Estimation of Reliability in the Two-Parameter Geometric Distribution

TL;DR

This paper derives and compares maximum likelihood and unbiased estimators for reliability measures in two-parameter geometric distributions, including stress-strength and k-out-of-m systems, supported by simulation results.

Contribution

It introduces new estimators for reliability in two-parameter geometric distributions and compares their performance through simulation.

Findings

MLE and UE estimators are derived for various reliability measures.

Simulation shows the estimators' performance and comparison.

New methods improve reliability estimation accuracy in geometric models.

Abstract

In this article, the reliabilities $R(t)=P(X\geq t)$, when $X$ follows two-parameter geometric distribution and $R=P(X\leq Y)$, arises under stress-strength setup, when X and Y assumed to follow two-parameter geometric independently have been found out. Maximum Likelihood Estimator (MLE) and an Unbiased Estimator (UE) of these have been derived. MLE and UE of the reliability of k-out-of-m system have also been derived. The estimators have been compared through simulation study.