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This paper considers a multi-objective reliability-redundancy allocation problem (MORRAP) of a series-parallel system, where system reliability and system cost are to be optimized simultaneously subject to limits on weight, volume, and redundancy level. Precise computation of component reliability is very difficult as the estimation of a single num...
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Citations
... Guilani et al. [17] introduced a mathematical model for the RRAPs. By maintaining the limits on weight, Kundu [18] simultaneously optimized system reliability with system cost of a MORRAP for a series-parallel system. ...
This study introduces a time-dependent fuzzy multi-objective reliability redundancy allocation problem (TF-MORRAP) for the n-stage (level) series–parallel system. System reliability maximization and system cost minimization according to time by optimizing the redundant components counting at every stage of the system is the main objective of this study. This optimization is done by satisfying the entropy constraints with limited redundant components at every stage and in the whole system. The reliability and cost of every component are represented as triangular fuzzy numbers (TFN) to handle the uncertainty of input information of the system. According to time, the component reliability and cost decrease by some factor of their previous existing value. This factor follows the change in the length of radius of the inverse logarithmic spiral with respect to angle which is regarded as time here. The proposed problem is analyzed by using an over-speed protection system of a gas turbine. We compare the membership values of optimal solutions obtained by using two well-known techniques namely non-dominated sorting genetic algorithm-II (NSGA-II) and a multi-objective particle swarm optimization algorithm called NF-MOPSO. Various performances of the algorithms are compared to solve the aforementioned problem by using some performance metrics. NF-MOPSO shows the high satisfaction level of objective functions and better performance than NSGA-II.
... For example, RAPs may be considered with a single objective function, e.g., aiming to maximizing system reliability [1,[3][4][5][6][7][8][9][10][11]27,28,30,31,[35][36][37][39][40][41]44,[46][47][48][53][54][55]], minimizing total system cost [12][13][14][15] or maximizing/minimizing other parameters [16,29]. Alternatively, RAPs may consider multi-objective functions [18][19][20][21][22][23][24][25]32,34,38,42,45,50,[56][57][58][59]. ...
... Regarding the components, they might be represented as binary or multi-state. In the binary state representation, the components can only be totally healthy or completely failed [1,[3][4][5][6][7][8][9][10][11][12][13][17][18][19][20][21][22][23][25][26][27][28][29][30][31][32][33][34][35]40,41,[43][44][45][46][47][48]53,55]; in the multi-state, the components might have other states, intermediate between these two [14][15][16]24,[60][61][62][63][64][65]. The type of the components in the subsystems can be characterized from different viewpoints. ...
The Redundancy Allocation Problem (RAP) is well-known in the field of reliability optimization. In this paper, RAP is investigated assuming that the distribution of the time to failure of the components has the form of an Erlang distribution with a time-dependent rate parameter and considering that the choice of redundancy for each subsystem can be none, active, standby or mixed. A genetic algorithm is used to solve the problem of optimal allocation. To analyze the effect of the time dependence, some numerical examples are worked out. Then, a case study of RAP from the literature is analyzed. The obtained results show that time dependence of the failure time distribution parameters can lead to significant differences in the optimal redundancy allocation.
... The efficiency of this method was shown to improve the system performance. Kundu [25] considered the multi-objective reliability-redundancy allocation problem (MOR-RAP) of mixed configuration, which was used to compromise the solution of maximum probability of maximum probability and minimize cost of the system. To recoup the impreciseness and accuracy in the data, type-2 fuzzy numbers were used to model the interval reliabilities of the components and defuzzification technique was used to convert the fuzzy values to defuzzify values. ...
... Based on the above Table 5, the expressions for the failure rate and repair time of the structure system can be obtained as: (24) τ SS = λA * τA + λB * τB + λC * τC + λZ * τZ + λE * τE + λF * τF + λG * τG λ SS (25) Therefore, based on the above Table 6 and using the arithmetic operations defined in section 4.2 (Case 3), the failure rate and repair time of the structure system can be obtained and shown in Table 7. Now expressions for reliability parameters are given (Table 8) as ...
