A Bayesian Method for Estimation of 3-Parameter Time Dependent Hazard Rate. Enrique Lopez Droguett, Franciscus Groen, and Ali Mosleh, Center for Reliability Engineering, University of Maryland at College Park, Maryland
The application of Bayesian techniques for data analysis has gained increasing popularity as reliability engineers are frequently faced with the problem of lack of statistically significant data. In such a scenario, for instance, if only a very few units can be tested to failure because of cost or production constrains, the classical and traditional statistical methods are no longer very helpful in order to make reliable assessments. However, through the application of Bayesian analysis it is possible for the risk and reliability analyst to use information from different sources, such as handbooks, expert opinion and previous experiences in order to formulate a probability distribution expressing the uncertainty in the true value of a parameter. For a given reliability measure, for example, hazard rate, the results can be systematically updated as new information becomes available. Under the Bayesian framework, the main result is the Posterior Probability Density Function (PDF) of the parameters of an assumed model. From the posterior PDF it is possible to obtain further results that are, in general, more useful in practical application, such as the Hazard Rate or the Reliability. In commonly used distributions such as the Weibull-Poisson model, the hazard rate derived from the posterior distribution is constant, decreasing or increasing. This paper uses the Bayesian approach to estimate a more general time dependent hazard rate, i.e., the three-parameter Increasing . . . . . . . [RiskWorld Note: Submitted abstract incomplete]