Multi-mode failure models in reliability systems: A Bayesian analysis approach

In reliability theory, the most important problem is to determine the reliability of a complex system from the reliability of its components. The weakness of most reliability theories is that the systems are described and explained as simply functioning or failed. In many real situations, the failures may be from many causes depending upon the age and the environment of the system and its components.;Another problem in reliability theory is one of estimating the parameters of the assumed failure models. The estimation may be based on data collected over censored or uncensored life tests. In many reliability problems, the failure data are simply quantitatively inadequate. The Bayesian analyses are more beneficial than classical analyses in such cases. The Bayesian estimation analyses allow us to combine past knowledge or experience in the form of an a apriori distribution with life test data to make inferences of the parameter of interest. In this research, we have investigated the application of the Bayesian estimation analyses to multi-mode failure systems. The cases are limited to the models with independent causes of failure.;The investigation is made by using the Weibull, exponential, gamma, and Binomial distributions as our model. A simulation is conducted for the Weibull distribution with the objectives of verifying the analyses and the estimators and investigating the performance of the estimators for varying sample size. The simulation data are analyzed by using the Bayesian and maximum likelihood analyses.;The simulation results show that the change in the true value of one parameter relative to another will change the values of both risks standard deviations in an opposite direction. For a perfect information on the prior distribution, the Bayesian analyses are better than the maximum likelihood. The analyses show some amount of sensitivity over the shifts of the prior locations. They also show the robustness of the Bayesian analysis within the range of the true value line and the estimated maximum likelihood value line.