Mean residual life and other properties of Weibull related bathtub shape failure rate distributions

The two-parameter Weibull distribution is widely used in reliability analysis. Because of its monotonic ageing behaviour, its applicability is hampered in certain reliability situations. Several generalizations and extensions of the Weibull model have been proposed in the literature to overcome this limitation but their properties have not yet been described in a unified manner. In this paper, graphical displays of the mean residual life curves of several families of Weibull related life distributions are given together with their corresponding failure rate functions. The relationship between these two functions are visibly demonstrated. We focus our attention on the Weibull related families that have bathtub or modified bathtub shape failure rates. Important reliability characteristics such as burn-in, change point and flatness of bathtub of these families are examined. Model selection and parameters estimation are also discussed.