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14 pages, 1957 KB

Open AccessArticle

Reliability and Availability Analysis of a Two-Unit Cold Standby System with Imperfect Switching

by Nariman M. Ragheb, Emad Solouma, Abdullah A. Alahmari and Sayed Saber

Axioms 2025, 14(8), 589; https://doi.org/10.3390/axioms14080589 - 29 Jul 2025

Viewed by 475

This paper presents a stochastic analysis of a two-unit cold standby system incorporating imperfect switching mechanisms. Each unit operates in one of three states: normal, partial failure, or total failure. Employing Markov processes, the study evaluates system reliability by examining the mean time to failure (MTTF) and steady-state availability metrics. Failure and repair times are assumed to follow exponential distributions, while the switching mechanism is modeled as either perfect or imperfect. The results highlight the significant influence of switching reliability on both MTTF and system availability. This analysis is crucial for optimizing the performance of complex systems, such as thermal power plants, where continuous and reliable operation is imperative. The study also aligns with recent research trends emphasizing the integration of preventive maintenance and advanced reliability modeling approaches to enhance overall system resilience. Full article

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16 pages, 4011 KB

Open AccessArticle

Novel Analysis between Two-Unit Hot and Cold Standby Redundant Systems with Varied Demand

by Reetu Malhotra, Faten S. Alamri and Hamiden Abd El-Wahed Khalifa

Symmetry 2023, 15(6), 1220; https://doi.org/10.3390/sym15061220 - 7 Jun 2023

Cited by 15 | Viewed by 2251

Abstract

Decisive applications, such as control systems and aerial navigation, require a standby system to meet stringent safety, availability, and reliability. The paper evaluates the availability, reliability, and other measures of system effectiveness for two stochastic models in a symmetrical way with varying demand: Model 1 (a two-unit cold standby system) and Model 2 (a two-unit hot standby system). In Model 1, the standby unit needs to be activated before it may begin to function; in Model 2, the standby unit is always operational unless it fails. The current study demonstrates that the hot standby system is more expensive than the cold standby system under two circumstances: a decrease in demand or the hot standby unit’s failure rate exceeding a predetermined threshold. The cold standby system’s activation time is at most a certain threshold, and turning both units on at once is necessary to handle the increasing demand. In that case, the hot standby will be more expensive than the cold standby system. The authors used semi-Markov and regenerative point techniques to analyze both models. They collected actual data from a cable manufacturing plant to illustrate the findings. Plotting several graphs and obtaining cut-off points make it easier to choose the standby to employ. Full article

(This article belongs to the Special Issue Stochastic Analysis with Applications and Symmetry)

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13 pages, 1455 KB

Open AccessEditor’s ChoiceArticle

A System with Two Spare Units, Two Repair Facilities, and Two Types of Repairers

by Vahid Andalib and Jyotirmoy Sarkar

Mathematics 2022, 10(6), 852; https://doi.org/10.3390/math10060852 - 8 Mar 2022

Cited by 21 | Viewed by 3797

Abstract

Assuming exponential lifetime and repair time distributions, we study the limiting availability

A_{\infty}

as well as the per unit time-limiting profit

ω

of a one-unit system having two identical, cold standby spare units using semi-Markov processes. The failed unit is repaired either [...] Read more.

Assuming exponential lifetime and repair time distributions, we study the limiting availability

A_{\infty}

as well as the per unit time-limiting profit

ω

of a one-unit system having two identical, cold standby spare units using semi-Markov processes. The failed unit is repaired either by an in-house repairer within an exponential patience time T or by an external expert who works faster but charges more. When there are two repair facilities, we allow the regular repairer to begin repair or to continue repair beyond T if the expert is busy. Two models arise accordingly as the expert repairs one or all failed units during each visit. We show that (1) adding a second spare to a one-unit system already backed by a spare raises

A_{\infty}

as well as

ω

; (2) thereafter, adding a second repair facility improves both criteria further. Finally, we determine whether the expert must repair one or all failed units to maximize these criteria and fulfill the maintenance management objectives better than previously studied models. Full article

(This article belongs to the Special Issue Statistical Simulation and Computation II)

