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The internet of things and just-in-time are the embryonic model of innovation for the state-of-the-art design of the service system. This paper aims to develop a fault-tolerant machining system with active and standby redundancy. The availability of the fault-tolerant redundant repairable system is a key concern in the successful deployment of the service system.

In this paper, the authors cogitate a fault-tolerant redundant repairable system of finite working units along with warm standby unit provisioning. Working unit and standby unit are susceptible to random failures, which interrupt the quality-of-service. The system is also prone to common cause failure, which tends its catastrophe. The instantaneous repair of failed unit guarantees the increase in the availability of the unit/system. The time-to-repair by the single service facility for the failed unit follows the arbitrary distribution. For increasing the practicability of the studied model, the authors have also incorporated real-time machining practices such as imperfect coverage of the failure of units, switching failure of standby unit, common cause failure, reboot delay, switch over delay, etc.

For deriving the explicit expression for steady-state probabilities of the system, the authors use a supplementary variable technique for which the only required input is the Laplace–Stieltjes transform (LST) of the repair time distribution.

For complex and multi-parameters distribution of repair time, derivation of performance measures is not possible. The authors prefer numerical simulation because of its importance in the application for real-time uses.

The stepwise recursive procedure, illustrative examples, and numerical results have been presented for the diverse category of repair time distribution: exponential (M), n-stage Erlang (Ern), deterministic (D), uniform (U(a,b)), n-stage generalized Erlang (GE_[n]) and hyperexponential (HE_[n]).

Concluding remarks and future scopes have also been included. The studied fault-tolerant redundant repairable system is suitable for reliability analysis of a computer system, communication system, manufacturing system, software reliability, service system, etc.

As per the survey in literature, no previous published paper is presented with so wide range of repair time distribution in the machine repair problem. This paper is valuable for system design for reliability analysis of the fault-tolerant redundant repairable.

The purpose of this paper is to covenant with the cost assessment of a complex repairable system, consisting of two subsystems (Subsystem 1 and Subsystem 2) connected in series configuration and being operated by a human operator. Each subsystem has two identical units in parallel configuration and has different types of failure and two types of repairs (general repair and copula repair). Through the transition diagram, the system of first-order partial differential equations is derived and solved using a supplementary variable technique, Laplace transforms. All failures are assumed to follow exponential distribution, whereas repairs follow two types of distributions that are general and Gumbel–Hougaard family copula. In this paper, explicit expressions for reliability, availability, mean time to failure (MTTF) and cost analysis functions have been obtained. In this paper, two types of repairs (copula repair and general repair) have been studied, and it has been concluded that copula repair is more reliable as compared to general repair. Some computations are taken as particular case by evaluating: reliability, availability, MTTF and cost analysis, so as to capture the effect of both failure and repair rates to reliability measures. The results have been shown in tables and graphs. The convincing part has been discussed in last section of this study.

This paper is focused on the cost assessment of a system consisting two subsystem series configuration. Each subsystem has two identical units in parallel configuration. The performance of the system has been analyzed by supplementary variable techniques and Laplace transforms. Various measures of the reliability have been discussed by evaluations. Software called Maple 13 is used for computations.

In this research paper, the authors have evaluated the operational cost and incurred profit of the system together with other reliability measures for various situations and different types of failures and two types of repairs using Gumbel–Hougaard family copula distribution.

The present research focuses on the series and parallel configured complex systems that is used everywhere in industry and other sectors. The authors main aim is to claim that repair through the joint probability distribution copula is far better than general repair. Copula repair for a completely failed system is more beneficial for industrial system operations that will increase profit to the industrial sector.

The authors have observed that when repair follows general distribution the values of reliability obtained of the system are less compared to the those obtained when the authors apply copula repair, a joint probability distribution. It is a clear implication for industrial sector and organization to use the policy for a better generate revenue.

According to the best of authors’ knowledge, there is no social implication as this study is meant for reliability section. The study in management and case study matters is considered to have social implication.

This research is the original work of authors. Nothing has been copied from any paper or book. The references are cited according to the relevance of study.

In this paper, we consider a repair‐time limit replacement problem with imperfect repair and develop a graphical method to determine the optimal repair‐time limit which minimizes the expected total discounted cost over an infinite time horizon. The method proposed can be applied to an estimation problem of the optimal repair‐time limit from the empirical repair‐time data. Then, the modified scaled total time on test transform of the underlying repair‐time distribution function is used. Numerical examples are devoted to examine asymptotic properties of the nonparametric estimator for the optimal repair‐time limit.

