BAYESIAN STUDY OF A CONTINUOUS PARAMETRIC MARKOV CHAIN MODEL OF A THREE IDENTICAL UNIT COLD STANDBY SYSTEM WITH RANDOM SHOCKS.

This paper analyzes with the cost of a single-server three identical unit cold standby system. Initially one unit is functioning, while the other two are kept in cold standby. The operating system occasionally faces random shocks. As a result of each shock, there is a fixed known probability that (i) the operating unit is unaffected by the random shock,(ii) the operating unit enters into quasi-normal mode whereas its failure rate increases as compared to that when it is functioning in normal mode, (iii) the unit enters into total failure mode. An operating unit can also fail due to its ageing effect that is without being faced to a random shock. The repair is carried out only when all the units fail totally. Failure time distribution of each unit is taken as exponential whereas repair time distribution of all the three units are taken as general. The system model is analyzed by using the supplementary variable technique in order to derive a number of useful measures of system effectiveness. Unknown parameters that are used to evaluate the measures of system effectiveness such as MTSF and Profit function, have been estimated by using maximum likelihood approach and Bayesian approach under different priors. A simulation study at the end exhibits the behavior of such a system. Monte Carlo simulation is used to derive the posterior distribution for the mean time to system failure and Profit function. [ABSTRACT FROM AUTHOR]