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 estimation 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.

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