基于运行过程失效预防的重大装备并联型关键系统定期维修模型

doi:10.16381/j.cnki.issn1003-207x.2023.0245

摘要/Abstract

摘要：

为有效预防并联型关键系统在重大装备运行过程中发生失效，本文在现有模型的基础上，充分考虑装备的运行时段，提出一种基于运行过程失效预防的重大装备并联型关键系统定期维修模型。首先，建立基于运行时段的重大装备并联型关键系统定期维修模型。然后，为权衡经济性与维修性，按照“先更换”以及“后更换”两种优化原则，构建基于计划更换原则的重大装备并联型关键系统定期维修优化模型，并通过数值算例验证最优解推导的正确性以及本文模型的有效性。最后，将本文模型运用于某大型船舶电气系统的定期维修问题，旨在呈现最优策略的分析过程以及为决策者在研究类似问题时提供科学依据。

关键词: 运行过程, 重大装备, 并联型关键系统, 定期维修模型, 计划更换原则

Abstract:

Most of the preventive maintenance researches just focus on the whole life the systems but ignore the operation process. For some major equipment， they can not be always in working condition and might be shut down in most time. Therefore， the high reliability in the whole life dose not mean that the systems have high reliability during the operation process. Nowadays， some scholas have integrated the operation duration into the preventive maintenance models and proved that if the operation duration is considered， the maintenance policies can be more effective to guarantee high reliability for the systems. However， the related works just considered the one-unit system. Then， in order to prevent failure of parallel critical system when the major equipment is operating， the operation duration is considered into the present model， and a periodic maintenance model of parallel critical system for major equipment is proposed to prevent the failure during the operation process. Firstly， a periodic maintenance model of parallel critical system for major equipment with operation duration is formulated. Then， in order to balance the trade-off between the cost and maintainability， the periodic maintenance optimized models of parallel critical system for major equipment with scheduled replacement principle are formulated， according to replacement first and replacement last. Via the numerical examples， the optimum numbers of the units would be underestimated if the operation duration is not considered. In reliability theory， the smaller numbers of the units of the parallel systems would lead to the lower reliability. It verifies that the proposed models can be more effective to guarantee the high reliability. Finally， the suggested models are illustrated in maintaining the electrical system of a large ship based on the assumed data， which presents the analysis process of optimal polices and provide the decision-makers with the suggestions when they study the similar problems.

Key words: operation duration, major equipment, parallel critical system, periodic maintenance model, scheduled replacement principle

中图分类号:

TP273

张秦,徐鹏,方志耕, 等. 基于运行过程失效预防的重大装备并联型关键系统定期维修模型[J]. 中国管理科学, 2025, 33(10): 67-75.

Qin Zhang,Peng Xu,Zhigeng Fang, et al. Periodic Maintenance Model of Parallel Critical System for Major Equipment to Prevent the Failure During the Operation Process[J]. Chinese Journal of Management Science, 2025, 33(10): 67-75.

图/表 11

表1

当cm=200.0时的n*与C(tx,n*)"

$c 1$	$t x = 0$		$t x = 0.3$		$t x = 0.6$		$t x = 0.9$
$c 1$	$n *$	$C (t x, n *)$	$n *$	$C (t x, n *)$	$n *$	$C (t x, n *)$	$n *$	$C (t x, n *)$
10.0	5	107.635	6	97.049	7	92.269	8	90.703
15.0	4	129.952	5	117.527	6	111.948	6	109.853
20.0	3	149.036	4	134.125	5	127.814	5	125.318
25.0	3	164.036	4	149.510	4	141.302	5	138.476
30.0	3	179.036	3	161.447	4	153.802	4	149.763
35.0	2	192.741	3	172.985	3	164.597	4	160.289
40.0	2	202.741	3	184.523	3	173.972	3	169.858
45.0	2	212.741	2	195.449	3	183.347	3	177.753

表1

表2

当cm=200.0，tx=0.9时的Tf*与Cf(tx,n;Tf*)"

