外文翻譯--當(dāng)檢驗(yàn)檢測(cè)失敗時(shí)基于恒基區(qū)間風(fēng)險(xiǎn)的一個(gè)多級(jí)層次時(shí)間延遲來(lái)預(yù)防維修檢查模型【中英文文獻(xiàn)譯文】
外文翻譯-當(dāng)檢驗(yàn)檢測(cè)失敗時(shí)基于恒基區(qū)間風(fēng)險(xiǎn)的一個(gè)多級(jí)層次時(shí)間延遲來(lái)預(yù)防維修檢查模型【中英文文獻(xiàn)譯文】,中英文文獻(xiàn)譯文,外文,翻譯,檢驗(yàn),檢修,檢測(cè),失敗,基于,區(qū)間,風(fēng)險(xiǎn),一個(gè),多級(jí),層次,時(shí)間,延遲,預(yù)防,維修,檢查,模型,中英文,文獻(xiàn),譯文
當(dāng)檢驗(yàn)檢測(cè)失敗時(shí),基于恒基區(qū)間風(fēng)險(xiǎn)的一個(gè)多級(jí)層次時(shí)間延遲來(lái)預(yù)防維修檢查模型G. B. WILLIAMS and R. S. HIRANI (Received 17 November 1995)摘要:本文是用時(shí)間延遲的概念來(lái)描述模型是其中要素之一,它決定了對(duì)于一個(gè)隨機(jī)惡化的多個(gè)子系統(tǒng)最佳的檢測(cè)維修方法。子系統(tǒng)的惡化被認(rèn)為是一個(gè)非遞減的半馬爾可夫過(guò)程,其中的狀態(tài)是各個(gè)層次在宣布檢查檢測(cè)未解決故障失敗的標(biāo)志。重點(diǎn)被放在持續(xù)可得到的和減少的產(chǎn)量損失,惡化率和后續(xù)子系統(tǒng)的故障上。在這方面,檢測(cè)被列為一種對(duì)于在每個(gè)檢測(cè)區(qū)間內(nèi)保持故障風(fēng)險(xiǎn)恒定的方法。兩套數(shù)學(xué)模型和軟件已經(jīng)發(fā)展,得到的結(jié)論是采用兩個(gè)最優(yōu)的標(biāo)準(zhǔn)。這些結(jié)論是通過(guò)用仿真模型軟件包進(jìn)行仿真實(shí)驗(yàn)驗(yàn)證。1997年Elsevier科學(xué)有限公司1緒論生產(chǎn)系統(tǒng)可以被看作是多態(tài)復(fù)雜的系統(tǒng),隨機(jī)惡化。從維護(hù)的觀點(diǎn)來(lái)看其零部件,可分為五個(gè)特點(diǎn)不同的子系統(tǒng)。因此,獨(dú)立的最佳限制主要維護(hù)的政策已經(jīng)提出1-5。本文討論隨機(jī)惡化的子系統(tǒng),其目前的狀態(tài)是自公布和檢驗(yàn)檢測(cè),待故障,過(guò)渡態(tài),它的地位和過(guò)渡時(shí)期的標(biāo)志。延遲時(shí)間的概念首先是由Christer提出的6,視為一個(gè)兩階段的過(guò)程中失敗的機(jī)制。故障啟動(dòng)子系統(tǒng),并成為突發(fā)的時(shí)刻,當(dāng)檢測(cè)時(shí)可以進(jìn)行識(shí)別。如果沒(méi)有故障,故障子系統(tǒng)進(jìn)一步推遲,Christer稱(chēng)為故障延遲時(shí)間。使用這個(gè)概念的研究已經(jīng)開(kāi)展7-10,6,11-18,在兩個(gè)等級(jí)的單一或便服組件7,8,18系統(tǒng),為維護(hù)建模完善和不完善的檢查間隔檢查常量或變量11,修理恢復(fù)系統(tǒng),同時(shí)考慮到主觀和客觀的7,8,18數(shù)據(jù)。它實(shí)際上似乎是不合理的,要考慮到其原始狀態(tài)作為一個(gè)系統(tǒng)的重建維修19和不斷的檢查間隔,可能沒(méi)有一個(gè)恒定的失敗的風(fēng)險(xiǎn),導(dǎo)致不一致的可用性,也將導(dǎo)致生產(chǎn)率和高庫(kù)存,勞動(dòng)力和生產(chǎn)成本等的變化5。因此,延遲時(shí)間的概念在這里延伸到多狀態(tài)子系統(tǒng)的維修,失敗風(fēng)險(xiǎn)的每次檢查間隔恒是常數(shù)20,21。2數(shù)學(xué)模型對(duì)一個(gè)子系統(tǒng)的惡化過(guò)程與半馬爾可夫過(guò)程的狀態(tài)空間狀態(tài)的描述是依靠系統(tǒng)惡化的程度以及過(guò)程性質(zhì)對(duì)轉(zhuǎn)變的限制。子系統(tǒng)目前的狀態(tài)是自我宣布,而檢測(cè)則是檢驗(yàn)宣布失敗的標(biāo)志。維護(hù)方法選擇是一個(gè)偽控制限制方法 ,維修動(dòng)作是由狀態(tài)確定的,是一組沒(méi)有修復(fù)動(dòng)作的狀態(tài),其互補(bǔ)的集是一套的,這就要求一些更好的狀態(tài)集的一個(gè)子系統(tǒng)的維修或更換。每當(dāng)檢驗(yàn)檢測(cè)待下次檢查前失敗,條件預(yù)防性維護(hù)(OCPM)瞬間完成。OCPM不改變目前的過(guò)渡態(tài)和過(guò)渡時(shí)間,但過(guò)渡的可能性降低到一個(gè)非功能狀態(tài)。 在數(shù)學(xué)上,這樣的偽控制限制政策 (其中k* 既表示函數(shù)狀態(tài) ,又代表非函數(shù)狀態(tài) )可以表示為:令子系統(tǒng)進(jìn)入在參考狀態(tài) ,或?qū)е聲r(shí)間 的 概率繼承與制造故障,或者以后在使用中因概率 引起的故障,從而造成其向任意高狀態(tài) 的轉(zhuǎn)變,伴隨著概率P(i,j),此時(shí)的過(guò)渡狀態(tài)可能是功能性 和非功能 的聯(lián)合概率密度函數(shù)的概率。