Multi-State Semi-Markov Model of the Operation Reliability

Semi-Markov processes theory delivers some methods that allow us to construct models of the operation process, especially in the reliability aspect. Semi-Markov model of the many steps operation is presented in the chapter. The considered operation consists of many stages which follow in turn. The duration of each stage is supposed to be the non-negative random variable. On each step the operation may be perturbed by faults. Time to event causing an operation perturbation on each stage is a random variable having the exponential distribution. The repair time of an object and continuation of operation process on each stage is assumed to be non-negative random variable. Time to a total failure is a non-negative random variable with an exponential distribution. Two cases are investigated: (a) the final failure finishes operation process and (b) it is possible a renewal of the object after the total failure. A renewal time in this case, is a non-negative random variable. Some results of the semi-Markov processes theory enable to obtain reliability parameters and characteristics of the operation process. A multi-state reliability function, the corresponding expectations for a model without repair and the 1-level and 2-level limiting availability coefficient for the model with repair are calculated.