A novel iterative approach of lifetime estimation for standby systems with deteriorating spare parts

Standby redundancy is an effective fault-tolerant technique for enhancing reliability and prolonging the standby system's operating lifetime. How to estimate the total lifetime of a standby system with a predetermined number of standby components (i.e., spare parts) presents an interesting practical issue. Most existing studies, however, have mainly focused on the lifetime or remaining useful lifetime prediction of a single online product. Moreover, spare parts usually deteriorate in storage, which will worsen their performance and even lead to failure. This makes lifetime estimation for a standby system more challenging. This study, therefore, focused on how to estimate a standby system's lifetime (SSL) with deteriorating spare parts. Unlike prior work, we fully considered the uncertainty and randomness caused by the spare parts' storage degradation in the SSL estimation. By establishing the transition probability function of the storage degradation process, we first proposed a general iterative algorithm for SSL estimation under the concept of the first passage time (FPT) and provided the proof based on mathematical induction. Then, we extended this result to a Wiener-process-based model and obtained the iterative result in a single integral form. Moreover, we attained the analytical expressions of SSL mean and variance under a non-storage-failure hypothesis and further provided the requirement for the establishment of the hypothesis. Finally, a numerical case and a practical case of the gyroscope are introduced for illustration.