聯(lián)合概率密度函數(shù)(PDF)代表了這些故障,此后的過(guò)渡進(jìn)程f(*)中將稱(chēng)之為繼承故障(IF)和惡化的故障(DF)。在T(i,L),T(i,2),.,和T(i,N)時(shí)間點(diǎn)遍歷n次以對(duì)獨(dú)立的故障和過(guò)渡態(tài)的性質(zhì)進(jìn)行檢查,鑒于這一進(jìn)程已經(jīng)開(kāi)始在狀態(tài)i(圖1)中給出,在這樣的檢測(cè)中,過(guò)渡狀態(tài)A(*)的預(yù)期風(fēng)險(xiǎn)之間的任何兩個(gè)連續(xù)視察是連續(xù)的。檢查點(diǎn)(恒基區(qū)間的風(fēng)險(xiǎn))圖1:初始狀態(tài)j= 1,2的過(guò)渡過(guò)程的聯(lián)合概率密度函數(shù)圖2:繼承故障延時(shí)時(shí)間的概率密度函數(shù)和預(yù)期過(guò)渡過(guò)渡子系統(tǒng)的概率,其預(yù)期的時(shí)間,在第m次檢查間隔T(i,m),T(i,m+1)(圖2),存在下面一組條件,下文均稱(chēng)之為設(shè)置條件,(1)在時(shí)間,子系統(tǒng)已經(jīng)進(jìn)入狀態(tài)i,其中包含的遺傳缺陷的概率(2)在一個(gè)小的時(shí)間間隔(x,x+x)內(nèi),該事件的概率為(3)該子系統(tǒng)將使下一個(gè)過(guò)渡狀態(tài)轉(zhuǎn)換到狀態(tài)j,分別為5:且又且子系統(tǒng)的過(guò)渡概率和其預(yù)期的時(shí)間(圖3),在第m次檢測(cè)的時(shí)間間隔,提供了下面的一組條件,此后將設(shè)置2個(gè)條件(1)在時(shí)間,子系統(tǒng)已經(jīng)進(jìn)入狀態(tài)i,(2) 故障將在在第l檢查間隔T(I,l),T(I,l +1)被測(cè)試,在一個(gè)小的時(shí)間間隔y,y+y),其概率為g(i,j,y)y,在一個(gè)小的時(shí)間間隔內(nèi),該事件的概率為(3)子系統(tǒng)將過(guò)渡到j(luò)狀態(tài),分別為:又其中,且圖3:預(yù)期故障過(guò)渡時(shí)間、啟動(dòng)時(shí)間、延遲時(shí)間和檢查錯(cuò)誤惡化故障時(shí)間概率密度函數(shù)因此,對(duì)于一個(gè)初始狀態(tài),預(yù)計(jì)總?;^(guò)渡區(qū)間的風(fēng)險(xiǎn)函數(shù)A(m),不論第m次間隔的狀態(tài)和性質(zhì),是:把子系統(tǒng)的條件或狀態(tài)看作具有多個(gè)參數(shù)的函數(shù),其中一些參數(shù)可以直接測(cè)量,而另一些卻不能,因此反映已經(jīng)存在或啟動(dòng)的故障的參數(shù),它能衡量故障存在的概率。因此,不完善的檢測(cè)只反映了故障發(fā)生的概率,一旦進(jìn)行故障檢測(cè),過(guò)渡狀態(tài)的狀態(tài)概率,其過(guò)渡時(shí)間誤差為,因此,在第m次對(duì)過(guò)渡時(shí)間估測(cè)的錯(cuò)誤的上限及下限的約束,是:又其中,且 關(guān)于過(guò)渡時(shí)間的檢驗(yàn)評(píng)估,有兩種形式的錯(cuò)誤:(1)檢驗(yàn)的時(shí)候正在失效,但還沒(méi)有完全失效(其中,IF概率為,DF概率為)(2)評(píng)定為正常,直到下一次檢測(cè),然后失效(IF概率為,DF概率為),這些概率可以作為初始狀態(tài)i和過(guò)渡狀態(tài)j的函數(shù),在即將到來(lái)的檢查期間的過(guò)渡概率,其寬度(T(i,m),T(i,m+1),故障間隔。由于政策決策的經(jīng)濟(jì)影響是錯(cuò)誤性質(zhì)的函數(shù),因此,檢驗(yàn)的次數(shù)及錯(cuò)誤次數(shù),過(guò)渡的概率和時(shí)間,政策決策的性質(zhì)及其結(jié)果,檢查的時(shí)間間隔進(jìn)一步分為子間隔(圖2和3)。在這種情況下,當(dāng)子系統(tǒng)在時(shí)間間隔 ,和, 內(nèi)包含繼承性錯(cuò)誤時(shí),其概率和預(yù)期時(shí)間分別為,和,子系統(tǒng)的過(guò)渡時(shí)間及其概率,當(dāng)子系統(tǒng)發(fā)生故障時(shí),假設(shè)存在2個(gè)條件:,和及,和5。假設(shè)滿(mǎn)足條件1和條件2,在第m次檢測(cè)時(shí),OCPM的概率和分別為:且,對(duì)于且;對(duì)于,且其中,且其中,且其中, ,且其中,且;其中,且;其中,+1m=n-1且假使花費(fèi)為恒定的比率,單位的生產(chǎn)時(shí)間,由于子系統(tǒng)不可用狀態(tài)i,獨(dú)立的過(guò)渡狀態(tài)j的為其不可用的原因。檢測(cè)費(fèi)用通過(guò)分期付款,其中,第v次分期付款相當(dāng)于,是的一部分。在時(shí)間進(jìn)行付款,從檢測(cè)開(kāi)始的時(shí)間計(jì)起。因此,預(yù)期在檢查時(shí)所支付的檢查,加上罰款單步成本的凈現(xiàn)值(NPV)是:其中,且令OCPM花費(fèi)分期支付,第v次的分期付款相當(dāng)于,是的一部分,在時(shí)間即故障被檢測(cè)出開(kāi)始,有:其中,且最低維修率,其中,其時(shí)間花費(fèi)為,通過(guò)分期付款,第v次的付款相當(dāng)于,是總成本的一部分,這是從非功能狀態(tài)過(guò)渡到預(yù)期的時(shí)間再加上通過(guò)檢查時(shí)間。