A generic model of equipment availability under imperfect maintenance

This paper explores the impact of imperfect repair on the availability of repairable equipment. Kijima´s first virtual age model is used to describe the imperfect repair process. Due to the complexity of the underlying assumptions of this model, we are unable to derive a closed-form equation for availability. Therefore, simulation modeling & analysis are used to evaluate equipment availability. Based on initial availability plots, a generic availability function is proposed. A 2³ factorial experiment is performed to evaluate the accuracy of this model. The maximum absolute error between the simulation output, and the corresponding values of the availability function is 3.82%. This indicates that our proposed function provides a reasonable approximation of equipment availability, which simplifies meaningful analysis for the unit. Therefore, a method is defined for determining optimum equipment replacement intervals based on average cost. Next, meta-models are developed to convert equipment reliability & maintainability parameters into the coefficients of the availability model. We expand on our initial experiment using a circumscribed central composite experimental design. We evaluate the accuracy of the meta-models for the 15 experiments & 50 random experiments within the design space. For the 50 new experiments, we compare the replacement policy obtained from analysis of the meta-model to the policy obtained directly from the simulation output. The average increase in cost resulting from the sub-optimal replacement policy is only 0.10%. Therefore, we conclude that the meta-models are robust, and provide good estimates of the parameters of our proposed availability function. By doing this, we eliminate the need to perform simulation to obtain the parameters of the availability model.