The reliability of an industrial system plays a significant role in new technological era where everyone is concerned about the performance of associated industry. With the frequent demands of the customers, the job of the production industries becomes more tedious to produce the required products at a high rate. To fulfill the customer’s demand, the initial focus of the industries is to work well without any interruption/failure in the entire production process. In this paper, Reliability, Availability, MTTF, MTTR, MTBF, ENOF is proposed for an industrial system namely “Injection moulding machine”. For this, the membership function for right triangular generalized fuzzy numbers (RTrGFN) is proposed with the certain level of confidence. The real data of the Injection moulding machine is taken to validate the proposed methodology. The input data is extracted from the records/maintenance sheets of several years and found uncertainty due to the loss of any information or human mistakes. The parameters of the system like failure rate and repair time is retrieved. Based on data, AND-OR combination for the system is constructed. The lambda-tau methodology along with RTrGFN and its corresponding arithmetic operations is used for the performance analysis of the considered “Injection moulding machine”. For better understanding the results are discussed with the aid of graphs. Also after seeing the result one can conclude that this methodology is one of the best methodology for the performance analysis of a conventional system. Also authors have added the highlights and future scope of the research work at the end of the manuscript.
... Guilani et al. [17] introduced a mathematical model for the RRAPs. By maintaining the limits on weight Kundu [18] simultaneously optimized system reliability with system cost of a MORRAP for a series-parallel system. ...
This study introduces a time dependent fuzzy multi-objective reliability redundancy allocation problem (TF-MORRAP) for the $n$-stage (level) series parallel system. System reliability maximization and system cost minimization according to time by optimizing the redundant components counting at every stage of the system is the main objective of this study. This optimization is done by satisfying the entropy constraints with limited redundant components at every stage and in the whole system. The reliability and cost of every component are represented as triangular fuzzy numbers (TFN) to handle the uncertainty of input information of the system. According to time the component reliability and cost decrease by some factor of their previous existing value. This factor follows the change in the length of radius of the inverse logarithmic spiral with respect to angle which is regarded as time here. The proposed problem is analysed by using an over-speed protection system of a gas turbine. We compare the membership values of optimal solutions obtained by using two well-known techniques namely Non-dominated sorting genetic algorithm-II (NSGA-II) and a multi-objective particle swarm optimization algorithm called NF-MOPSO. Various performances of the algorithms are compared to solve the aforementioned problem by using some performance metrics. NF-MOPSO shows the high satisfaction level of objective functions and better performance than NSGA-II.
... Calik [29] studied supplier decision making and order allocation in the context of sustainability, in which an interval type-2 fuzzy AHP approach was used to determine the weight of the selected standard. Kundu [30] considered a redundant allocation decision making under interval type-2 fuzzy environment, and applied NIMBUS method to obtain compromise solution. The literature related to FMOP mentioned above and the corresponding approaches for solving them are summarized in Table 1. ...
... As shown in Table 1, most of the papers on FMOP related to our research considered non-interactive methods, and only a small number of the related works investigated interactive methods. Moreover, even fewer are associated with T2-FS (see, e.g., [27,30]), in which the presented methods involve complex operations and are difficult for solving realistic problems. Therefore, in order to better handle the type-2 fuzzy multi-objective programming (T2-FMOP) that often occurs in real life, we develop the two-stage fuzzy interactive multi-objective approach based on the operational law for T2-FS proposed recently by Li and Cai [31], which is easier to understand, saves time and better reflects the preference information of the DM compared with the current research. ...