是:其中,且其中且如果子系統(tǒng)在i狀態(tài)做出轉(zhuǎn)變到任意非函數(shù)的狀態(tài),或者是函數(shù)狀態(tài),OCPM之后,在保證時(shí)間之前5:因此,單步的時(shí)間,預(yù)計(jì)總檢查,OCPM,和最小利用生產(chǎn),維修,加時(shí),不論過(guò)渡狀態(tài)和故障的性質(zhì),考慮到初始狀態(tài)是狀態(tài)i是:預(yù)計(jì)累計(jì)檢驗(yàn)成本的凈現(xiàn)值,預(yù)計(jì)成本OCPM,預(yù)計(jì)成本減去子系統(tǒng)保修恢復(fù)之后,是:其中,這里目前的狀態(tài)和自我的地位是確定的,而檢查確定掛起失敗的標(biāo)志,和OCPM改變未來(lái)過(guò)渡的過(guò)渡期和過(guò)渡時(shí)間不變的概率只有狀態(tài)。因此,在作出第一次轉(zhuǎn)變之前對(duì)生產(chǎn)有用的總的時(shí)間是;其中,且因此,檢驗(yàn)累計(jì)消耗的時(shí)間,OCPM以及最少維修時(shí)間是:其中,且無(wú)論子系統(tǒng)進(jìn)入任何狀態(tài),其狀態(tài)將轉(zhuǎn)變至另一更好狀態(tài)=作為其方式。且又其中,且同時(shí)其中,且其中,且Alpha由于OCPM減少過(guò)渡的概率沒(méi)有任何非功能狀態(tài)轉(zhuǎn)變的過(guò)渡期和過(guò)渡狀態(tài)的時(shí)間,從而有效的概率作為一個(gè)過(guò)渡狀態(tài)的子系統(tǒng)任何非功能性和結(jié)果OCPM功能狀態(tài)和如下:又且其中,由于優(yōu)化的標(biāo)準(zhǔn)可能是狀態(tài)在該子功能系統(tǒng)修理或更換,檢查的時(shí)間間隔的數(shù)量,控制狀態(tài),最佳的購(gòu)買(mǎi)狀態(tài),最優(yōu)控制狀態(tài)月和最佳數(shù)量檢查間隔是指那些結(jié)果在預(yù)期的最大可用性子系統(tǒng),或最低成本率/單位的周期:且其中,其中,且,其中,3結(jié)果及推論子系統(tǒng)被認(rèn)為是常服,國(guó)家多組分子系統(tǒng)(或便服,狀態(tài)常服維單組分子系統(tǒng)),惡化的過(guò)程是一個(gè)有限狀態(tài)空間的半馬爾可夫過(guò)程。這些狀態(tài)在一個(gè)非重疊的同等數(shù)量的缺陷或惡化的累積水平方面,和過(guò)程的性質(zhì)限制較高的狀態(tài)發(fā)生轉(zhuǎn)換。子系統(tǒng)目前的狀態(tài)是自我宣布,在過(guò)渡狀態(tài),其狀態(tài)和過(guò)渡時(shí)間,而檢驗(yàn)檢測(cè)掛起失敗的標(biāo)志。重點(diǎn)是放在一個(gè)子系統(tǒng)的持續(xù)可用性,在這方面的檢查,在這樣一種方式失敗的風(fēng)險(xiǎn),每次檢查間隔是恒定的。為了驗(yàn)證數(shù)學(xué)模型的開(kāi)發(fā),并提供一個(gè)合理的準(zhǔn)確的決策機(jī)程序工具,它表明在合理時(shí)間內(nèi)的最佳決定,另一個(gè)MAIN-3和SIM-3,被寫(xiě)在Turbo Pascal上。這些方案有一個(gè)內(nèi)置的規(guī)定產(chǎn)生的所有可供選擇的政策。主要使用歷史數(shù)據(jù)預(yù)計(jì),而SIM-3采用基于歷史數(shù)據(jù)分布的自我生成的模擬數(shù)據(jù)。每個(gè)程序運(yùn)行時(shí)計(jì)算最優(yōu)決策的政策:(一)購(gòu)買(mǎi)的理想狀態(tài),(二)在最佳控制狀態(tài),(三)每個(gè)州E X最佳檢查進(jìn)度和高(四)決策功能狀態(tài)。一般的決策是:(a)伊恩執(zhí)行確定的時(shí)間表,并保持子系統(tǒng)的運(yùn)行,直到它使得過(guò)渡到更高的境界,或檢查,定期檢查前過(guò)渡到一個(gè)非功能狀態(tài),(b)執(zhí)行條件的預(yù)防性維護(hù)時(shí),檢驗(yàn)檢測(cè)下次檢查前的過(guò)渡到一個(gè)非功能狀態(tài),(c)執(zhí)行最少的檢查 Pergamon Int. J. Math. Tools Manufact. Vol. 37, No. 6. pp. 823.836, 1997 1997 Elsevier Science Lid All fights r-erved. Printed in Great Britain 0890-6955/97517.00 + .00 PII: S0890-6955(96)00026-0 A DELAY TIME MULTI-LEVEL ON-CONDITION PREVENTIVE MAINTENANCE INSPECTION MODEL BASED ON CONSTANT BASE INTERVAL RISK-WHEN INSPECTION DETECTS PENDING FAILURE G. B. WILLIAMS and R. S. HIRANIt (Received 17 November 1995) Abstract-The model described in this paper