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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.

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.

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.

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 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.

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.

Define, measure, analyze, improve and control (DMAIC) and define, measure, analyze, design and verify (DMADV) are two Six Sigma methodologies that improve quality in a process or product. In general, if the product design improvement in reliability cannot satisfy the failure‐free performance of Six Sigma, the DMADV process is used to create or redesign new product designs. However, the original function may be affected, and the product development cycle time may be enhanced due to a redesigned process. This paper aims to propose a new procedure to combine the reliability parameter and critical to quality (CTQ) to improve a product's reliability and to reduce the number of engineering changes without redesigning.

The study influences the failure parameter to find out the mean time to failure (MTTF) tree and utilizes the DMAIC process for improvement. It is important to maintain the function while improving time. This study looks at a cold cathode fluorescent lamp (CCFL) case.

The CCFL case uses the DMAIC process finds that important root cause improvement can increase MTTF twofold.

The paper provides useful information on product reliability improvement using the DMAIC process.

The purpose of this study is to investigate the effect of electrical and thermal stresses on the void formation of the Sn3.0Ag0.5Cu (SAC305) lead-free ball grid array (BGA) solder joints and to propose a modified mean-time-to-failure (MTTF) equation when joints are subjected to coupling stress.

The samples of the BGA package were subjected to a migration test at different currents and temperatures. Voltage variation was recorded for analysis. Scanning electron microscope and electron back-scattered diffraction were applied to achieve the micromorphological observations. Additionally, the experimental and simulation results were combined to fit the modified model parameters.

Voids appeared at the corner of the cathode. The resistance of the daisy chain increased. Two stages of resistance variation were confirmed. The crystal lattice orientation rotated and became consistent and ordered. Electrical and thermal stresses had an impact on the void formation. As the current density and temperature increased, the void increased. The lifetime of the solder joint decreased as the electrical and thermal stresses increased. A modified MTTF model was proposed and its parameters were confirmed by theoretical derivation and test data fitting.

This study focuses on the effects of coupling stress on the void formation of the SAC305 BGA solder joint. The microstructure and macroscopic performance were studied to identify the effects of different stresses with the use of a variety of analytical methods. The modified MTTF model was constructed for application to SAC305 BGA solder joints. It was found suitable for larger current densities and larger influences of Joule heating and for the welding ball structure with current crowding.

The main aim of this paper is to improve reliability characteristics namely availability, mean time to failure (MTTF), and expected profit of a complex system.

The paper discusses the availability of a complex system, which consists of two independent repairable subsystems A and B in (1‐out‐of‐2: F) and (1‐out‐of‐n: F) arrangement respectively. Subsystem A has two identical units arranged in parallel redundancy (1‐out‐of‐2: G), subsystem B has n units in series (1‐out‐of‐n: F) with two types of failure, namely, partial and catastrophic. Except at two transitions where there are two types of repair namely exponential and general possible. The failure and repair time for both subsystems follow exponential and general distributions respectively. The model is analysed under “preemptive‐repeat repair discipline” where A is a priority and B is non‐priority.

By employing supplementary variable technique, Laplace transformation and Gumbel‐Hougaard family copula various transition state probabilities, availability, MTTF and cost analysis (expected profit) are obtained along with steady‐state behaviour of the system. Inversions have also been carried out so as to obtain time dependent probabilities, which determine availability of the system at any instant.

This paper, through a systematic view, presents a mathematical model of a complex system from which the reliability characteristics namely availability, MTTF, and expected profit of a complex 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.