Analysis of Repairable Systems Availability with Lindley Failure and Repair Behavior

TL;DR

This paper introduces a new analytical framework for system maintainability that uses the Lindley distribution instead of the traditional exponential, providing more realistic reliability assessments for repairable systems.

Contribution

It develops closed-form expressions for availability and repair time using Lindley distribution and extends the analysis to complex system configurations, overcoming exponential distribution limitations.

Findings

Lindley distribution offers more accurate modeling of repair times.

Significant differences observed between Lindley and exponential models.

Enhanced realism improves reliability assessment accuracy.

Abstract

Maintainability analysis is a cornerstone of reliability engineering. While the Markov approach is the classical analytical foundation, its reliance on the exponential distribution for failure and repair times is a major and often unrealistic limitation. This paper directly overcomes this critical constraint by investigating and modeling system maintainability using the more flexible and versatile Lindley distribution, which is represented via phase-type distributions. We first present a comprehensive maintainability analysis of a single-component system, deriving precise closed-form expressions for its time-dependent and steady-state availability, as well as the mean time to repair. The core methodology is then systematically generalized to analyze common series and parallel system configurations with n independent and identically distributed components. A dedicated numerical study compares the system performance under the Lindley and exponential distributions, conclusively demonstrating the significant and practical impact of non-exponential repair times on key reliability metrics. Our work provides a versatile and more widely applicable analytical framework for accurate maintainability assessment that successfully relaxes the restrictive exponential assumption, thereby offering greater realism in reliability modeling.