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The purpose of this paper is to explore the reliability and sensitivity analysis of a system with M primary units, W standby units, and one repair facility when switching to primary units may fail.

Failure times of primary and standby units are assumed to have exponential distributions, and repair times of the failed units are also assumed to have an exponential distribution. Different failure rates and switching failure probabilities are given depending on the readiness states of standby units, designated hot, warm, or cold. The Laplace transform technique is used to transform a set of ordinary differential equations to a set of equations. After finding the solution, we can obtain the desired measures in the time domain by using the inverse Laplace transform.

Expressions for system reliability and mean time to failure (MTTF) are derived. Sensitivity analysis of the system reliability and the MTTF with respect to system parameters are investigated.

This paper presents the first time that a contour of the MTTF with respect to standby states has been obtained, which is quite useful for the decision makers.

To present the bootstrap procedure to correct biases in maximum likelihood estimator of mean time to failure (MTTF) and percentiles in a Weibull regression model.

A reliability model is described by a Weibull regression model with parameters being estimated by maximum likelihood method and they will be used estimate other quantities of interest as MTTF or percentiles. When a small sample is employed it is known that the estimates of these quantities are biased. A simulation study varying sample size, censored mechanisms, allocation mechanisms and levels of censored data are designed to quantify these biases.

The bootstrap procedure corrects the biased maximum likelihood estimates of MTTF and percentiles.

A minor sample may be required if the bootstrap procedure is required to produce estimator of the quantities as MTTF and percentiles.

The employment of bootstrap procedure to quantify the biases since analytical expression of the biases are very difficult to calculate. And the minor samples are needed to obtain unbiased estimates for bootstrap corrected estimator.

The purpose of this paper is to examine the cost/benefit (C/B) analysis of four configurations for a repairable system with two primary components/units and one standby.

The four configurations are set to the status of the detection and switching failure of standby, as well as the possible reboot of failed units. The time to failure for each of the primary and standby is assumed to follow an exponential distribution. The time to repair and the time to reboot is assumed to have a k‐stage Erlang distribution. The paper develops the explicit expressions of the mean time to failure (or MTTF) and the steady‐state availability (or A) for four various configurations and performed some comparative analysis. Based on the C/B criterion, comparisons are made for specific values of distribution parameters and of the costs of the units. The four various configurations for a repairable system are ranked by using MTTF, A and C/B, where B is either MTTF or A.

Although it is uncertain which configuration is the optimal one among the four ones, the paper provides much comparative information to manager and manufacturers. Managers can use these results to choose the best configuration according to the used data of parameters and selections of the weight of MTTF or Cost/MTTF.

This paper shows a comparative analysis for a two‐unit online repairable system with one standby under four different configurations. It is the first discussion of comparable work on reliability and availability models for redundant repairable systems in which the units are characterized by detection, switching failure and reboot.

Key performance indicators (KPIs) of maintenance systems serve as benchmarks to workers and organizations to compare their goals for decision-making purposes. Unfortunately, the effects of one KPI on the other are least known, restraining decisions on prioritization of KPIs. This article examines and prioritizes the KPIs of the maintenance system in a food processing industry using the novel Taguchi (T) scheme-decision-making trial and evaluation laboratory (DEMATEL) method, Taguchi–Pareto (TP) scheme–DEMATEL method and the DEMATEL method.

The causal association of maintenance process parameters (frequency of failure, downtime, MTTR, MTBF, availability and MTTF) was studied. Besides, the optimized maintenance parameters were infused into the DEMATEL method that translates the optimized values into cause and effect responses and keeping in view the result of analysis. Data collection was done from a food processing plant in Nigeria.

The results indicated that downtime and availability have the most causal effects on other criteria when DEMATEL and T-DEMATEL methods were respectively applied to the problem. Furthermore, the frequency of failure is mostly affected by other criteria in the key performance indication selection using the two methods. The combined Taguchi scheme and DEMATEL method is appropriate to optimize and establish the causal relationships of factors.

Hardly any studies have reported the joint optimization and causal relationship of maintenance system parameters. However, the current study achieves this goal using the T-DEMATEL, TP-DEMATEL and DEMATEL methods for the first time. The applied methods effectively ease decisions on prioritization of KPIs for enhancement.

The main objective of this paper is to study the optimal system for series systems with mixed standby (including cold standby, warm standby and hot standby) components.

The paper deals with the reliability and availability characteristics of four different series system configurations. The failure time of the operative, hot standby and warm standby are assumed to be exponentially distributed with parameters λ, λ, and α respectively. The repair time distribution of each server is also exponentially distributed with parameter μ.

