周炳海, 劉子龍

(同濟(jì)大學(xué) 機(jī)械與能源工程學(xué)院,上海 201804)

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考慮質(zhì)量損失的退化系統(tǒng)維護(hù)建模

周炳海, 劉子龍

(同濟(jì)大學(xué) 機(jī)械與能源工程學(xué)院,上海 201804)

為有效解決退化系統(tǒng)的預(yù)防性維護(hù)問(wèn)題,以“兩設(shè)備帶緩沖區(qū)”的系統(tǒng)模型為研究對(duì)象,綜合考慮產(chǎn)品質(zhì)量損失和緩沖區(qū)的影響,建立以最小化單位運(yùn)行成本為目標(biāo)的預(yù)防性維護(hù)模型.基于田口質(zhì)量損失理論,構(gòu)建系統(tǒng)狀態(tài)與質(zhì)量損失間的函數(shù)關(guān)系；針對(duì)退化系統(tǒng)中的瓶頸設(shè)備和非瓶頸設(shè)備,分別建立基于可靠度和時(shí)間的預(yù)防性維護(hù)策略.根據(jù)約束理論,以瓶頸設(shè)備的預(yù)防性維護(hù)作為機(jī)會(huì)維護(hù)(OM)的決策點(diǎn),利用期望成本節(jié)余函數(shù)來(lái)判斷是否對(duì)非瓶頸設(shè)備進(jìn)行機(jī)會(huì)維護(hù).利用迭代算法尋找最優(yōu)決策組合,并通過(guò)蒙特卡羅仿真對(duì)算例進(jìn)行分析.結(jié)果表明,所建模型是可行且有效的；與計(jì)劃維護(hù)策略相比,機(jī)會(huì)維護(hù)(OM)策略在降低成本和提高產(chǎn)出方面的表現(xiàn)更優(yōu).

退化系統(tǒng)；質(zhì)量損失；緩沖區(qū)容量；機(jī)會(huì)維護(hù)；預(yù)防性維護(hù)；蒙特卡洛法

合理的預(yù)防性維護(hù)策略可以有效地保障系統(tǒng)的可靠性、提高產(chǎn)出并降低運(yùn)行成本.緩沖區(qū)的設(shè)置能夠有效地減少因上游設(shè)備故障或計(jì)劃維護(hù)而導(dǎo)致的生產(chǎn)系統(tǒng)停滯,因此,帶有緩沖區(qū)的生產(chǎn)系統(tǒng)的預(yù)防性維護(hù)問(wèn)題一直受到學(xué)界的關(guān)注.Ribeiro等[1]在已知預(yù)防性維護(hù)策略的條件下,利用整數(shù)規(guī)劃求解了最優(yōu)緩沖區(qū)的大小.Dimitrakos等[2]在已知緩沖區(qū)容量的條件下,應(yīng)用半馬爾可夫鏈(Semi-Markov)求解了上游設(shè)備的最優(yōu)維護(hù)狀態(tài)點(diǎn).Meller等[3]提出了以緩沖區(qū)容量來(lái)觸發(fā)上游設(shè)備預(yù)防性維護(hù)的策略.成國(guó)慶等[4]在假設(shè)上游設(shè)備“修復(fù)如舊”的條件下,以最小化系統(tǒng)運(yùn)行成本為目標(biāo),運(yùn)用幾何過(guò)程建立了退化系統(tǒng)維修更換模型.Zequeira等[5]以在上游設(shè)備停機(jī)時(shí)最大化滿足下游設(shè)備所需為目標(biāo),研究了緩沖區(qū)大小和預(yù)防性維護(hù)周期的優(yōu)化.Karamatsoukis等[6]在文獻(xiàn)[2]的基礎(chǔ)上利用離散時(shí)間馬爾科夫決策模型研究了帶緩沖區(qū)的串聯(lián)設(shè)備預(yù)防性維護(hù)問(wèn)題.余佳迪等[7]同時(shí)考慮上、下游設(shè)備的隨機(jī)退化，提出了基于周期的預(yù)防性維護(hù)策略.Zhou等[8]針對(duì)帶有緩沖區(qū)的串行系統(tǒng)提出了基于動(dòng)態(tài)規(guī)劃的機(jī)會(huì)維護(hù)策略.Li等[9]研究了多機(jī)串行系統(tǒng)的機(jī)會(huì)維護(hù)和調(diào)度聯(lián)合優(yōu)化問(wèn)題.Javid等[10]研究了機(jī)會(huì)維護(hù)在基于狀態(tài)的預(yù)防性維護(hù)下的作用效果.Sun等[11]考慮了刀具退化對(duì)質(zhì)量的影響,以系統(tǒng)成本最小化為目標(biāo),建立了多設(shè)備系統(tǒng)的預(yù)防性維護(hù)模型.Radhoui等[12]對(duì)“非完美”生產(chǎn)系統(tǒng)提出了質(zhì)量控制與預(yù)防性維護(hù)的聯(lián)合優(yōu)化策略.Lesage等[13]對(duì)質(zhì)量控制在提高維護(hù)水平中的潛在作用提出了評(píng)價(jià)方法.Panagiotidou等[14]提出了利用休哈特圖(Shewhart chart)來(lái)安排預(yù)防性維護(hù)的模型.Radhoui等[15]綜合考慮質(zhì)量損失和預(yù)防性維護(hù)對(duì)退化系統(tǒng)成本的影響,提出了基于不合格品數(shù)的預(yù)防性維護(hù)觸發(fā)機(jī)制.上述預(yù)防性維護(hù)模型通常未區(qū)分設(shè)備種類(lèi)而采用單一的預(yù)防性維護(hù)策略,將產(chǎn)品的質(zhì)量損失和緩沖區(qū)的容量同時(shí)納入考慮的研究則鮮有報(bào)道.

