Some reliability properties of the proportional hazard rate model with upside down bathtub shaped hazard rate

In this paper, a lifetime model with upside‐down bathtub shaped hazard rate function has been considered, and the change point of the mean residual life function has been compared with the corresponding point of a proportional hazard model in terms of their locations. It has been shown that like the mean residual life function, the α‐percentile residual life function α ∈ (0,1) of an upside‐down bathtub shaped hazard rate model is increasing or bathtub shaped. But, unlike the mean residual life function its change points may not be unique. Then, the points minimising the α‐percentile residual life have been compared with the corresponding points of a proportional hazard rate model in terms of their locations.