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.

翻译：可维护性分析是可靠性工程的基石。虽然马尔可夫方法是经典的分析基础，但其对失效时间和修复时间服从指数分布的依赖是一个主要且通常不现实的限制。本文通过使用更灵活通用的Lindley分布（通过阶段型分布表示）来研究和建模系统可维护性，直接克服了这一关键约束。我们首先对单部件系统进行了全面的可维护性分析，推导出其瞬态与稳态可用性以及平均修复时间的精确闭式表达式。随后将该核心方法系统性地推广至分析具有n个独立同分布部件的常见串联与并联系统构型。一项专门的数值研究比较了系统在Lindley分布与指数分布下的性能，确凿地证明了非指数修复时间对关键可靠性指标的显著实际影响。我们的工作为准确的可维护性评估提供了一个通用且更广泛适用的分析框架，该框架成功放宽了限制性的指数假设，从而在可靠性建模中提供了更高的现实性。