本文在前期研究[16]的基礎(chǔ)上,以約束理論(theory of constraints, TOC)為基礎(chǔ)，綜合考慮產(chǎn)品的質(zhì)理?yè)p失和緩沖區(qū)的容量，針對(duì)退化系統(tǒng)中不同設(shè)備的“角色”，確定不同的預(yù)防性維護(hù)策略,以實(shí)現(xiàn)在給定任務(wù)期內(nèi)單位運(yùn)行成本的最小化.在此基礎(chǔ)上,以瓶頸設(shè)備的預(yù)防性維護(hù)作為機(jī)會(huì)維護(hù)的決策點(diǎn),建立非瓶頸設(shè)備的動(dòng)態(tài)機(jī)會(huì)維護(hù)模型,實(shí)現(xiàn)成本的進(jìn)一步降低.

1 問(wèn)題描述

根據(jù)TOC可知,瓶頸設(shè)備決定了系統(tǒng)的產(chǎn)出,因此可以將系統(tǒng)作如下假設(shè)：瓶頸設(shè)備的上游機(jī)器為非能力約束資源(non-capacity constraint resources, NCCR),視為供應(yīng)機(jī)M1；瓶頸設(shè)備及其后面的機(jī)器為能力約束資源(capacity constraint resources, CCR),視為瓶頸機(jī)M2.退化系統(tǒng)包括供應(yīng)機(jī)和瓶頸機(jī)以及兩者之間的緩沖區(qū),如圖1所示.當(dāng)緩沖區(qū)未滿時(shí),供應(yīng)機(jī)以速率p將原材料加工為半成品,存入緩沖區(qū),待其滿后,速率保持與瓶頸機(jī)的速率一致；瓶頸機(jī)以速率d從緩沖區(qū)中取走半成品加工成成品.