is one of a series, which determines the optimal multi-level inspection-maintenance policy for a stochastically deteriorating multi-state sub-system, using the delay-time concept. The sub-system deterioration is assumed to be a non-decreasing semi-Markov process, where states are self-announced and inspection detects the sign of pending failure. Emphasis is placed on constant availability and reduction of production losses, deterioration rate and subsequent sub-system failure. In this respect, inspection is scheduled in such a way that the risk of failure is a constant for each inspection interval. Two pairs of mathematical models and softwares have been developed, and the policy decisions taken have been based on two criteria for optimisation. These decisions have then been validated by carrying out a simulation exercise using the ProModel simulation package. 1997 Elsevier Science Ltd. 1. INTRODUCTION Production systems can be viewed as multi-state stochastically deteriorating complex sys- tems. Their parts, from a maintenance point of view, can be grouped into five characteristi- cally different sub-systems. Thus, separate optimum multi-level pseudo-control limit main- tenance policies have been proposed 1-5. This paper deals with a gradually deteriorating sub-system, whose present state is self-announced and inspection detects the sign of pend- ing failure, the transition state, its status and the time of transition. A delay-time concept, first introduced by Christer 6, regards the failure mechanism as a two-stage process. A fault initiates in a sub-system and becomes prominent at time y. This can be identified if inspection is carded out at the time. If the fault is not attended to, the faulty sub-system subsequently changes its state after some further interval h, which Christer called the failure delay time. Research has been carded out 7-10, 6, 11-18 using this concept in maintenance mod- elling for two-state single- or multi-component 7, 8, 18 systems, where inspection inter- vals for perfect and/or imperfect inspections are taken as constant or variable 11, and repair restores the system, taking into account subjective and objective 7, 8, 18 data. It would seem practically unreasonable to consider repair as a renewal of a system to its original condition 19 and constant inspection intervals may not have a constant risk of failure, which results in inconsistent availability, and hence a variable production rate and high inventory, labour and production costs 5. Thus, the concept of delay time is here extended to multi-level maintenance of a multi-state sub-system, where inspections are scheduled in such a way that the risk of failure is constant for each inspection interval 20, 21. 