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16 pages, 3406 KB

Open AccessArticle

Mathematical and Simulation Model for Reliability Analysis of a Heterogeneous Redundant Data Transmission System

by Hector Gibson Kinmanhon Houankpo and Dmitry Kozyrev

Mathematics 2021, 9(22), 2884; https://doi.org/10.3390/math9222884 - 12 Nov 2021

Cited by 7 | Viewed by 2778

Abstract

In the actual study, we carried out a reliability analysis of a repairable redundant data transmission system with the use of the elaborated mathematical and simulation model of a closed heterogeneous cold standby system. The system consists of one repair unit and two different data sources with an exponential cumulative distribution function (CDF) of their uptime and a general independent CDF of their repair time. We consider five special cases of the general independent CDF; including Gamma, Weibull-Gnedenko, Exponential, Lognormal and Pareto. We study the system-level reliability, defined as the steady-state probability (SSP) of failure-free system operation. The proposed analytical methodology made it possible to assess the reliability of the whole system in the event of failure of its components. Specific analytic expressions and asymptotic valuations are obtained for the steady-state probabilities of the system and the SSP of failure-free system operation. A simulation model of the system in cases where it is not workable to obtain expressions for the steady-state probabilities of the system in an explicit analytical form was considered, in particular for constructing the empirical system reliability function. The issue of sensitivity analysis of reliability characteristics of the considered system to the types of repair time distributions was also studied. The simulation modeling was done with the R statistics package. Full article

(This article belongs to the Special Issue Stochastic Modeling and Applied Probability)

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19 pages, 1242 KB

Open AccessArticle

Stochastic Analysis of a Priority Standby System under Preventive Maintenance

by Khalaf S. Sultan and Mohamed E. Moshref

Appl. Sci. 2021, 11(9), 3861; https://doi.org/10.3390/app11093861 - 24 Apr 2021

Cited by 7 | Viewed by 2155

Abstract

In this paper, we propose a system of two dissimilar units: one unit prioritizes operation (priority unit), and the other unit is kept as a cold standby (ordinary unit). In this system, we assume that the failures, repairs, and preventive maintenance (PM) times follow arbitrary distributions for both units, except for the fact that the repair time of the ordinary unit follows an exponential distribution. The priority unit has normal, partial failure or total failure modes, while the ordinary unit has normal or total failure modes. The PM of the system can be started after time t when (i) the priority unit is in the normal or partial failure modes up to time t and (ii) the standby unit is available up to time t. PM can be achieved in two types: the costlier type with probability p and the cheaper type with probability

(1 - p)

. Under these assumptions, we investigate the reliability measures of the system using the regenerative point technique. Finally, we show a numerical example to illustrate the theoretical findings and show the effect of preventive maintenance in the reliability measures of the proposed system. Full article

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29 pages, 7604 KB

Open AccessArticle

Optimizing a Multi-State Cold-Standby System with Multiple Vacations in the Repair and Loss of Units

by Juan Eloy Ruiz-Castro

Mathematics 2021, 9(8), 913; https://doi.org/10.3390/math9080913 - 20 Apr 2021

Cited by 11 | Viewed by 2502

Abstract

A complex multi-state redundant system with preventive maintenance subject to multiple events is considered. The online unit can undergo several types of failure: both internal and those provoked by external shocks. Multiple degradation levels are assumed as both internal and external. Degradation levels are observed by random inspections and, if they are major, the unit goes to a repair facility where preventive maintenance is carried out. This repair facility is composed of a single repairperson governed by a multiple vacation policy. This policy is set up according to the operational number of units. Two types of task can be performed by the repairperson, corrective repair and preventive maintenance. The times embedded in the system are phase type distributed and the model is built by using Markovian Arrival Processes with marked arrivals. Multiple performance measures besides the transient and stationary distribution are worked out through matrix-analytic methods. This methodology enables us to express the main results and the global development in a matrix-algorithmic form. To optimize the model, costs and rewards are included. A numerical example shows the versatility of the model. Full article

(This article belongs to the Special Issue Markov and Semi-markov Chains, Processes, Systems and Emerging Related Fields)

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