為了更好地描述本文提出的維護(hù)建模方法,結(jié)合生產(chǎn)實(shí)際,作出如下假設(shè).1)緩沖區(qū)的最大容量為Bmax,單位產(chǎn)品的庫(kù)存成本率為ch,缺貨成本率為cs.2)兩臺(tái)設(shè)備的狀態(tài)都隨使用時(shí)間而退化,因此在每個(gè)時(shí)期末需要對(duì)產(chǎn)品質(zhì)量和設(shè)備狀態(tài)進(jìn)行檢測(cè),以確定本階段產(chǎn)品質(zhì)量以及下一時(shí)間段內(nèi)的生產(chǎn)和維護(hù)決策,檢測(cè)可以即時(shí)完成.3)系統(tǒng)的初始狀態(tài)為全新,各設(shè)備的故障率hn(t)服從威布爾分布W[βn,ηn],當(dāng)設(shè)備狀態(tài)達(dá)到或超過(guò)臨界點(diǎn)時(shí)則設(shè)備發(fā)生故障,故障發(fā)生后立即采用“小修”模式維修,且“修復(fù)如舊”,小修成本率為cn,cm,其中n=1,2(1為供應(yīng)機(jī),2為瓶頸機(jī)).4)由于M1是NCCR,為了方便維護(hù),采用固定周期的預(yù)防性維護(hù)和機(jī)會(huì)維護(hù)；M2是CCR,為保證其可靠性,采用基于設(shè)備可靠度的預(yù)防性維護(hù)策略；維護(hù)成本率為cn,pm,且cn,pm

圖1 帶緩沖區(qū)的雙機(jī)系統(tǒng)模型Fig.1 Model of two machines system with buffer

2 問(wèn)題建模

2.1 質(zhì)量損失

實(shí)際生產(chǎn)中,設(shè)備狀態(tài)的退化(如：刀具磨損等)會(huì)造成加工品的規(guī)格參數(shù)波動(dòng),并且隨著設(shè)備退化,這種波動(dòng)會(huì)更大，且這種波動(dòng)會(huì)造成產(chǎn)品質(zhì)量損失.根據(jù)田口質(zhì)量損失公式[17],質(zhì)量損失函數(shù)可表述為

G(m)=K(m-m0)2.

(1)

式中：K為不依賴(lài)m的質(zhì)量損失函數(shù)系數(shù),m為產(chǎn)品質(zhì)量的實(shí)測(cè)值,m0為產(chǎn)品質(zhì)量的目標(biāo)值.

為了描述產(chǎn)品質(zhì)量特性與設(shè)備狀態(tài)間的關(guān)系,在文獻(xiàn)[11]的基礎(chǔ)上,結(jié)合本文設(shè)備狀態(tài)的描述形式,構(gòu)造兩者間的關(guān)系函數(shù)如下:

mj(τ)=α[1-exp (-S(τ)]+m0+δ.

(2)

式中：mj(τ)為τ階段第j個(gè)產(chǎn)品的質(zhì)量；α為影響系數(shù)；S(τ)表示τ時(shí)設(shè)備狀態(tài)；δ是未納入模型的噪音,且δ～N(0,σ2).若設(shè)備在某一時(shí)間段[τi,τi+1]內(nèi)的產(chǎn)量為Q(τi),則可求該時(shí)間段內(nèi)的質(zhì)量損失為

(3)

2.2 瓶頸機(jī)維護(hù)建模

根據(jù)假設(shè)3)和4),當(dāng)M2的可靠度達(dá)到預(yù)定閾值Rpm時(shí)需要對(duì)其進(jìn)行維護(hù).可靠性方程為

(4)

式中：t為時(shí)間,T2,l為M2的第l個(gè)維護(hù)周期.在τ時(shí)刻,設(shè)備的可靠度函數(shù)為

在實(shí)際生產(chǎn)中，一方面設(shè)備隨役齡的增加故障 率會(huì)逐漸提高，另一方面預(yù)防性維護(hù)通常都“修復(fù)非 新”．為了綜合這兩方面的考慮，引入役齡遞減因子 a和故障率遞增因子b，則瓶頸設(shè)備的故障率公式 h2(l)可表示為

根據(jù)假設(shè)2)，在每個(gè)時(shí)期末的檢測(cè)會(huì)根據(jù)設(shè)備 的狀態(tài)作出下一時(shí)期的生產(chǎn)與維護(hù)決策，變量的表 示如下：

(7)

(8)

式中：X(τ)表示時(shí)刻τ的生產(chǎn)決策,U(τ)表示時(shí)刻τ的維護(hù)決策.由此,在任意時(shí)刻τI,瓶頸機(jī)的狀態(tài)可以描述為

(1-X2(τi))[ΔsU2(τi)+(1-U2(τi))S2(τk)]}.

