Wearing-out of components in a variable environment

The probabilistic model for the wearing-out component's performance is studied, based on the Markov-Additive Principle (MAP) of wearing-out. It is proved that under certain assumptions this principle leads to the accelerated life model (ALM), according to which the lifetime distribution functions (DFs) in some baseline (reference) and real environments are connected via a general time transformation function. The specific linear transformation function is widely used in the accelerated testing procedures. The change point in environment is considered and the remaining lifetime DF is derived in the formal way for various settings. The effect of shocks, increasing the components wear-out, is studied as well as the effect of an operation of the opposite nature that decreases wear-out. Different maintenance activities usually can be considered as wear-out decreasing. Several generalisations are presented