A Generalization of the Exponential-Logarithmic Distribution for Reliability and Life Data Analysis

TL;DR

This paper introduces the exponential-generalized truncated logarithmic (EGTL) distribution, a new two-parameter lifetime model that extends the exponential-logarithmic distribution by considering the kth-smallest lifetime, with methods for parameter estimation and real data applications.

Contribution

It proposes a novel lifetime distribution, the EGTL, generalizing the EL distribution by modeling the kth-failure, and develops estimation methods with real data applications.

Findings

The EGTL distribution effectively models reliability data.

Maximum likelihood and Bayesian methods provide accurate parameter estimates.

Application to real data demonstrates the distribution's practical usefulness.

Abstract

In this paper, we introduce a new two-parameter lifetime distribution, called the exponential-generalized truncated logarithmic (EGTL) distribution, by compounding the exponential and generalized truncated logarithmic distributions. Our procedure generalizes the exponential-logarithmic (EL) distribution modelling the reliability of systems by the use of first-order concepts, where the minimum lifetime is considered (Tahmasbi 2008). In our approach, we assume that a system fails if a given number k of the components fails and then, we consider the kth-smallest value of lifetime instead of the minimum lifetime. The reliability and failure rate functions as well as their properties are presented for some special cases. The estimation of the parameters is attained by the maximum likelihood, the expectation maximization algorithm, the method of moments and the Bayesian approach, with a simulation study performed to illustrate the different methods of estimation. The application study is illustrated based on two real data sets used in many applications of reliability.