(9)

式中：Δs是單位時(shí)間段內(nèi)的退化量.

由假設(shè)4),當(dāng)R(τI)≤Rpm時(shí),需要進(jìn)行預(yù)防性維護(hù).若當(dāng)前τI為維護(hù)起始時(shí)時(shí)刻,維護(hù)時(shí)長(zhǎng)為tpm,則滿足

(10)

(11)

其中，式(10)為生產(chǎn)約束,表示維護(hù)階段不進(jìn)行生產(chǎn)；式(11)為維護(hù)約束,表示該階段為預(yù)防性維護(hù).

當(dāng)R(τI)>Rpm且當(dāng)前狀態(tài)S2(τI)大于失效閾值S2,bd時(shí),進(jìn)行“小修”,即故障維修(correctivemaintenance,CM),維護(hù)時(shí)長(zhǎng)為tcm,并滿足

(12)

(13)

其中，式(12)為生產(chǎn)約束,表示“小修階段”不進(jìn)行生產(chǎn)；式(13)為維修約束,表示該階段為小修.

由以上策略可知預(yù)防性維護(hù)的間隔期不一定相等,因此,模型以整個(gè)加工周期內(nèi)的單位運(yùn)行成本最小化為目標(biāo).所考慮的成本因素有質(zhì)量損失、維護(hù)成本和懲戒成本,計(jì)算方法如下.

(14)

(15)

式中：Δτ為[τi,τi+1]的時(shí)長(zhǎng),本文取Δτ=1.式(14)為產(chǎn)量約束,保證瓶頸機(jī)的產(chǎn)量不會(huì)超過(guò)期初庫(kù)存量與本期供應(yīng)機(jī)產(chǎn)量之和.式(15)為產(chǎn)能約束,保證產(chǎn)量不超出瓶頸機(jī)的能力.總的質(zhì)量損失為

(16)

(17)

3)懲戒成本：瓶頸機(jī)決定了整個(gè)系統(tǒng)的產(chǎn)出,而實(shí)際產(chǎn)出必然低于理想值,為了盡量縮小差距,施以懲戒成本.假設(shè)單位成本為c2,th,則整個(gè)任務(wù)周期內(nèi)的懲罰成本為

(18)

此外,當(dāng)供應(yīng)機(jī)處于維護(hù)狀態(tài)且緩沖區(qū)內(nèi)的在制品消耗殆盡時(shí),會(huì)導(dǎo)致瓶頸停產(chǎn),發(fā)生缺貨.缺貨成本在本節(jié)不予考慮,將在緩沖區(qū)建模中予以體現(xiàn).

2.3 供應(yīng)機(jī)維護(hù)建模

2.3.1 固定周期的計(jì)劃維護(hù) 對(duì)于供應(yīng)機(jī),采用固定周期的預(yù)防性維護(hù)策略.假設(shè)維護(hù)周期為T(mén)1,pm,整個(gè)任務(wù)周期可劃分為N次.假設(shè)前一次維護(hù)結(jié)束時(shí)刻為τk.

(19)

式(19)約束了預(yù)防性維護(hù)階段不進(jìn)行生產(chǎn).

(20)

式(20)約束了“小修”階段不進(jìn)行生產(chǎn).

基于以上維護(hù)策略,供應(yīng)機(jī)在任務(wù)期內(nèi)發(fā)生的成本如下.

