Integrated model of system degradation and production lot sizing with considering covariate
Xue-juan LIU1(),Fei ZHAO2
1. School of Economics and Management, University of Science and Technology Beijing, Beijing 100083, China 2. School of Management, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
The system degradation process was modeled by random coefficient regression model, in which the covariate was considered based on the accelerated failure time model, and the product quality was also considered in the model. The integrated cost model of condition-based maintenance and economic production quantity was proposed based on renewal reward theory. The optimal value of decision variables could be obtained by analyzing the integrated cost model. The optimal critical level of preventive maintenance and the optimal lot size were obtained by analysis of numerical case. Result shows that the optimal lot size decreases gradually with the increasing of covariate, but the optimal critical level of preventive maintenance does not change. Influence of optimal results caused by relevant parameter is explained by sensitive analysis.
Xue-juan LIU,Fei ZHAO. Integrated model of system degradation and production lot sizing with considering covariate. Journal of ZheJiang University (Engineering Science), 2021, 55(12): 2390-2396.
Fig.1Degradation process and production process with PM renewal
Fig.2Degradation process and production process with failure renewal
Fig.3Expected cost per unit time with different values of covariate
X
$\tau^*$/d
$C^*$/丝
${E_{\rm{C}}}(\tau^*;C^*)$/(元·d?1)
0.1
1.45
2.55
123.6
0.2
1.42
2.55
125.5
0.3
1.40
2.56
127.5
0.4
1.38
2.56
129.5
0.5
1.36
2.56
131.6
0.6
1.33
2.56
133.7
0.7
1.31
2.56
135.8
0.8
1.29
2.56
138.1
0.9
1.27
2.56
140.3
Tab.1Optimal results of parameters with different values of covariate
$ {C_f} $/元
$\tau^*$/d
$C^*$/丝
${E_{\rm{C}}}(\tau^*;C^*)$/(元·d?1)
300
2.61
4.0
105.3
400
1.81
3.34
120.2
500
1.39
2.56
128.1
600
1.28
2.52
131.3
700
1.21
2.51
133.4
800
1.17
2.50
135.0
Tab.2Optimal results of parameters with different unit fault repair cost when X=1/3
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