Reliability Characteristics of Industrial System Using Copula in Repair

The current research paper examined the reliability of bleaching unit of paper mill. To model the block diagram of proposed bleaching unit of paper mill in which authors introduced the concepts of Markov processes incorporating copula in repair to find the reliability. The considered system can have three possible states namely, operable, partial failure, complete failure. When the system failed completely, it repaired with two types of repair rates namely, general and exponential. The general and exponential distributions have incorporated with the use of copula given by Gumbel-Hougaard. Several reliability characteristics such as State Probabilities, Availability, Reliability, Expected lifetime of the proposed system has been calculated with the help of Markov processes using the copula of Gumbel-Hougaard family, supplementary variable techniques and Laplace transforms.