  In engineering systems, it is usually assumed that 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 change. For modeling this kind of
systems, 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 then developed. Finally, a real data
on failure times of aircraft components, due to Mann and Fertig (1973), is
analyzed to illustrate the model and inferential methods developed here.
