Shapley Value Allocation Model of Responsibility during the Degradation of System Reliability

doi:10.3901/JME.2017.20.202

Abstract

Abstract: Using the cooperative game theory, the allocation of responsibility during the reliability degradation of system which has many composing components and complex structure is studied. A Shapley value allocation model of responsibility during the degradation of system reliability is constructed. The construction process and solution steps of the model are combed as well. Based on the cooperation rules between components and the types, quantities and forming probatility of cooperative alliance are obtained. Characteristic function of the responsibility allocation which is based on the structure relation of the coalition is also proposed and proved. The correctness and rationality of the model is verified based on the simulation method. Finally, a case study shows that the proposed model is feasible and effective by contrast with the traditional reliability allocation methods.

Key words: responsibility allocation, Shapley value, simulation, system reliability degradation

CLC Number:

N945

CAO Yingsai, LIU Sifeng, FANG Zhigeng, ZHANG Qin. Shapley Value Allocation Model of Responsibility during the Degradation of System Reliability[J]. Journal of Mechanical Engineering, 2017, 53(20): 202-208.

References

[1] WANG Y,ZHANG F,CUI T,et al. Fault diagnosis for manifold absolute pressure sensor (MAP) of diesel engine based on Elman neural network observer[J]. Chinese Journal of Mechanical Engineering,2016,29(2):386-395.
[2] GERTSBAKH I B,KORDONSKIY K B. Models of failure[M]. New York:Springer-Verlag,1969.
[3] ESCOBAR L A,MEEKER W Q,KUGLER D L,et al. Accelerated destructive degradation tests:Data,models,and analysis[J]. Mathematical & Statistical Methods in Reliability,2015:319-337.
[4] TAKEDA E,SUZUKI N. An empirical model for device degradation due to hot-carrier injection[J]. Electron Device Letters IEEE,1983,4(4):111-113.
[5] RAMÍREZ J G,GORE W L,JOHNSTON G. New methods for modeling reliability using degradation data[J]. Statistics Data Analysis and Data Mining,2001,9(5):226-263.
[6] 周志刚,徐芳. 考虑强度退化和失效相关性的风电齿轮传动系统动态可靠性分析[J]. 机械工程学报,2016,52(11):80-87. ZHOU Zhigang,XU Fang. Dynamic reliability analysis of gear transmission system of wind turbine considering strength degradation and dependent failure[J]. Journal of Mechanical Engineering,2016,52(11):80-87.
[7] 陈保家,陈雪峰,李兵,等. Logistic回归模型在机床刀具可靠性评估中的应用[J]. 机械工程学报,2011,47(18):158-164. CHEN Baojia,CHEN Xuefeng,LI Bing,et al. Reliability estimation for cutting tool based on logistic regression model[J]. Journal of Mechanical Engineering,2011,47(18):158-164.
[8] 邓爱民. 高可靠长寿命产品可靠性技术研究[D]. 长沙:国防科学技术大学,2006. DENG Aimin. Research on Reliability Technology of high reliability and long life products[D]. Changsha:National Defense Science and Technology University,2006.
[9] 马纪明,詹晓燕. 具有随机退化特性的柱塞泵性能可靠性分析[J]. 机械工程学报,2010,46(14):189-193. MA Jiming,ZHAN Xiaoyan. Reliability analysis of piston pump with random degradation[J]. Journal of Mechanical Engineering,2010,46(14):189-193.
[10] 尤琦,赵宇,胡广平,等. 基于时序模型的加速退化数据可靠性评估[J]. 系统工程理论与实践,2011,31(2):328-332. YOU Qi,ZHAO Yu,HU Guangping,et al. Reliability evaluation of accelerated degradation data based on time series model[J]. System Engineering Theory and Practice,2011,31(2):328-332.
[11] 夏新涛,孟艳艳,邱明. 用灰自助泊松方法预测滚动轴承振动性能可靠性的变异过程[J]. 机械工程学报,2015,51(9):97-103. XIA Xintao,MENG Yanyan,QIU Ming. Forecasting for variation process of reliability of rolling bearing vibration performance using grey bootstrap poison method[J]. Journal of Mechanical Engineering,2015,51(9):97-103.
[12] 彭宝华. 基于Wiener过程的可靠性建模方法研究[D]. 长沙:国防科学技术大学,2010. PENG Baohua. Research on reliability modeling method based on Wiener process[D]. Changsha:National Defense Science and Technology University,2010.
[13] TSAI C C,TSENG S T,BALAKRISHNAN N. Optimal design for degradation tests based on gamma processes with random effects[J]. IEEE Transactions on Reliability,2012,61(2):604-613.
[14] AUMANN R J,DREZE J H. Cooperative games with coalition structures[J]. International Journal of game theory,1974,3(4):217-237.
[15] SHAPLEY L S. A value for n-person games[J]. The Shapley Value,1988:31-40.
[16] MASCHLER M,PELEG B. The structure of the kernel of a cooperative game[J]. SIAM Journal on Applied Mathematics,1967,15(3):569-604.
[17] SCHMEIDLER D. The nucleolus of a characteristic function game[J]. SIAM Journal on Applied Mathematics,1969,17(6):1163-1170.
[18] 董振亚,戴葵,王蕾. 元部件重要度分析的一种神经网络方法[J]. 计算机科学,2002,29(6):149-151. DONG Zhenya,DAI Kui,WANG Lei. A neural network method for the analysis of the importance of component parts[J]. Computer Science,2002,29(6):149-151.