arXiv subjects

Afshin Yaghoubi

Publications and source records attributed to Afshin Yaghoubi.

4 recordsLinked to original sources

arXiv2026

Analysis of Repairable Systems Availability with Lindley Failure and Repair Behavior

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.

stat.AP↗

arXiv2025

A Recursive Exponential-Gamma Mixture: a New Generalized of the Lindley Distribution

The Lindley distribution was first introduced by Lindley in 1958 for Bayesian computations. Over the past years, various generalizations of this distribution have been proposed by different authors. The generalized Lindley distributions sometimes have many parameters, and although they show good flexibility, their statistical form becomes complicated. In this article, we propose a new and simple distribution determined by the recursive relation of the Lindley distribution and the Gamma distribution with specific weights. Subsequently, some statistical properties of this distribution are examined, and with real numerical examples, its superiority over the Lindley generalizations is demonstrated.

math.ST↗

arXiv2025

Reliability Analysis of a 1-out-of-n Cold Standby Redundant System under the Generalized Lindley Distribution

Cold standby 1-out-of-n redundant systems are well-established models in system reliability engineering. To date, reliability analyses of such systems have predominantly assumed exponential, Erlang, or Weibull failure distributions for their components. The Lindley distribution and its generalizations represent a significant class of statistical distributions in reliability engineering. Certain generalized Lindley distributions, due to the appealing characteristics of their hazard functions, can serve as suitable alternatives to other well-known lifetime distributions like the Weibull. This study investigates the reliability of a 1-out-of-n cold standby redundant system with perfect and imperfect switching, assuming that the active component failure times follow the Generalized Lindley distribution. We derive a closed-form expression for the system reliability. To achieve this, the distribution of the sum of n independent and identically distributed random variables following the Generalized Lindley distribution is first determined using the moment-generating function approach.

stat.AP↗

arXiv2022

Sum of independent random variable for Shanker, Akash, Ishita, Pranav, Rani and Ram Awadh distributions

In statistics and probability theory, one the most important statistics is the sums of random variables. After introducing a probability distribution, determining the sum of n independent and identically distributed random variables is one of the interesting topics for authors. This paper presented the probability density function for the sum of n independent and identically distributed random variables such as Shanker, Akash, Ishita, Rani, Pranav and Ram Awadh. In order to determine all aforementioned distributions, the problem-solving methods are applied which is based on the change-of-variables technique. The mth moments for them were also accurately calculated. Besides, the reliability and the mean time to failure of a 1 out of n cold standby spare system has also been evaluated under the Lindley components failure time.

math.PR↗