Stochastic behaviour analysis of a Markov model under multi-state failures

Abstract

To solve a real problem, how to calculate the reliability of a system with time-varying failure rates in an industry system. This is a study of a system consisting of three identical units in parallel, each of which can be in two states: operational or non-operational. Under the assumptions that each unit has a constant failure and repair time rate. The system is regarded as operational if at least one of its elements is working. The system analyzed incorporating three types of failures namely partial failure, human failure and catastrophic failure, which also leads to the system failure. With the help of probability analysis, supplementary variable technique, Laplace transformations, and the Markov process theory, the transition state probabilities, availability, reliability, mean time to failure, sensitivity analysis and cost effectiveness of the system have been evaluated. Finally, some particular cases, numerical examples and graphical illustrations have also been taken to describe the model.