Preventive maintenance decision optimization considering maintenance effect and planning horizon

Transcription

1 JOURNAL OF SYSTEMS ENGINEERING Vol30 No2 Apr , 2, 3 (1, ; 2, ; 3, ) :,,,,,,, :;; ; : O2132 : A : (2015) doi: /jcnkijse Preventive maintenance decision optimization considering maintenance effect and planning horizon Zhou Yu 1, Kou Gang 2, Ergu Daji 3 (1 School of Economics and Management, Inner Mongolia University, Hohhot , China; 2 School of Business Administration, Southwestern University of Finance and Economics, Chengdu , China; 3 School of Electrical and Information Engineering, Southwest University for Nationalities, Chengdu , China) Abstract: Preventive maintenance plays an important role on the operational reliability improvement The maintenance effect and finite planning horizon are introduced into the basal periodic and sequential preventive maintenance policies simultaneously When configuring maintenance optimization, the impact of the alternation between downtime and uptime on failure intensity is considered The failure process is regarded as a failure-counting process, and then the maintenance effect assessment model based on cumulative-failurecounting is proposed In addition, the preventive maintenance cost is developed to consider the maintenance effect as a function of allocated maintenance cost Numerical examples show that the proposed method can reduce the maintenance cost rate and improve the operational reliability Key words: repairable system; preventive maintenance; maintenance effect; planning horizon : ;: :( ; ; ), ( )

2 ,,,,,, [1, 2],, [2],,, [1],,,,, [3 7] [3 6], [7],,, [8 11] [12, 13],,,,,, [14, 15],,,,,, [16, 17], 2 21, 6:00 23:00, 23:00 6:00,, 1), x 1, x 2, x, x = x 1 + x 2 ; 2) t j, t j t u, t d, t T, t u = x 1 t j, (1) t d = x 2 t j, (2) t T = xt j = t u + t d (3) 3) N(t u ), N(t d ), N(t T ),

3 2 : 283 α 1,α 2,γ 1,γ 2,β 1 β 2 ( ) β1 ( ) β2 x1 t j + γ 1 x2 t j + γ 2 t T = t u + t d = +, (4) α 1, α 1 = α 2,β 1 = β 2 γ 1 = γ 2,, ( ) β1 x1 t j + γ 1, (4) t T = t u + t d = x 1 x 2,, 22, t i, t i = it(t ), 1 1,N(t ji T ) j i,, 1 1)M(t ji T ), j i ; 2)ρ j j ; 3)X(t ji T ) Table 1 1 Cumulative failure number α 2 α 1 t PM t N(t 01 T ) 2t N(t 02 T ) it N(t 0i T ) N(t11 T ) N(tj1 T ) N(t12 T ) N(tj2 T ) N(t1i T ) N(tji T ),, N(t ji T ) N(t (j 1)i T ) ρ j X(t ji T ) X(tji T ) = M(tji T ) N(t(j 1)i T ), N(t ji T ) = N(t(j 1)i T ( X(t ji T ) = M(tji T ) N ) + ρ j X(t ji T t (j 1)i T ), (5) ) (6), N(t 0i T) = M (t 0i T) n n N(t j T ) = N(t0i T ) + ρ j M(t ji T ) ρ j N(t (j 1)i T ) (7) ρ = 05, 1, 05 23, C r,

4 W S W S W S W S j C pj, C pj = a + bρ j + cρ 2 j (8), ρ j, C p n n C p = C pj = an + (bρ j + cρ 2 j) (9) s t 2 n d 3 r d 4 t h W = S = P M / h 1 ρ = Fig 1 Failure paths when ρ = 05 [3],,,,: 1); 2) N 0 ; 3) L A, (( Min J(T) = 1 m ) ) N(L A t j T T ) + N(t j T ) C r + C p st N(t j T) N 0,T L A,j = 1,2,,m,,, m, T 1,T 2,,T m, N 0, L A T, K, Min J ((K + 1)T ) = N(t j T ), (7) st N(t j T ) N 0,T L A N(t j T ) = M(T ) + ( K+1 1 (K + 1)T N(t j T )C r + C p ) (10) (11) K (ρ j M(jT ) N ((j 1)T )) (12)

5 2 : 285,, 25,,, L A = (K + 1)T, (13) N [(K + 1)T ] = N 0 (14), N[(K+1)T ] = ρm[(k+1)t ]+ρ(1 ρ)m(kt )+ρ(1 ρ) 2 M[(K 1)T ]+ +(1 ρ) 2 M(T ), (15) 1, K(13), : 1 N 0 ; m 2 1, j = 1,2,,m, N(L A t j T ) + N(t j T ) N 0, m; 3 m, 1, N 0 1,N 0 2,,m,, 3,, α = 2,β = 16, L A = 180, N 0 = 80 2 Table 2 2 Preventive maintenance effects and corresponding preventive maintenance costs j ρ j C pj , a = 20528,b = 64189,c = C r = 50, C p = ρ ρ 2,,, 2,,,,, ( 22282, 18933; 745, 651 )

6 5 0 / Fig 2 Failure trends under different maintenance policies [01, 07],, 3 3(a),,, ρ 045,,,,,,, M P ( a ) ( b ) 3 Fig 3 Comparison results under different maintenance effect 3(b),,,,,,

7 2 : 287,,, 3/4, 1/4 ρ = 01,,, 3 3 (ρ = 01) Table 3 The effect on preventive maintenance optimization results by intermittent work(ρ = 01) PM ( ) ( ) ,,,,, 3,,, 45%, 35% 4,,,,,,,, : [1] Zhou X, Xi L, Lee J Opportunistic preventive maintenance scheduling for a multi-unit series system based on dynamic programming[j] International Journal of Production Economics, 2009, 118(2): [2] Berrade M D, Cavalcante C A V, Scarf P A Modelling imperfect inspection over a finite horizon[j] Reliability Engineering and System Safety, 2013, 111(3): [3],, [J], 2014, 34(1): Wang Wenbin, Zhao Fei, Peng Rui Modeling of the optimal multiple inspection policy based on a three-stage failure process[j] Systems Engineering: Theory and Practice, 2014, 34(1): (in Chinese) [4], PH [J], 2010, 25(1): Cheng Zhijun, Yang Zheng, Guo Bo Analysis of system optimal maintenance model with phase type approximation[j] Journal of Systems Engineering, 2010, 25(1): (in Chinese) [5] Wu S M, Zuo M J Linear and nonlinear preventive maintenance models[j] IEEE Transactions on Reliability, 2010, 59(1): [6] Chun Y H Optimal number of periodic preventive maintenance operations under warranty[j] Reliability Engineering and System Safety, 1992, 37(3):

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