Wind power is an important source of renewable energy and accounts for significant portions in supplying electricity in many countries and locations. The purpose of this paper is to develop a method for wind power system reliability assessment and condition-based maintenance (CBM) optimization considering both turbine and wind uncertainty. Existing studies on wind power system reliability mostly considered wind uncertainty only and did not account for turbine condition prediction.

Wind power system reliability can be defined as the probability that the generated power meets the demand, which is affected by both wind uncertainty and wind turbine failures. In this paper, a method is developed for wind power system reliability modeling considering wind uncertainty, as well as wind turbine condition through health condition prediction. All wind turbine components are considered. Optimization is performed for maximizing availability or minimizing cost. Optimization is also conducted for minor repair activities to find the optimal number of joint repairs.

The wind turbine condition uncertainty and its prediction are important for wind power system reliability assessment, as well as wind speed uncertainty. Optimal CBM policies can be achieved for optimizing turbine availability or maintenance cost. Optimal preventive maintenance policies can also be achieved for scheduling minor repair activities.

This paper considers uncertainty in both wind speed and turbine conditions and incorporates turbine condition prediction in reliability analysis and CBM optimization. Optimization for minor repair activities is studied to find the optimal number of joint repairs, which was not investigated before. All wind turbine components are considered, and data from the field as well as reported studies are used.

The purpose of this paper is to provide results for a complete maintainability analysis utilizing data sets from a production system in a shaving blades division of a large high-tech razor manufacturer. Through the illustrated case study, the authors demonstrate how to spot improvement points for enhancing availability by carrying out an equipment effectiveness analysis.

Descriptive statistics of the repair data and the best fitness index parameters were computed. Repair data were collected from departmental logs, and a preliminary screening analysis was conducted to validate their usefulness for the indicated period of 11 months. Next, the maintainability and repair rate modes for all the machines of the production system were calculated. Maintainability and availability estimations for different time periods that took in account the overall system were obtained by trying out and selecting an optimum statistical model after considering of several popular distributions.

Out of the five considered machines in the system, two particular units received about half of the repairs (M2 and M3). The time to repair follows a loglogistic distribution and subsequently the mean time to repair is estimated at 25 minutes at the machine level. Repair time performance is approximated at 55 minutes if the availability of the system is to attain a 90 percent maintainability.

This study is anticipated to serve as an illuminating effort in conducting a complete maintainability analysis in the much advertised field of shavers, for which on the contrary so little has been published on operational availability and equipment effectiveness. The case study augments the available pool of sources where executing maintainability studies is highlighted usually under the direction of combined total quality management and total productive maintenance programs.

The purpose of this paper is to deliberate the system reliability of a system in combination of three subsystems in a series configuration in which all three subsystems function under a k-out-of-n: G operational scheme. Based on computed results, it has been demonstrated that copula repair is better than general repair for system better performance. The supplementary variable approach with implications of copula distribution has been employed for assessing the system performance.

Probabilistic assessment of complex system consisting three subsystems, multi-failure threats and copula repair approach is used in this study. Abbas Jubrin Bin, V.V. Singh, D.K. Rawal, in this research paper, have analyzed a system consisting of three subsystems in a series configuration in which all three subsystems function under a k-out-of-n: G operational scheme. The supplementary variable approach with implications of copula distribution has been employed for assessing the system performance. Based on computed results, it has been demonstrated that copula repair is better than general repair for system better performance.

In this analysis, four different cases of availability are analysed for Gumbel–Hougaard family copula and also four cases for general repair with similar failure rates are studied. The authors found that when failure rates increase, the system availability decreases, and when the system follows copula repair distribution, the system availability is better than general repair.

This research may be implemented in various industrial systems where the subsystems are configured under k-out-of-n: G working policy. It is also advisable that copula repair is highly recommended for best performances from the system. On the basis of mean time to system failure (MTSF) computations, the failure rate which affects system failure more needs to be controlled by monitoring, servicing and replacing stratagem.

This research work has great implications in various industrial systems like power plant systems, nuclear power plant, electricity distributions system, etc. where the k-out-of-n-type of system operation scheme is validated for system operations with the multi-repair.

This work is a new work by authors. In the previously available technical analysis of the system, the researchers have analyzed the repairable system either supplementary variable approach, supplementary variable and system which have two subsystems in a series configuration. This research work analyzed a system with three subsystems with a multi-repair approach and supplementary variables.

