An approach for the Bayesian estimation in the case of ordered piecewise constant failure rates

In this paper we present an approach for the Bayesian estimation of piecewi se constant failure rates under the constraint that the constant value of t he failure rate in an interval of time is greater than a function of its va lues in the prior intervals. We apply this approach to the estimation of pi ecewise constant failure rates for conditional IFR, IFRA and NBU distributi ons. The prior distribution for the failure rate in each interval is specif ied through gamma distributions with functions of the failure rate values c orresponding to the rest of the intervals as location parameters. Using thi s approach the prior distribution parameters have interpretations through p rior means and variances of the values of the piecewise constant failure ra te. The posterior distributions and expected values can be found in terms o f gamma functions, without the necessity of numerical integrations. We appl y this approach to a model for reliability estimation when two operational modes exists and the number of failures in each operational mode is unknown . Finally a numerical example is presented in which simulations of posterio r densities are carried out. (C) 2001 Elsevier Science Ltd. All rights rese rved.