$c 1$	$n = 2$		$n = 3$		$n = 4$		$n = 5$
$c 1$	$T f *$	$C f (t x, n; T f *)$	$T f *$	$C f (t x, n; T f *)$	$T f *$	$C f (t x, n; T f *)$	$T f *$	$C f (t x, n; T f *)$
10.0	0.385	117.567	0.550	89.569	0.724	78.825	0.893	74.590
15.0	0.522	132.099	0.706	106.557	0.909	97.736	1.109	95.434
20.0	0.665	143.909	0.863	121.115	1.095	114.403	1.328	114.151
25.0	0.820	153.987	1.029	134.050	1.292	129.538	1.566	131.389
30.0	0.995	162.839	1.211	145.792	1.514	143.522	1.843	147.503
35.0	1.199	170.766	1.420	156.606	1.775	156.594	2.191	162.714
40.0	1.448	177.964	1.669	166.665	2.106	168.915	2.686	177.172
45.0	1.772	184.567	1.988	176.094	2.572	180.599	3.616	190.987

表2

表3

当cm=200.0，tx=0.9时的nf*与Cf(tx,nf*;T)"

$c 1$	$T = 1.0$		$T = 1.5$		$T = 2.0$		$T = 2.5$
$c 1$	$n f *$	$C f (t x, n f *; T)$	$n f *$	$C f (t x, n f *; T)$	$n f *$	$C f (t x, n f *; T)$	$n f *$	$C f (t x, n f *; T)$
10.0	6	73.629	7	75.476	8	79.506	8	83.024
15.0	5	95.747	6	96.880	6	100.099	6	103.315
20.0	4	114.621	5	114.493	5	117.168	5	119.869
25.0	4	131.273	4	129.974	5	132.385	5	134.204
30.0	3	146.556	4	143.524	4	144.595	4	146.201
35.0	3	159.046	3	156.648	4	156.769	4	157.668
40.0	3	171.535	3	166.810	3	166.964	3	167.788
45.0	3	184.024	3	176.972	3	176.095	3	176.389

表3

表4

当cm=200.0，tx=0.9时的Tl*与Cl(tx,n;Tl*)"

$c 1$	$n = 2$		$n = 3$		$n = 4$		$n = 5$
$c 1$	$T l *$	$C l (t x, n; T l *)$	$T l *$	$C l (t x, n; T l *)$	$T l *$	$C l (t x, n; T l *)$	$T l *$	$C l (t x, n; T l *)$
10.0	0.900	149.072	1.052	122.464	1.194	107.458	1.327	98.396
15.0	0.989	154.331	1.150	130.281	1.313	117.683	1.470	110.859
20.0	1.090	159.568	1.259	138.005	1.444	127.692	1.624	122.934
25.0	1.205	164.754	1.380	145.593	1.588	137.421	1.794	134.541
30.0	1.339	169.853	1.517	152.996	1.749	146.803	1.985	145.603
35.0	1.498	174.819	1.673	160.161	1.932	155.772	2.202	156.044
40.0	1.687	179.600	1.853	167.029	2.143	164.260	2.455	165.792
45.0	1.917	184.134	2.064	173.541	2.392	172.200	2.761	174.772

表4

表5

当cm=200.0，tx=0.9时的nl*与Cl(tx,nl*;T)"

$c 1$	$T = 1.0$		$T = 1.5$		$T = 2.0$		$T = 2.5$
$c 1$	$n l *$	$C l (t x, n l *; T)$	$n l *$	$C l (t x, n l *; T)$	$n l *$	$C l (t x, n l *; T)$	$n l *$	$C l (t x, n l *; T)$
10.0	8	90.528	9	87.384	10	86.304	12	89.003
15.0	6	109.686	7	106.516	8	105.716	9	108.529
20.0	5	125.157	6	122.106	7	121.427	7	123.912
25.0	5	138.281	5	135.271	6	134.508	6	136.431
30.0	4	149.598	4	147.240	5	145.605	5	147.296
35.0	4	160.098	4	157.002	4	155.801	5	156.549
40.0	3	169.719	4	166.763	4	164.374	4	164.845
45.0	3	177.593	3	174.962	4	172.947	4	172.247

表5

图1

图2

图3

图4

图5

图6

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