1)質(zhì)量損失：每個(gè)時(shí)期τ內(nèi)的產(chǎn)量為

(21)

(22)

(23)

3)懲戒成本：當(dāng)緩沖區(qū)已滿且瓶頸機(jī)處于維護(hù)時(shí),供應(yīng)機(jī)將發(fā)生閑置,造成能力上的浪費(fèi).若單位能力懲罰成本為c1,d,則總的能力懲罰為

(24)

E(ccm)=c1,cmΔtcm=

(25)

式中：“new”為新周期,“old”為原周期,Δtcm為小修的期望總時(shí)長(zhǎng).

期望節(jié)省的質(zhì)量損失為

(26)

期望節(jié)省的供應(yīng)機(jī)閑置損失與瓶頸機(jī)饑餓成本的總和為

(27)

式中：第一個(gè)大括號(hào)內(nèi)的式子表示進(jìn)行機(jī)會(huì)維護(hù)的成本,第二個(gè)大括號(hào)內(nèi)的式子表示按原計(jì)劃維護(hù)的成本.

此外,由于供應(yīng)機(jī)提前維護(hù),造成了設(shè)備剩余可用能力的浪費(fèi),設(shè)單位懲罰成本為cw,則總的能力浪費(fèi)為

(28)

由式(25)～(28)可得，在τb時(shí)刻若進(jìn)行機(jī)會(huì)維護(hù)的期望成本節(jié)余函數(shù)為

(29)

2.4 緩沖區(qū)建模

假設(shè)單位產(chǎn)品庫(kù)存成本率為ch,缺貨成本為cs,則在[τi,τi+1]內(nèi)的緩沖區(qū)容量可表示為

B(τi)=B(τi-1)+p(1-|X1(τi)-1|)Δτ-

dΔτ(1-|X2(τi)-1|) ，

(30)

B(τi)≤Bmax.

(31)

在此,引入二進(jìn)制輔助變量δ(τ),用1表示發(fā)生庫(kù)存成本,0表示發(fā)生缺貨成本,即

(32)

則[τi,τi+1]以及整個(gè)任務(wù)期內(nèi)的緩沖區(qū)成本可分別表示為

cb(τi)= 0.5chδ(τi)|B(τi)-B(τi-1)|+

cs(1-δ(τi))|B(τi)| ,

(33)

(34)

G2(Tlen)+C2,m+C2,th+Cb].

(35)

約束：式(1)～(34)并且0

3 數(shù)值分析

圖2 設(shè)備狀態(tài)與質(zhì)量損失間的關(guān)系Fig.2 Relationship of machine state and quality loss

如圖2所示為質(zhì)量特性與設(shè)備狀態(tài)間的函數(shù)關(guān)系,結(jié)果如圖2所示.圖中,S為狀態(tài)值,G為質(zhì)量損失.由圖2可知,質(zhì)量特性隨設(shè)備狀態(tài)退化而劣化,表現(xiàn)為質(zhì)量損失的增加,而當(dāng)設(shè)備狀態(tài)恢復(fù)時(shí),質(zhì)量特性也隨之恢復(fù).

3.1 供應(yīng)機(jī)維護(hù)周期T1的分析

圖3 各方案(計(jì)劃維護(hù)、機(jī)會(huì)維護(hù)、正常運(yùn)行)下維護(hù)周期對(duì)產(chǎn)量的影響Fig.3 Effects of preventive maintenance (PM) period on output under policies of scheduled maintenance, optimistic maintenance and running without maintenance

如圖3所示為在確定緩沖區(qū)容量和瓶頸機(jī)可靠度(Bmax=10,R=0.85)時(shí),在不同的維護(hù)策略下,供應(yīng)機(jī)維護(hù)周期對(duì)系統(tǒng)產(chǎn)出O的影響.圖中“正常運(yùn)行”表示瓶頸機(jī)一直正常運(yùn)行.整體上,系統(tǒng)產(chǎn)量隨供應(yīng)機(jī)維護(hù)周期的延長(zhǎng)先增加后降低,最后在低水平上趨于穩(wěn)定.分析其原因,瓶頸機(jī)在維護(hù)過(guò)于頻繁時(shí)得不到足夠的輸入,導(dǎo)致低產(chǎn)出；而隨著維護(hù)周期的延長(zhǎng),由于供應(yīng)機(jī)的過(guò)多失效導(dǎo)致系統(tǒng)產(chǎn)出降低.這一結(jié)果也與前人的分析相一致[4,6],從而驗(yàn)證了所建模型及方法的正確性.由圖3可知,當(dāng)緩沖區(qū)容量不能在供應(yīng)機(jī)失效時(shí)滿足瓶頸機(jī)的需求時(shí),對(duì)供應(yīng)機(jī)進(jìn)行動(dòng)態(tài)機(jī)會(huì)維護(hù)可以節(jié)省停機(jī)時(shí)間,從而提高系統(tǒng)產(chǎn)出.

