Reliability for single-unit systems via virtual ages under cyclic environments

Systems commonly operate in varying environments which are harmful in most situations for system reliability. The usage of virtual ages in reliability increases gradually, which is a powerful tool for analyzing system reliability. In the paper, by employing virtual ages, a system reliability model is developed for a single-unit system operating in cyclic environments. The system reliability formula is given in an expectation form of a random survival function whose variables include a virtual age, and the asymptotic estimates of system reliability are derived in terms of the law of large numbers and the central limit theorem. Meanwhile, some special cases are discussed, and the simulation algorithm is established. We believe this work may shed light on the related researches in future not only in the area of reliability but also in the subject of maintenance.