🤖 AI Summary
This study addresses the limitations of traditional Markovian approaches in availability analysis of repairable systems, which rely on the restrictive assumption of exponential distributions and thus fail to accurately capture real-world failure and repair time characteristics. To overcome this constraint, the work introduces the Lindley distribution—represented via phase-type approximation—into availability modeling for the first time, establishing a general analytical framework applicable to both single-component and n-component series-parallel systems. Closed-form expressions for time-dependent and steady-state availability are derived, along with an exact computation of mean time to repair. Numerical experiments demonstrate that incorporating non-exponential repair times significantly influences system reliability metrics, thereby underscoring the practical relevance and theoretical contribution of the proposed methodology.
📝 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.