Reliability inference on composite dynamic systems based on Burr type-XII distribution

Failure of a component in a composite dynamic system often induces a higher load on surviving components, and increases the hazard rate. Statistical inferential procedures on composite dynamic systems are developed here based on a Burr type-XII distribution with a power-trend hazard rate function. Point estimates of the Burr type-XII parameters, and interval estimates of the baseline survival function are obtained based on the maximum-likelihood estimates, and the Fisher information matrix. A test procedure is presented for examining the relationship between the hazard rate function and the number of failed components. The performance of the proposed method is then evaluated by means of an extensive Monte Carlo simulation study. An example is finally presented for illustrative purpose.