Two-parameter Gompertz distribution has been introduced as a lifetime model for reliability inference recently. In this paper, the Gompertz distribution is proposed for the baseline lifetimes of components in a composite system. In this composite system, failure of a component induces increased load on the surviving components and thus increases component hazard rate via a power-trend process. Point estimates of the composite system parameters are obtained by the method of maximum likelihood. Interval estimates of the baseline survival function are obtained by using the maximum-likelihood estimator via a bootstrap percentile method. Two parametric bootstrap procedures are proposed to test whether the hazard rate function changes with the number of failed components. Intensive simulations are carried out to evaluate the performance of the proposed estimation procedure.
Journal of Statistical Computation and Simulation 88(4), p.752-768