Expected termination times of progressively Type-I censored step-stress accelerated life tests under continuous and interval inspections

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 Also, progressive Type-I censoring is a generalized form of time censoring where functional test units are withdrawn successively from the life test at some prefixed nonterminal time points.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.