Abstract
Modeling reliability data with nonmonotone hazards is a prominent research topic that is quite rich and still growing rapidly. Many studies have suggested introducing new families of distributions to modify the Weibull distribution to model the nonmonotone hazards. In the present study, we propose a new family of distributions called a new lifetime exponential-X family. A special submodel of the proposed family called a new lifetime exponential-Weibull distribution suitable for modeling reliability data with bathtub-shaped hazard rates is discussed. The maximum-likelihood estimators of the model parameters are obtained. A brief Monte Carlo simulation study is conducted to evaluate the performance of these estimators. For illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models.
Highlights
In the last two decades, many new life distributions capable of modeling data with the bathtub-shaped hazard rate function have been introduced in the literature
A three-parameter modified Weibull extension (MWEx) of Xie et al [2] exhibits data modeling with bathtub shape. e truncated Weibull distribution of Zhang and Xie [3] has a bathtub-shaped hazard function. e two-parameter flexible Weibull extension (FWEx) of Bebbington et al [4] has increasing, decreasing, or bathtub-shaped function
An appropriate parametric model is always of interest in survival and reliability analysis, as it provides a concise description of the characteristics of failure times as well as hazard function that may not be available with nonparametric methods [10]
Summary
Some mathematical properties of the NLTEX distributions are derived. E quantile function of NLTE-X family is derived as follows:. For any positive integer r, the rth moment of the NLTE-X distributions is given by. We obtain skewness and kurtosis measures of the NLTE-Weibull distribution. E skewness of NLTE-Weibull distribution is obtained using the following expression: skewness μμ323/2,. Let X follow NLTE-X family of distributions, the residual life of X is given by. E residual life parameters can be determined using E(Xr) and t− ∞ xrg(x; θ, η)dx for several values of r. (ii) e mean reversed residual life is defined as follows: L(t) E(t − X | X ≤ t) t −.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
