A Versatile Model for Lifetime of a Component Under Stress

Abstract

In this study, a versatile model, called alpha-monotone inverse Weibull distribution ( alpha IW), for lifetime of a component under stress is introduced by using the alpha-monotone concept. The alpha IW distribution is also expressed as a scale-mixture between the inverse Weibull distribution and uniform distribution on (0, 1). The alpha IW distribution includes alpha-monotone inverse exponential and alpha-monotone inverse Rayleigh distributions as submodels and converenges to the inverse Weibull, inverse exponential, and inverse Rayleigh distributions as limiting cases. Also, slash Weibull, slash Rayleigh, and slash exponential distribuitons can be obtained under certain variable transformation and parameter settings. The alpha IW distribution is characterized by its hazard rate function and characterizing conditions are provided as well. Maximum likelihood, maximum product of spacing, and least squares methods are used to estimate distribution parameters. A Monte-Carlo simulation study is conducted to compare the efficiencies of the considered estimation methods. In the application part, two practical data sets, Kevlar 49/epoxy and Kevlar 373/epoxy, are modeled via the alpha IW distribution. Modeling performance of the alpha IW distribution is compared with its rivals by means of some well-known goodness-of-fit statistics and results show that alpha IW distribution performs better modeling than them. Results of comparison also indicate that obtaining the alpha IW distribution by using the alpha-monotone concept is cost effective since the new shape parameter added to the distribution by using the alpha-monotone concept significantly increases the modeling capability of the IW distribution. As a result of this study, it is shown that the alpha IW distribution can be an alternative to the well-known and recently-introduced distributions for modeling purposes.