Redundancy Optimization of an Uncertain Parallel-Series System with Warm Standby Elements

The redundancy optimization problem is formulated for an uncertain parallel-series system with warm standby elements. The lifetimes and costs of elements are considered uncertain variables, and the weights and volumes of elements are random variables. The uncertain measure optimization model (UMOM), the uncertain optimistic value optimization model (UOVOM), and the uncertain cost optimization model (UCOM) are developed through reliability maximization, lifetime maximization, and cost minimization, respectively. An efficient simulation optimization algorithm is provided to calculate the objective values and optimal solutions of the UMOM, UOVOM, and UCOM. A numerical example is presented to illustrate the rationality of the models and the feasibility of the optimization algorithm.

[1]  Junzo Watada,et al.  Modelling redundancy allocation for a fuzzy random parallel-series system , 2009, J. Comput. Appl. Math..

[2]  Baoding Liu.  Extreme value theorems of uncertain process with application to insurance risk model , 2013, Soft Comput..

[3]  L. Zadeh.  Fuzzy sets as a basis for a theory of possibility , 1999 .

[4]  Xiaosheng Wang,et al.  Uncertain hypothesis testing for two experts' empirical data , 2012, Math. Comput. Model..

[5]  Rui Kang,et al.  Reliability analysis in uncertain random system , 2016, Fuzzy Optimization and Decision Making.

[6]  Baoding Liu.  Uncertain Risk Analysis and Uncertain Reliability Analysis , 2010 .

[7]  Yuan Gao.  Existence and Uniqueness Theorem on Uncertain Dierential Equations with Local Lipschitz Condition , 2012 .

[8]  Wei Liu.  Reliability Analysis of Redundant System with Uncertain Lifetimes , 2012 .

[9]  Enrico Zio,et al.  Uncertainty theory as a basis for belief reliability , 2018, Inf. Sci..

[10]  G. S. Mahapatra,et al.  Entropy based region reducing genetic algorithm for reliability redundancy allocation in interval environment , 2014, Expert Syst. Appl..

[11]  C. Jiang,et al.  Reliability-based design optimization for problems with interval distribution parameters , 2016, Structural and Multidisciplinary Optimization.

[12]  Baoding Liu,et al.  Uncertainty Theory - A Branch of Mathematics for Modeling Human Uncertainty , 2011, Studies in Computational Intelligence.

[13]  Baoding Liu,et al.  Standby redundancy optimization problems with fuzzy lifetimes , 2005, Comput. Ind. Eng..

[14]  Xiang Li,et al.  Uncertain Alternating Renewal Process and Its Application , 2012, IEEE Transactions on Fuzzy Systems.

[15]  Yuan Gao.  Variation analysis of semi-canonical process , 2011, Math. Comput. Model..

[16]  Xiaozhong Li,et al.  Reliability Analysis of Unrepairable Systems with Uncertain Lifetimes , 2015 .

[17]  Lev V. Utkin.  Redundancy optimization by fuzzy reliability and cost of system components , 1994 .

[18]  X. Chen,et al.  Existence and uniqueness theorem for uncertain differential equations , 2010, Fuzzy Optim. Decis. Mak..

[19]  Lixing Yang,et al.  On distribution function of the diameter in uncertain graph , 2015, Inf. Sci..

[20]  Yuan Gao,et al.  Uncertain inference control for balancing an inverted pendulum , 2012, Fuzzy Optim. Decis. Mak..

[21]  Yan Lindsay Sun,et al.  Order statistics of uncertain random variables with application to k-out-of-n system , 2017, Fuzzy Optim. Decis. Mak..

[22]  A. F. Jameel,et al.  Solution of Fuzzy Redundancy Reliability Optimization Problem by Modified Penalty Function Method , 2014 .

[23]  Robert LIN,et al.  NOTE ON FUZZY SETS , 2014 .

[24]  Yuan Gao.  Uncertain models for single facility location problems on networks , 2012 .

[25]  Baoding Liu.  Uncertain Set Theory and Uncertain Inference Rule with Application to Uncertain Control , 2010 .

[26]  Baoding Liu.  Uncertain Logic for Modeling Human Language , 2011 .

[27]  Hao Hu,et al.  An adaptive hybrid approach for reliability-based design optimization , 2015 .

[28]  Xiaowei Chen,et al.  A note on truth value in uncertain logic , 2011, Expert Syst. Appl..

[29]  Yuan Gao,et al.  On Liu's Inference Rule for Uncertain Systems , 2010, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[30]  Baoding Liu.  Uncertain Entailment and Modus Ponens in the Framework of Uncertain Logic , 2009 .

[31]  Tapan Kumar Roy,et al.  Fuzzy multi-objective mathematical programming on reliability optimization model , 2006, Appl. Math. Comput..

[32]  Lev V. Utkin.  A new heuristic method redundancy optimization in a consecutive-k-out-of-n:F system by fuzzy probability , 1993 .

[33]  Qingwei Chen,et al.  Multi-objective reliability redundancy allocation in an interval environment using particle swarm optimization , 2016, Reliab. Eng. Syst. Saf..