We consider an open problem of obtaining the optimal operational sequence for the 1-out-of-n system with warm standby. Using the virtual age concept and the cumulative exposure model, we show that the components should be activated in accordance with the increasing sequence of their lifetimes. Lifetimes of the components and the system are compared with respect to the stochastic precedence order and its generalization. Only specific cases of this optimal problem were considered in the literature previously.

This paper considers simple step-stress accelerated life tests (SSALTs) for one-shot devices. The one-shot device is an item that cannot be used again after the test, for instance, munitions, rockets, and automobile air-bags. Either left-or right-censored data are collected instead of actual lifetimes of the devices under test. An expectation-maximization algorithm is developed here to find the maximum likelihood estimates of the model parameters based on one-shot device testing data collected from simple SSALTs. Furthermore, the asymptotic variance of the mean lifetime under normal operating conditions is determined under the expectation-maximization framework. On the other hand, the optimal design that minimizes the asymptotic variance of the estimate of the mean lifetime under normal operating conditions in terms of three decision variables, including stress levels, inspection times, and sample allocation is discussed. A procedure then is presented to determine the decision variables when a range of stress levels and the termination time of the test as well as normal operating conditions of the devices are given. The properties of the optimal design and the effects of errors in pre-specified planning values of the model parameters are also investigated. Comprehensive simulation studies show that the procedure is quite reliable for the design of simple SSALTs.

We study the allocation strategies for redundant components in the load-sharing series/parallel systems. We show that under the specified assumptions, the allocation of a redundant component to the stochastically weakest (strongest) component of a series (parallel) system is the best strategy to achieve its maximal reliability. The results have been studied under cumulative exposure model and for a general scenario as well. They have a clear intuitive meaning; however, the corresponding additional assumptions are not obvious, which can be seen from the proofs of our theorems.