圖4 各方案(計(jì)劃維護(hù)、機(jī)會(huì)維護(hù)、正常運(yùn)行、事后維護(hù))下,維護(hù)周期對(duì)單位成本的影響Fig.4 Effects of PM period on average cost under polices of scheduled maintenance, opportunistic maintenance, running without maintenance and breakdown maintenance

圖5 緩沖區(qū)容量對(duì)各類(lèi)成本(總成本、總?cè)必洺杀尽⒖値?kù)存成本)的影響Fig.5 Effects of buffer size on total cost, total shortage cost and total holding cost

3.2 緩沖區(qū)最大容量Bmax分析

緩沖區(qū)容量對(duì)系統(tǒng)成本的影響主要作用于庫(kù)存成本和缺貨成本.由圖5可知,圖中c表示單位時(shí)間內(nèi)的成本,隨著緩沖區(qū)最大容量的提高,庫(kù)存成本相應(yīng)提高.最后趨于穩(wěn)定的原因是周期性預(yù)防性維護(hù)的實(shí)施使得緩沖區(qū)尚未達(dá)到最大值.缺貨成本逐漸降低,最后趨近于0,而總成本也逐漸降低,最后趨于穩(wěn)定.圖6則反映了緩沖區(qū)在一定程度上可提高系統(tǒng)產(chǎn)出.

圖6 緩沖區(qū)容量對(duì)系統(tǒng)產(chǎn)出的影響Fig.6 Effect of buffer size on system output

3.3 瓶頸機(jī)可靠性R分析

瓶頸機(jī)的可靠性直接影響系統(tǒng)的產(chǎn)出,但若為了提高可靠度而過(guò)度維護(hù),不僅增加維護(hù)成本,也占用生產(chǎn)時(shí)間,從而導(dǎo)致產(chǎn)出降低.由圖7可知,隨著可靠度的提高,PM成本急速增加,CM成本和質(zhì)量損失相應(yīng)降低,但總成本先降低后升高.這也說(shuō)明瓶頸機(jī)的可靠度并非越高越好.圖例中,單位運(yùn)行成本最低時(shí)為22.63元,對(duì)應(yīng)可靠度為0.83；而圖8反映了產(chǎn)出隨可靠度的變化曲線,最大產(chǎn)出為23 151件,其對(duì)應(yīng)可靠度為0.90,說(shuō)明兩目標(biāo)下的最優(yōu)可靠度可能相異.機(jī)會(huì)維護(hù)的實(shí)施使得最大產(chǎn)出提高為23 636件,對(duì)應(yīng)的可靠度為0.89.

圖7 瓶頸機(jī)可靠度對(duì)各類(lèi)成本(總成本、預(yù)防維護(hù)成本、小修成本、質(zhì)量損失)的影響Fig.7 Effects of realiability on total cost, PM cost, CM cost and quality loss

圖8 2種方案(計(jì)劃維護(hù)與機(jī)會(huì)維護(hù))下,瓶頸機(jī)可靠度對(duì)產(chǎn)出的影響Fig.8 Effects of realiability on output under scheduled maintenance and opportunistic maintenance

3.4 計(jì)劃維護(hù)與機(jī)會(huì)維護(hù)策略的對(duì)比

表1 計(jì)劃維護(hù)和機(jī)會(huì)維護(hù)方案下最優(yōu)解組合對(duì)比

Tab.1 Comparison of optimal combinations under scheduled maintenance and opportunistic maintenance

