Modified generalized linear failure rate distribution: Properties and reliability analysis

Ezzatallah Baloui Jamkhaneh

doi:10.5267/j.ijiec.2014.4.005

Abstract

This paper introduces a new comprehensive four-parameter distribution called the modified generalized linear failure rate (MGLFR) distribution. The method generalizes some well-known and most commonly used distributions in reliability such as exponential, Rayleigh, linear failure rate, generalized linear failure rate and modified Weibull distribution. The study also investigates some essential properties of this new distribution and considers the problem of the evaluation of system reliability by describing the lifetimes of components based on a fuzzy MGLFR distribution and by developing fuzzy reliability characteristics. The results can be applied to determine the reliability of real objects where parameters of lifetime variable are subject to uncertainty.

Highlights

There are literally numerous distributions for modeling lifetime data such as exponential, Weibull, Rayleigh, linear failure rate or generalized exponential distributions
We propose the concept of a fuzzy hazard function based on the fuzzy probability measure and named cut hazard band
We have introduced a new four-parameter modified generalized linear failure rate distribution and different properties of the new model have been presented

Summary

Introduction

There are literally numerous distributions for modeling lifetime data such as exponential, Weibull, Rayleigh, linear failure rate or generalized exponential distributions. Sarhan and Zaindin (2009) introduced a new three-parameter distribution called the Modified Weibull distribution (MWD) This distribution generalizes the well-known (1) exponential distribution, (2) linear failure rate distribution, (3) generalized exponential distribution, and (4) generalized Rayleigh distribution. Sarhan and Kundu (2009) introduced generalized linear failure rate distribution It can have increasing, decreasing and bathtub shaped hazard functions. Utkin (1994) discussed imprecise reliability models for the general lifetime distribution classes He applied the theory of imprecise probability to reliability analysis. Pak et al (2013) presented a Bayesian approach to estimate the parameter and reliability function of Rayleigh distribution from fuzzy lifetime data. We consider the problem of the evaluation of system reliability, in which the lifetimes of components are described using MGLFR distribution with fuzzy parameter

Moments

Distribution of order statistics

Fuzzy reliability function

Fuzzy hazard function

Conclusions