Journal of Systems Engineering and Electronics ›› 2019, Vol. 30 ›› Issue (3): 613623.doi: 10.21629/JSEE.2019.03.18
• Reliability • Previous Articles Next Articles
Junyuan WANG(), Jimin YE*(), Pengfei XIE()
Received:
20180514
Online:
20190601
Published:
20190704
Contact:
Jimin YE
Email:jywang215@stu.xidian.edu.cn;jmye@mail.xidian.edu.cn;PengfeiXie@stu.xidian.edu.cn
About author:
WANG Junyuan was born in 1987. He received his B.S. degree in mathematics and applied mathematics in 2011, his M.S. degree in Probability theory and mathematical statistics in 2014. Now he is a Ph.D. candidate in Xidian University, Xi'an China. His research interests are applied stochastic processes, maintenance theory and reliability analysis. Email:Supported by:
Junyuan WANG, Jimin YE, Pengfei XIE. New repairable system model with two types repair based on extended geometric process[J]. Journal of Systems Engineering and Electronics, 2019, 30(3): 613623.
Table 1
Values of $\mathit{\boldsymbol{C(T = 50, N)}}$ and $\mathit{\boldsymbol{C(\infty, N)}}$"
 
1  9.53  10.48 
2  –214.70  –202.32 
3  –276.16  –254.22 
4  –300.39  –272.03 
5  
6  –308.63  –272.22 
7  –302.14  –276.39 
8  –290.71  –250.67 
9  –274.93  –234.70 
10  –255.15  –215.89 
11  –231.72  –194.61 
12  –205.08  –171.24 
13  –175.86  –146.25 
14  –144.90  –120.21 
15  –113.22  –93.79 
16  –81.94  –67.70 
17  –52.14  –42.64 
18  –24.73  –19.28 
19  –0.35  1.91 
20  20.66  20.59 
21  38.26  36.66 
22  52.63  50.14 
23  64.11  61.21 
24  73.10  70.14 
25  80.04  77.21 
26  85.30  82.74 
27  89.26  87.00 
28  92.20  90.26 
29  94.37  92.73 
30  95.96  94.59 
Table 2
Values of $\mathit{\boldsymbol{C(T, N)}}$ and $\mathit{\boldsymbol{f(N)}}$ when $\mathit{\boldsymbol{T = 50}}$"
 
1  9.53  0.058 6 
2  –214.70  0.129 3 
3  –276.16  0.285 9 
4  –300.39  0.613 7 
5  1.166 9  
6  –308.63  1.944 1 
7  –302.14  2.866 6 
8  –290.71  3.812 4 
9  –274.93  4.679 7 
10  –255.15  5.419 6 
11  –231.72  6.027 6 
12  –205.08  6.521 0 
13  –175.86  6.922 6 
14  –144.90  7.252 5 
15  –113.22  7.526 7 
16  –81.94  7.757 2 
17  –52.14  7.952 8 
18  –24.73  8.119 8 
19  –0.35  8.263 3 
20  20.66  8.387 1 
21  38.26  8.494 0 
22  52.63  8.586 6 
23  64.11  8.667 0 
24  73.10  8.736 7 
25  80.04  8.797 3 
26  85.30  8.849 9 
27  89.26  8.895 6 
28  92.20  8.935 4 
29  94.37  8.969 9 
30  95.96  9.000 0 
Table 3
Values of $\mathit{\boldsymbol{C(T = 50, N)}}$ when $\mathit{\boldsymbol{p_n = 0}}$"
1  9.53  10.58 
2  214.70  167.62 
3  276.16  210.89 
4  300.39  
5  205.71  
6  308.63  183.40 
7  302.14  153.77 
8  290.71  119.66 
9  274.93  83.79 
10  255.15  48.77 
11  231.72  16.74 
12  205.08  10.91 
13  175.86  33.60 
14.  144.90  51.46 
15  113.22  65.04 
16  81.94  75.10 
17  52.14  82.40 
18  24.73  87.62 
19  0.35  91.31 
20  20.66  93.91 
21  38.26  95.72 
22  52.63  96.99 
23  64.11  97.87 
24  73.10  98.49 
25  80.04  98.92 
26  85.30  99.23 
27  89.26  99.44 
28  92.20  99.60 
29  94.37  99.71 
30  95.96  99.78 
Table 4
Optimal $\mathit{\boldsymbol{N_{T_i }^*}}$ and $\mathit{\boldsymbol{C(T_i, N_{T_i }^*)}}$ for different $\mathit{\boldsymbol{\lambda, \mu, \gamma}}$, when $\mathit{\boldsymbol{T_i = 100}}$"
