A rate randomized geometric process with applications

The geometric process has been widely studied in various disciplines and applied in reliability, maintenance and warranty cost analysis, among others. In its applications in maintenance policy optimisation, the geometric process assumes constant repair effectiveness by its process rate. Nevertheless, in practice, maintenance effectiveness may differ from time to time and can therefore be better depicted by a random variable. Motivated by this argument, this paper proposes a new variant of the geometric process, which is referred to as the rate randomized geometric process (RRGP). The probabilistic properties of the RRGP are then investigated. The maximum likelihood method is utilised to estimate the parameters of the RRGP. Numerical examples are given to show its applicability in both maintenance policy optimization and fitting real-world failure datasets.