Weibull Analysis with Sequential Order Statistics Under a Power Trend Model for Hazard Rates with Application in Aircraft Data Analysis

‎In engineering systems‎, ‎it is usually assumed that the lifetimes of components are independent and identically distributed (iid)‎. ‎But‎, ‎the failure of a component results in a higher load on the remaining components and hence causes the distribution of the surviving components to change‎. ‎For modelling this kind of system‎, ‎the theory of sequential order statistics (SOS) can be used‎. ‎Assuming Weibull distribution for lifetimes of components and conditionally proportional hazard rates model as a special case of the SOS theory‎, ‎the maximum likelihood estimates of the unknown parameters are obtained in different cases‎. ‎A new model‎, ‎denoted by PTCPHM‎, ‎as a generalization of the iid case is proposed‎, ‎and then statistical inferential methods including point and interval estimations as well as hypothesis tests‎ ‎under PTCPHM are developed‎. ‎Finally‎, ‎real data on failure times of aircraft components‎, ‎due to Mann and Fertig (1973) ‎, ‎are analysed to illustrate the model and inferential methods developed here‎.