0.1  5  –309.049 9  0.1  5  –309.046 0  0.1  3  –122.573 6 
0.2  6  –169.484 4  0.2  5  –309.048 2  0.2  3  –188.414 9 
0.3  7  –68.949 9  0.3  5  –309.049 0  0.3  4  –226.042 6 
0.4  8  1.184 8  0.4.  5  –309.049 3  0.4  4  –249.808 1 
0.5  9  48.156 7  0.5  5  –309.049 5  0.5  5  –266.136 0 
0.6  11  76.646 3  0.6  5  –309.049 7  0.6  5  –280.169 3 
0.7  14  92.387 9  0.7  5  –309.049 8  0.7  5  –280.870 2 
0.8  18  98.797 1  0.8  5  –309.049 9  0.8  5  –299.299 7 
0.9  30  99.996 6  0.9  5  –309.049 9  0.9  5  –306.111 7 
Table 5
Optimal $\mathit{\boldsymbol{N_{T_i }^*}}$ and $\mathit{\boldsymbol{C(T, N_{T_i }^*)}}$ for different $\mathit{\boldsymbol{a, b, c, }}$ when $\mathit{\boldsymbol{T_i = 100}}$"
1.11  6  –320.650 9  0.05  5  –309.045 1  0.1  3  –234.482 9 
1.12  6  –317.634 7  0.10  5  –309.049 0  0.2  3  –257.919 0 
1.13  6  –314.639 8  0.15  5  –309.049 5  0.3  4  –267.773 5 
1.14  6  –311.666 8  0.20  5  –309.049 7  0.4  4  –283.549 6 
1.15  5  –309.049 9  0.25  5  –309.049 7  0.5  4  –292.431 2 
1.16  5  –306.571 2  0.30  5  –309.049 8  0.6  5  –304.089 9 
1.17  5  –304.111 2  0.35  5  –309.049 8  0.7  6  –313.280 2 
1.18  5  –301.670 3  0.40  5  –309.049 8  0.75  6  –318.057 6 
1.19  5  –299.248 7  0.45  5  –309.049 9  0.80  7  –322.309 5 
1.20  5  –296.846 4  0.5  5  –309.049 9  0.85  7  –327.189 9 
1.25  5  –285.131 5  0.55  5  –309.049 9  0.90  8  –331.667 7 
1.30  5  –273.918 1  0.60  5  –309.049 9  0.95  8  –336.318 8 
1.35  5  –263.209 6  0.65  5  –309.049 9  0.96  9  –337.245 7 
1.40  4  –253.969 9  0.70  5  –309.049 9  0.97  9  –338.280 9 
1.45  4  –245.801 5  0.80  5  –309.049 9  0.98  9  –339.279 9 
1.50  4  –237.988 2  0.90  5  –309.049 9  0.99  9  –340.244 3 
1 
BROWN M, PROSCHAN F. Imperfect repair. Journal of Applied Probability, 1983, 20, 851 859.
doi: 10.2307/3213596 
2 
LAM Y. Geometric process and replacement problem. Acta Mathematicate Applicatae, 1988, 4, 366 377.
doi: 10.1007/BF02007241 
3 
LAM Y. A note on the optimal replacement problem. Advances in Applied Probability, 1988, 20, 479 482.
doi: 10.2307/1427402 
4 
STADJE W, ZUCKERMAN D. Optimal strategies for some repair replacement models. Advances in Applied Probability, 1990, 22, 641 656.
doi: 10.2307/1427462 
5 
ZHANG Y L. A bivariate optimal replacement policy for a repairable system. Journal of Applied Probability, 1994, 31, 1123 1127.
doi: 10.2307/3215336 
6 
LAM Y. A geometric process δshock maintenance model. IEEE Trans. on Reliability, 2009, 58 (2): 389 396.
doi: 10.1109/TR.2009.2020261 
7 
WANG G J, ZHANG Y L. Optimal periodic preventive repair and replacement policy assuming geometric process repair. IEEE Trans. on Reliability, 2006, 55 (1): 118 122.
doi: 10.1109/TR.2005.863808 
8 
LAM Y. A geometric process maintenance model with preventive repair. European Journal of Operational Research, 2007, 182, 806 819.
doi: 10.1016/j.ejor.2006.08.054 
9  WU S, CLEMENTSCROOME D. A novel repair model for imperfect maintenance. IMA Journal of Management Mathematics, 2018, 17 (3): 235 243. 
