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Gamma lifetimes and one-shot device testing analysis

机译：伽马寿命和一次性测试测试分析

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Gamma distribution is widely used to model lifetime data in reliability and survival analysis. In the context of one-shot device testing, encountered commonly in testing devices such as munitions, rockets, and automobile air-bags, either left- or right-censored data are collected instead of actual lifetimes of the devices under test. The destructive nature of one-shot devices makes it difficult to collect sufficient lifetime information on the devices. For this reason, accelerated life-tests are commonly used in which the test devices are subjected to conditions in excess of its normal use-condition in order to induce more failures, so as to obtain more lifetime information within a relatively short period of time. In this paper, we discuss the analysis of one-shot device testing data under accelerated life-tests based on gamma distribution. Both scale and shape parameters of the gamma distribution are related to stress factors through log-linear link functions. Since lifetimes of devices under this test are censored, the EM algorithm is developed here for the estimation of the model parameters. The inference on the reliability at a specific mission time as well as on the mean lifetime of the devices is also developed. Moreover, by using missing information principle, the asymptotic variance-covariance matrix of the maximum likelihood estimates under the EM framework is determined, and is then used to construct asymptotic confidence intervals for the parameters of interest. For the reliability at a specific mission time and also for the mean lifetime of the devices, transformation approaches are proposed for the construction of confidence intervals. These confidence intervals are then compared through a simulation study in terms of coverage probabilities and average widths. Recommendations are then made for an appropriate approach for the construction of confidence intervals for different sample sizes and different levels of reliability. A distance-based statistic is suggested for testing the validity of the model to an observed data. Finally, since current status data with covariates in survival analysis and one-shot device testing data with stress factors in reliability analysis share the same data structure, a real data from a toxicological study is used to illustrate the developed methods.
机译：伽玛分布广泛用于在可靠性和生存分析中对寿命数据进行建模。在弹药，火箭和汽车安全气囊等测试设备中经常遇到的一次测试设备测试中，将收集左检查数据或右检查数据，而不是被测设备的实际寿命。一次性设备的破坏性使得难以在设备上收集足够的使用寿命信息。为此，通常使用加速寿命测试，其中使测试设备经受超出其正常使用条件的条件，以便引起更多的故障，从而在相对较短的时间内获得更多的寿命信息。在本文中，我们讨论了在基于伽玛分布的加速寿命测试下单次设备测试数据的分析。通过对数线性链接函数，伽马分布的比例和形状参数都与应力因子相关。由于受此测试的设备的寿命受到检查，因此在此开发了EM算法来估算模型参数。还可以推断出特定任务时间的可靠性以及设备的平均寿命。此外，通过使用信息丢失原理，确定了EM框架下最大似然估计的渐近方差-协方差矩阵，然后将其用于构造感兴趣参数的渐近置信区间。为了在特定任务时间的可靠性以及设备的平均寿命，建议使用变换方法来构建置信区间。然后，通过模拟研究比较这些置信区间的覆盖率和平均宽度。然后针对构建不同样本量和不同可靠性水平的置信区间的适当方法提出了建议。建议使用基于距离的统计数据来测试模型对观测数据的有效性。最后，由于在生存分析中具有协变量的当前状态数据和在可靠性分析中具有应力因子的单次设备测试数据共享相同的数据结构，因此使用毒理学研究中的真实数据来说明所开发的方法。

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