[in Japanese]

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[in Japanese]

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The experiments on the lifetime distribution of the interconnects need long intervals and expensive costs even under accelerated tests. Nowadays semiconductor devices can contain up to several millions of possible failure interconnects, and early failures in electromigration has been highlighted in the last decade. In the literature, the sudden death test is applied to observe early failures. Though this test enables us to have the specified number of early failures with spending a long term, the issue on distrbituions remains unsolved. There are many articles on the failure times in electromigration of interconnects which analyse data with probablity plots of log-normal distributions or Weibull distributions. However they just check the distributional assumptions by plots. In this article, we invesitgate distributional assumptions by applying likelihood-based inference, and determine a suitable distribution for early failures using likelihood ratio tests and AIC. We conclude that the log-normal distribution is appropriate for the model with early failures, using three data sets on hand. Then we investigate the properties of the sudden death tests and observe that the precision of the estimator of the scale parameter is insensitive to the number of items in a group, and that of the location parameter depends on it. But the precision of MLE of the location parameter can be recovered by increasing the number of groups.

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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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