Reliability Measures of a Single-Unit System with Gamma Failure Laws

Most of the research work on reliability modeling of systems has been carried out by assuming exponential failure and repair laws.And, gamma distribution has been proved as a natural extension of exponential distribution and it is alsoconsidered as a good fit to some sets of failure data. The purpose of this paper is to determine reliability measures of a single unit system reliability model with gamma failure and repair laws. A single repair facility (called server) is used to carry out repair of the failed system. The system has only two modes- normal and completer failure. The expressions for reliability, mean time to system failure (MTSF) and availability are derived in steady state using Markov process and regenerative point technique.  The values of these measures are obtained for arbitrary values of shape and scale parameters. Graphs are drawn to depict the behavior of MTSF, reliability and availability with respect to failure rate and operating time for fixed values of the shape parameters and repair rate.