最優(yōu)解組合 計(jì)劃維護(hù) 機(jī)會(huì)維護(hù) RBmax/件T1/dC/元O/件C/元O/件0.9843822.972409722.0625.6920.9536720.412483219.6226.2610.9035824.162405423.8725.5160.8539829.242318828.0124.6520.8031833.422210435.1223.148

當(dāng)[T1,Bmax,R]的值為[7,36,0.95]時(shí),單位運(yùn)行成本最低值20.41元,產(chǎn)出最高值24 832件；而使用動(dòng)態(tài)機(jī)會(huì)維護(hù)策略,最低成本降為19.62元,系統(tǒng)產(chǎn)出增加為26.261件.

4 結(jié) 論

(1)產(chǎn)品的質(zhì)量損失在成本方面占有重要部分,而設(shè)備的狀態(tài)對(duì)產(chǎn)品質(zhì)量具有直接影響.

(2)維護(hù)周期長(zhǎng)短、緩沖區(qū)大小以及預(yù)防性維護(hù)閾值對(duì)系統(tǒng)的表現(xiàn)具有綜合的影響,需要權(quán)衡決策.

(3)區(qū)分對(duì)待瓶頸設(shè)備與非瓶頸設(shè)備的綜合預(yù)防性維護(hù)模型比傳統(tǒng)不做區(qū)分的維護(hù)更加有效.

(4)基于TOC提出的成本節(jié)余函數(shù)可以用于確定機(jī)會(huì)維護(hù)的實(shí)施,且機(jī)會(huì)維護(hù)策略能夠很好地降低成本、提高產(chǎn)出.

(5)蒙特卡洛仿真可以解決模型中的隨機(jī)失效問(wèn)題,進(jìn)而可利用數(shù)值迭代算法對(duì)問(wèn)題求解.

本文在考慮質(zhì)量損失的條件下研究了退化系統(tǒng)的預(yù)防性維護(hù)問(wèn)題,對(duì)刀具車(chē)床、加工中心等設(shè)備的維護(hù)具有一定的參考作用.未來(lái)可進(jìn)一步探究質(zhì)量與維護(hù),以及多產(chǎn)品系統(tǒng)的維護(hù)問(wèn)題.

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Maintenance modeling for deteriorating system considering quality loss

ZHOU Bing-hai,LIU Zi-long

(CollegeofMechanicalEngineering,TongjiUniversity,Shanghai201804,China)

An optimization decision model was built to minimize operation cost per unit time, thus to efficiently solve the preventive maintenance (PM) problem of deteriorating systems. This model considered the production quality loss and influence of buffer, where “two machines with an intermediate buffer” system model was taken as research object. First, a function relation between system status and quality loss was constructed based on the Taguchi quality loss theory. Next, the condition-based PM policy and time-based PM policy were adopted for the bottleneck machines and non-bottleneck machines, respectively. Then, an opportunistic maintenance (OM) policy was proposed based on the theory of constrains (TOC). According to TOC and using PM of bottleneck machines as decision point of OM, the expected cost saving function was used to determine whether to operate OM for non-bottleneck machines or not. Finally, the iterative algorithm was applied to find the optimal decision combinations; Monte Carlo method was applied to analyze the results. Results show that the proposed model is feasible and effective; OM policy is better for saving cost and improving output compared with scheduled maintenance.

deteriorating system; quality loss; buffer size; opportunistic maintenance; preventive maintenance; Monte Carlo method

2015-11-13.

國(guó)家自然科學(xué)基金資助項(xiàng)目(61273035，71471135).

周炳海(1965—),男,教授,博導(dǎo).從事離散制造系統(tǒng)維護(hù)、調(diào)度與仿真研究.ORCID： 0000-0002-6599-9033. E-mail: bhzhou@#edu.cn

10.3785/j.issn.1008-973X.2016.12.004

TP 391

A

1008-973X(2016)12-2270-07