10 
CHENG G Q, LI L. A geometric process repair model with inspections and its optimization. International Journal of Systems Science, 2012, 43 (9): 1650 1655.
doi: 10.1080/00207721.2010.549586 
11 
ZHANG Y L, WANG G J. A bivariate optimal repairreplacement model using geometric processes for a cold standby repairable system. Engineering Optimization, 2006, 38 (5): 609 619.
doi: 10.1080/16066350600608877 
12  ZHANG Y L, YAM R C, ZUO M J. A bivariate optimal replacement policy for a multistate repairable system. Reliability Engineering & System Safety, 2007, 92 (4): 535 542. 
13 
WANG G J, ZHANG Y L. A bivariate mixed policy for a simple repairable system based on preventive repair and failure repair. Applied Mathematical Modelling, 2009, 33 (8): 3354 3359.
doi: 10.1016/j.apm.2008.11.008 
14  ZHANG Y L, WANG G J. A geometric process repair model for a repairable cold standby system with priority in use and repair. Reliability Engineering & System Safety, 2009, 94 (11): 1782 1787. 
15  LIANG X, LAM Y, LI Z. Optimal replacement policy for a general geometric process model with δshock. International Journal of Systems Science, 2011, 42 (11): 2021 2034. 
16  CHANG S H, CHOI D W. Performance analysis of a finitebuffer discretetime queue with bulk arrival, bulk service and vacations. Computers & Operations Research, 2005, 32 (9): 2213 2234. 
17  JIA J, WU S. A replacement policy for a repairable system with its repairman having multiple vacations. Computers & Industrial Engineering, 2009, 57 (1): 156 160. 
18 
SHEU S H, CHANG C C, ZHANG Z G, et al. A note on replacement policy for a system subject to nonhomogeneous pure birth shocks. IEEE Trans. on Reliability, 2012, 61 (3): 741 748.
doi: 10.1109/TR.2012.2206270 
19 
SHEU S H, ZHANG Z G, CHIEN Y H, et al. Age replacement policy with leadtime for a system subject to nonhomogeneous pure birth shocks. Applied Mathematical Modelling, 2013, 37 (1415): 7717 7725.
doi: 10.1016/j.apm.2013.03.017 
20  SHEU S H, CHIEN Y H, CHANG C C, et al. Optimal trivariate replacement policies for a deteriorating system. Quality Technology & Quantitative Management, 2014, 11 (3): 307 320. 
21 
CHIEN Y H, CHEN J A. Optimal maintenance policy for a system subject to damage in a discrete time process. Reliability Engineering and System Safety, 2012, 103, 1 10.
doi: 10.1016/j.ress.2012.03.002 
22  ZHANG Y L, WANG G J. An optimal agereplacement policy for a simple repairable system with delayed repair. Communications in StatisticsTheory and Methods, 2016, 46 (6): 2837 2850. 
23  ZHANG Y L, WANG G J. An extended geometric process repair model for a cold standby repairable system with imperfect delayed repair. International Journal of Systems Science:Operations & Logistics, 2016, 3 (3): 163 175. 
24 
ZHANG Y L, WANG G J. An extended geometric process repair model with delayed repair and slight failure type. Communications in StatisticsTheory and Methods, 2017, 46 (1): 427 437.
doi: 10.1080/03610926.2014.995824 
25  ROSS S M. Stochastic processes. 2nd ed. New York: Wiley, 1996. 
26  LAM Y. The geometric process and its applications. Signapore: World Scientific, 2007. 
[1]  Ning MA, Jimin YE, Junyuan WANG. A generalized geometric process based repairable system model with bivariate policy [J]. Journal of Systems Engineering and Electronics, 2021, 32(3): 631641. 
Viewed  
Full text 


Abstract 

