A step‐stress accelerated life test is a special life test where test units are subjected to higher stress levels than normal operating conditions so that the information on the lifetime parameters of a test unit can be obtained more quickly in a shorter period of time. Also, progressive Type‐I censoring is a generalized form of time censoring where functional test units are withdrawn successively from the life test at some prefixed nonterminal time points. Despite its flexibility and efficient utilization of the available resources, progressively censored sampling has not gained much popularity due to its analytical complexity compared to the conventional censoring schemes. In particular, understanding the mean completion time of a life test is of great practical interest in order to design and manage the life test optimally under frequent budgetary and time constraints. In this work, the expected termination time of a general k‐level step‐stress accelerated life test under progressive Type‐I censoring is derived using a recursive relationship of the stochastic termination time based on the conditional block independence. To be comprehensive, two different modes of failure inspections are considered: continuous inspection, where the exact failure times are observed, and interval inspection, where the exact failure times are not available but only the number of failures that occurred.

中文翻译：

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在连续和间隔检查下逐步进行I型检查的逐步应力加速寿命试验的预期终止时间

步进应力加速寿命测试是一种特殊的寿命测试，其中测试单元承受的应力水平高于正常操作条件，因此可以在较短的时间内更快地获得测试单元寿命参数的信息。同样，渐进式I类检查是时间检查的一种通用形式，在该检查中，功能测试单元在某些前缀的非终点时间点从寿命测试中连续撤出。尽管它具有灵活性和对可用资源的有效利用，但是与传统的检查方案相比，渐进式检查抽样由于其分析复杂性而并未获得很大的普及。尤其是，为了在频繁的预算和时间限制下优化设计和管理寿命测试，了解寿命测试的平均完成时间具有重大的实际意义。在这项工作中，一般的预计终止时间基于条件块独立性，使用随机终止时间的递归关系，可以得出在渐进式I型审查下的k级阶跃应力加速寿命测试。为全面起见，考虑了两种不同的故障检查模式：连续检查（观察到确切的故障时间）和间隔检查（其中没有可用的确切故障时间，而仅给出发生的故障数）。