On the Reliability Properties of Some Weighted Models of Bathtub Shaped Hazard Rate Distributions

Abstract

Let F be a bathtub-shaped (BT) hazard rate distribution function. It has been shown that the hazard rate function of the order statistics may be BT, increasing, etc. Then, we have carried out a graphical study for some useful lifetime models.Moreover, we are interested to compare the time that maximizes the mean residual life (MRL) function of F with the one related to a general weighted model in terms of their locations. Also, the times maximizing the conditional reliability proposed by Mi [13] of F have been compared with the corresponding times of a general weighted model. As special cases, we consider order statistics and the proportional hazard rate model.

EM Algorithm for Estimating the Parameters of Weibull Competing Risk Model

“…Lai et al [ 1 ] and Nadarajah [ 2 ] presented a list of distributions with BTS hazard rate. Many authors assumed a BTS hazard rate model in their research, and among them, we can point to Block et al [ 3 ], Glaser [ 4 ], Leemis and Beneke [ 5 ], Mi [ 6 , 7 ], Mitra and Basu [ 8 ], and Noughabi et al [ 9 ].…”