... In the second stage, we update the reference membership function through a continuous interaction with the DM, and then convert the problem into a minmax model so as to solve the MOP models with regular symmetric triangular interval type-2 fuzzy set (RSTIT2-FS). Khan et al. [9] intuitionistic and neutrosophic programming approaches Firouzi et al. [13] weighted additive function Pérez-Cañedo et al. [14] ε-constraint method Ehsani et al. [15] weighted max-min approach Ren C et al. [16] minimum deviation method Ali et al. [17] aggregated weighted criterion method Gupta et al. [18] LINGO Shahbeig et al. [19] min-max method El Sayed et al. [20] ε-constraint method Ahmad [27] interactive neutrosophic method Gupta et al. [28] compromise criterion Calik [29] generalized credibility measure Kundu [30] NIMBUS method Current paper fuzzy interactive approach Our contributions are mainly reflected in the following: First, we propose a twostage fuzzy interactive multi-objective approach so as to more efficiently figure out multiobjective problems with interval type-2 fuzzy parameters. Second, we propose a type-2 fuzzy chance-constrained programming (CCP) to transfer the interval T2-FMOP into its crisp equivalent form. ...
In this study, a two-stage approach is introduced to obtain a more interactive and flexible solution to deal with the multi-objective programming under interval type-2 fuzzy environment. In the first stage, the fuzzy multi-objective chance-constrained programming with regular symmetric triangular interval type-2 fuzzy set parameters is proposed and transferred into its crisp equivalent form. In the second stage, we use the fuzzy interactive approach to address the crisp multi-objective programming obtained in the first stage by introducing the trade-off rate, which helps the decision maker react via updating their reference member values to obtain a satisfactory solution. Finally, taking a remanufacture of old clothes problem as an example, the comparison of experimental results obtained using a non-interactive method and interactive method shows that the proposed approach is conducive to obtaining satisfactory solutions effectively and efficiently, which broadens the application scope of the multi-objective programming with regular symmetric triangular interval type-2 fuzzy set parameters for sustainable manufacturing.
... The goal was to optimize system reliability and cost at the same time, having the constraints on volume, weight, and redundancy level. Using interval type-2 fuzzy numbers, Muhuri and Ashraf (2018) 10 also worked on fuzzy multiobjective reliability-redundancy allocation problem with the same objective functions as Kundu,9 in which system reliability and cost were optimized simultaneously. In an extension to their previous work, Ashraf et al 11 proposed a variant of particle swarm optimization to solve fuzzy multiobjective reliability-redundancy allocation problem, while giving users the ability to set the importance weights for each objective. ...
System reliability is defined as the probability of satisfactory performance of a system under stated conditions for a specified period of time. According to this definition, four parameters, including probability, satisfactory performance, specific conditions, and time should be exactly characterized to evaluate the system reliability accurately. However, due to the uncertainty involved in real situations, it is hardly possible to assess the aforementioned parameters precisely. In this article, two general and distinct approaches, including Zadeh's extension principle and modification of fuzzy parametric programming (FPP), are proposed to take into account such uncertainty in a famous reliability problem called the overspeed protection system. According to Zadeh's extension principle, a pair of nonlinear programming problems is formulated to compute α ‐level cuts of fuzzy system reliability. The membership function of fuzzy system reliability can then be constructed analytically by numerating different values of α . This fuzzy system reliability presents flexibility for further system analysis. In the second approach, from a different point of view, a variant of FPP is improved that provides a crisp value as a system reliability measure. The rewarding point of the latter procedure is to handle the problem in a computationally easier way.
The demand for product manufacturing is gradually leading the direction of production. Therefore, a production line that can produce diversified products is critical for meeting the requirements of modern systems. This study investigates multi-objective optimization of the reliability of a multi-type production system. In particular, machine deployment at each workstation can be associated with different reliability depending on the purchasing year or brand. Consequently, this study applies a component mixing strategy to multi-type production systems to estimate the reliability of an ensemble of heterogeneous machines. The goal of the studied problem is to maximize all production lines, and the cold-standby redundancy strategy based on the continuous-time Markov chain model is employed to calculate the exact reliability of the system. A performance indicator-based multi-objective algorithm, ε-MOABC, was employed to search for a near-optimal solution. The experimental results show that the multi-objective solution effectively converges to the Pareto front of the knee region and, more importantly, it can achieve high system reliability at a streamlined cost.
