It can be seen that a mixture of an exponential distribution and a gamma distribution with increasing failure rate for the right choice of parameters can yield a distribution with a bathtub-shaped failure rate. In this paper we consider a continuous mixture of exponentials and a continuous mixture of gammas with increasing failure rates and show that the resulting mixture has a bathtub-shaped f...

Lifetime failure data usually presents a bathtub-shaped failure rate, and random failure phase dominates its life cycle. Relatively large errors always existed when single distribution model is used for analysis and modelling. Therefore, a bathtub-shaped reliability model based on piecewise intensity function was proposed for repairable system. Parameter estimation was studied by using maximum ...

The failure rate of a mixture of even the most standard distributions used in reliability can have a complicated shape. However, failure rates of mixtures of two carefully selected distributions will have the well-known bathtub shape. Here we show that mixtures of whole families of distribtions can have a bathtub-shaped failure rate.

In this paper, we introduce a new Bathtub shaped failure rate model named as x-Exponantial Model and present a comparative study with Generalized Lindley, Generalized Gamma and Exponentiated Weibull distributions.

The properties of x-Exponantial Bathtub shaped failure rate model are discussed. Estimation process and failure rate behavior is explained.

The failure rate function of non-repairable components can be bathtub shaped. Two change points can be defined for a bathtub failure rate curve, which can be viewed as the partition points between the early use, normal use and wear-out phases. There is practical significance to determine the change points, and several non-parametric methods have been developed for this purpose. This paper prese...

The lifetime distribution of many complex systems e xhibits bathtub-shaped failure rate (BFR). In this paper, we investigate the association between the m ean residual life (MRL) and failure rate (FR) of BFR distributions, especially with respect to their change points. Some generalizations of Weibull distribution that can be used to model bathtub-shap ed failure rate are used. The sensitivity ...

In many real life scenarios, system reliability depends on dynamic stress-strength interference, where shocks appear at random time points and the strength of a system varies over time. The resulting life distributions exhibit decreasing, increasing, upside-down and bathtub failure rate depending on the nature of strength function. This class of life distributions is useful for reliability anal...

The failure rate function and mean residual life function are two important characteristics in reliability analysis. Although many papers have studied distributions with bathtub-shaped failure rate and their properties, few have focused on the underlying associations between the mean residual life and failure rate function of these distributions, especially with respect to their changing points...

Mean residual life and failure rate functions are ubiquitously employed in reliability analysis. The term of useful period of lifetime distributions of bathtub-shaped failure rate functions is referred to the flat rigion of this function and has attracted authors and researchers in reliability, actuary, and survival analysis. In recent years, considering the change points of mean residual life ...