Analyses an n‐unit cold‐standby system with a single repair facility under the assumption that the failure and repair times are arbitrarily distributed. Develops a mathematical model using semi‐regenerative processes. Obtains a system of integral equations satisfied by various state probabilities corresponding to different initial conditions. Obtains explicit expressions for the expected number of failures and expected number of visits to down state in a specified interval of time. Discusses two special cases when either the failure or repair rate is constant. Analyses numerically and compares particular cases with one, two and three units by assuming Weibull distribution for failure time and normal distribution for repair time.

Maintaining a high level of availability of weapon systems during battles becomes important from the point of view of winning the battle. Due to attrition factors (failure due to battle damage and unreliability) and logistic delays in the repair process, maintaining the required level of availability is difficult. In this paper, we develop a simulation model for availability of fighter aircraft considering multiple failures causing system failure and logistic delays in the repair process. The methodology is based on discrete event simulation using Monte Carlo techniques. The failure time distribution (Weibull) and the repair time distribution (exponential) for the considered subsystems of the aircraft and the logistic delay time distribution (log‐normal) for the logistic factors spares, crew and equipment were chosen with suitable parameters. The results indicate the pronounced decrease in availability (as low as less than 10 per cent in some cases) due to multiple failures and logistic delays. The results are, however, highly sensitive to a combination of reliability, maintainability and logistic delay parameters.

The article addresses the optimization of safety stock service levels for parts in a repair kit. The work was undertaken to assist a public transit entity that stores thousands of parts used to repair equipment acquired over many decades. Demand is intermittent, procurement lead times are long, and the total inventory investment is significant.

Demand exists for repair kits, and a repair cannot start until all required parts are available. The cost model includes holding cost to carry the part being modeled as well as shortage cost that consists of the holding cost to carry all other repair kit parts for the duration of the part’s lead time. The model combines deterministic and stochastic approaches by assuming a fixed ordering cycle with Poisson demand.

The results show that optimal service levels vary as a function of repair demand rate, part lead time, and cost of the part as a percentage of the total part cost for the repair kit. Optimal service levels are higher for inexpensive parts and lower for expensive parts, although the precise levels are impacted by repair demand and part lead time.

The proposed model can impact society by improving the operational performance and efficiency of public transit systems, by ensuring that home repair technicians will be prepared for repair tasks, and by reducing the environmental impact of electronic waste consistent with the right-to-repair movement.

The optimization model is unique because (1) it quantifies shortage cost as the cost of unnecessary holding other parts in the repair kit during the shortage time, and (2) it determines a unique service level for each part in a repair kit bases on its lead time, its unit cost, and the total cost of all parts in the repair kit. Results will be counter-intuitive for many inventory managers who would assume that more critical parts should have higher service levels.

The objective of the paper is to consider the problem of the strength of a manufactured item against stress, when the component follows Weibull failure law. Different cases of stress and strength with varying parameters are discussed for the Weibull‐Weibull stress‐strength model considered in this paper. The application of the proposed technique will help in understanding the design methodology of the system and addressing the risks involved in perceived quality and reliability levels by eliminating or at least reducing the risk impact at the design phase.

Generalised Weibull‐Weibull stress‐strength models have been analysed for different cases of shape parameters for stress and strength to estimate the reliability of the system. The model is generalized using semi‐regenerative stochastic processes with the help of a state space approach to include a repair facility.

Different cases of stress and strength with varying parameters have been discussed for the Weibull‐Weibull stress‐strength models considered in this paper. The results show how the stress‐strength reliability model is affected by changes in the parameters of stress and strength. The application of the proposed technique will help in understanding the design methodology of the system, and also lead to the problem of addressing the risks involved in perceived quality and reliability levels by eliminating or at least reducing the risk impact in the design phase.

The present study is limited to a few special cases of Weibull‐Weibull stress‐strength models. The authors propose to continue to study the behaviour of general Weibull strength against exponential stress in particular and to identify the shape parameter that maximises the strength reliability.

The application of the proposed technique will help in understanding the design methodology of the system, and also lead to the problem of addressing the risks involved in perceived quality and reliability levels by eliminating or at least reducing the risk impact at the design phase. The model has been extended and generalized to include a repair facility under the assumption that all the random variables involved in the analysis are arbitrarily distributed (i.e. general).

In the Weibull‐Weibull stress‐strength model of reliability, different cases have been considered. In the first case, both parameters of stress‐strength have the same values and are independent of the distribution. In the second case, if the shape parameter of the strength is twice that of the stress, the probability will have a normal distribution with different parameter values. In the third case, if the shape parameter of the stress is twice that of the strength, then probability distribution is a parabolic cylindrical function. The study shows how to proceed in all cases. The model is generalized to include a repair facility, with all the random variables involved in the analysis being arbitrarily distributed using semi‐regenerative stochastic processes.