Development of models for designing maintenance service contracts considering imperfect repairs and stackelberg competition

Abstract

With the rapid evolution of industrial equipment technology, in-house maintenance has become an expensive and inefficient practice. Hiring an external maintenance service provider is often a better option in terms of costs, efficiency and effectiveness. This work presents three formulations of maintenance service contracts considering imperfect repairs and Stackelberg competition. The first presented model combines a generalized renewal process (GRP) with a queueing system, allowing for interaction between equipment manufacturer (maintenance service provider) and multiple customers. The second proposed formulation consists of a competing risks (CR) model in which the device is subjected to degraded failures and critical failures, which are repaired respectively by preventive maintenance (PM) and corrective maintenance (CM) actions. Both PM and CM consist of imperfect repairs, and are considered to have different repair effectiveness. The third model consists of a joined approach, based on the first two, where a CR model with imperfect repairs is implemented in a queueing system. For all three proposed models, a set of service contracts is enunciated, and the strategies for manufacturer and customer(s) are analyzed, leading to the development of optimal strategies for these agents. The application of game theory allows for a solution that takes into account the behavior of each agent, instead of just accounting for their expected profits. Real failure data from an angiography device in a Brazilian hospital is used as an application example for the proposed models. Sensitivity analyses are made for the three models. In the application examples, it was possible to conclude that the risk-averse behavior of customers makes them more favorable to purchasing warranty.