Stochastic analysis of a reheating‐furnace system subject to preventive maintenance and repair

This paper presents a stochastic model to determine the performance of a Reheating‐furnace system having different failure and repair modes under variable operational conditions, including preventive maintenance times. The system under study consists of three Reheating‐furnaces, one roll table and a controlling unit‐pulpit. As the failure phenomenon is stochastic and data analysis reveals negative exponential behaviour, Markov model has been found more appropriate in this study. Markov decision‐based model has been widely adopted for stochastic systems, because it delivers provable optimal policy. In the quantitative framework, after developing the Markov model of the system, the synthesis of failure and repair data is carried out, based on which, the failure time distributions are taken to be negative exponential, whereas repair and maintenance time distributions are assumed arbitrary. Various system characteristics of managerial importance, such as mean time to system failures, availability and expected utilisation of servers, are computed to quantify the behaviour of the model in terms of crisp values using Regenerative point technique. Another benefit of this method is its flexibility and applicability to both linear and non‐linear systems. At last, some graphs are plotted to highlight the important results.