Random maintenance policies for sustaining the reliability of the product through 2D-warranty

Rapid development and wide application of cyber-physical systems (CPS) have created the possibility of remotely monitoring product working cycles. This indicates that CPS can provide the technological support required for designing manufacturers’ warranties integrated with working cycle and for modelling users' (or consumers') random maintenance policies sustaining the reliability of the product through warranty. In this study, by designing limited working cycles as a warranty limit, we have proposed manufacturer's two-dimensional warranty first and last to ensure the product's reliability during the warranty coverage period. Subsequently, we have incorporated working cycle into the traditional maintenance policies and modelled users' random age replacement first and last to sustain the reliability of the product through its warranty. By analysing parameter values, we have offered some classic models, i.e., the expected long-run cost rates that represent certain special problems. Finally, sensitivities of both the proposed warranties and the modelled random age replacements have been analysed through numerical experiments. It has been demonstrated that whichever takes place first or last influences if the warranty cost of the proposed two-dimensional warranty is higher than that of the traditional one-dimensional warranty. Users can get a longer post-warranty period when the warranty limit m, i.e., the limited random working cycles, is lower.