-optimal design of inspection times for several lifetime distributions, that is almost optimal when close initial estimates are available. This article extends that design to multistage cases so as to examine the influences of initial estimates on maximum likelihood estimates. A conditionally D-optimal design is proposed which determines inspection times sequentially for multistage testings. Weibull distributions with known shape parameters are numerically investigated for biases and variances of maximum likelihood estimators. Small sample properties of maximum likelihood estimators and the properties of equally allocated designs are also investigated. These results suggest that when the initial estimates are set to be smaller than the true values, multistage testings work well and maximum likelihood estimates are obtained. Also, the single stage design is nearly optimal for cases with the shape parameter is less than or equal to 1.0. This means if we have such initial estimates, one stage testings give results with reasonable precisions.

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