The mean time to failure, MTTF_i, and the steady‐state availability A_i(∞) for four configurations are examined and comparisons made. For all four configurations, the configurations are ranked based on: MTTF_i, A_i(∞), and C_i/B_i where B_i is either MTTF_i or A_i(∞). Obviously, the system with height MTTF_i and A_i(∞), do not need frequent maintenance, i.e. less maintenance.

Numerical results for the cost/benefit measure have been obtained for all configurations. It is interesting to note first that the optimal configuration using the cost/MTTF_i measure is configuration 4. Next the optimal configuration using the cost/A_i(∞) measure is configuration 2.

A newly developed model for performing reliability and availability analysis of mechanical devices subject to multiple failure modes is presented. Using this model, reliability analyses of mechanical devices such as brakes, bearings, engines, fans, gears, generators, heat exchangers and pumps are developed. Real life failure rate data for these devices are obtained from various sources and are used in their reliability analyses. Principal failure modes of these devices are identified and expressions for reliability, state probabilities, mean time to failure and variance of time to failure are developed. For known field failure data reliability and state probability plots are shown.

The purpose of this paper is to evaluate various reliability metrics such as transition state probabilities, availability, reliability, mean time to failure and expected profit of two non-identical unit parallel system incorporating waiting time.

The present paper investigates the reliability of two non-identical unit parallel system with two types of failures: common cause failure and partial failure. Moreover, waiting time to repair, a significant aspect of reliability analysis, has also been incorporated. The considered system is assumed to function properly if at least one of the units is in operative mode. The present system is examined by using the supplementary variable technique and Laplace transformation.

Numerical calculation shows that the availability and the reliability of the system is minimum when the system is without partial failure and is maximum when the system is free from common cause failure. Finally, the cost analysis of the system reveals that the expected profit decreases with increase in service cost.

This paper presents a mathematical model of two dissimilar unit parallel system, through which the performance of the considered system can be improved.

This study deals with the reliability analysis of a hybrid series–parallel system consisting of two subsystems A and B with two human operators. Subsystem A has two units in active parallel while subsystem B consists of two-out-of-four units. Both units have exponential failure and repair time. The system under consideration has two states: partial failure state and complete failure state. The mathematical equations associated with the transition diagram have been formulated using regenerative point techniques. The system is analysed using Laplace transforms to solve the mathematical equations. Some important measures of reliability such as availability of system, reliability of the system, mean time to failure (MTTF), sensitivity for MTTF and cost analysis have been discussed. Some particular cases have also been derived and examined to see the practical effect of the model. The computed results are demonstrated by tables and graphs. Furthermore, the results of the designed model are beneficial for system engineers and designers, reliability and maintenance managers.

This paper considered a hybrid series–parallel system consisting of two subsystems A and B with two human operators. The performance of the system is studied using the supplementary variable technique and Laplace transforms. The various measures of reliability such as availability, reliability, mean time to system failure (MTSF), sensitivity for MTTF and cost analysis have been computed for various values of failure and repair rates. Maple 13 software has been used for computations.

In this research paper, the authors have computed various measures of reliability such as availability, reliability, MTSF, sensitivity for MTTF and cost analysis for various values of failure and repair rates and find that failure due to human operators are more responsible for successful operation of the system and also regular repair should be invoked to improve system performance.

This research paper is the original work of authors. The references are well cited based on the importance of study. Nothing has been detached from any research paper or books.

The operating costs and production losses due to equipment failure of offshore gas and oil production systems can exceed initial investment cost. The article explores the probability distribution of downtime associated with random equipment failure and applies availability assessment to design optimisation.

The purpose of this paper is to study various reliability measures like reliability, mean time to failure (MTTF) and sensitivity of transformer including different parameters of insulating oil/paper as health index.

The reliability characteristics of transformer incorporating different parameters of insulating oil as well as paper have been evaluated using Markov process incorporating Gumbel–Hougaard copula, Laplace transforms and supplementary variable technique. The parameters taken into consideration are breakdown voltage (BDV) and moisture content (MC) of both insulating oil and paper, and other parameters considered are interfacial tension (IFT), dissipation factor (DF), degree of polymerization (DOP) and furanic content (FC) for insulating oil and paper, respectively. By probability consideration and continuity influence, difference-differential equations have been obtained for the considered model.

Transition state probabilities, reliability, MTTF and sensitivity of the transformer corresponding to different parameters of insulating oil and paper have been evaluated with the help of aforementioned technique. Variations of reliability with respect to time along with the variations of MTTF and sensitivity have also been examined. Remarkable points during the study have also been pointed out.

Reliability characteristics of the transformer have been evaluated including two parameters: insulating oil and paper with the help of supplementary variable technique, considering two different types of repairs incorporating Gumbel–Hougaard family of copula unlike done earlier. Reliability, MTTF and sensitivity of transformer have been analyzed considering the parameters: BDV, MC, IFT and FC of insulating oil, and BDV, MC, DOP, DF of insulating paper.