2. MATHEMATICAL MODEL Let the deterioration process of a sub-system be a semi-Markov process with state space = 1, 2 . ,L, where states are described by the level of deterioration and the nature of the process limits the occurrence of transitions to higher states. The present state of the sub-system is self-announcing, whereas inspection detects the sign of pending failure. The tSchool of Manufacturing and Mechanical Engineering, University of Birmingham, Birmingham B 15 2Tl, U.K. 823 824 G.B. Williams and R. S. Hirani maintenance policy selected is a pseudo-control limit policy 6(), where maintenance action is determined by the control state/3. Let N= 1, 2 . /3- 1 be a set of states which asks for no repair action if they are functional, and minimal repair when they are non- functional. Its complementary set R=/3, /3+1 . L is the set of states which calls for repair or replacement of a sub-system to some better state in set pCN. Whenever inspection detects pending failure before the next inspection, on-condition preventive maintenance (OCPM) is performed instantaneously. This OCPM does not change the present and tran- sition states and their transition time, but reduces the probability of transition to a non- functional state. Mathematically, such a pseudo-control limit policy 6(k.) (where k. rep- resents either functional state kf or non-functional state knf) can be expressed as: I i = k for k./3eN and ieN 8(k.) = ik. for k,-/3eN and ie_CN (1) Let the sub-system be entered in state i eC_N, at reference or lead time TL(i), and inherit manufacturing faults with a probability of Pi(i), or faults may arise later on during use with a probability of 1-Pi(i), and subsequently cause its transition to any higher state j e , with a probability of P(ij), where the transition state j may be functional with a probability of P), and non-functional with a probability of 1-Pj). A joint probability density function (pdf) as a result of these faults, which hereafter will be called inherited faults (IF) and deterioration faults (DF), for the transition process is flo). Let n number of inspections be carried out at an inspection time T(i,1), T(i,2) . and T(i,n), independent of the nature of the faults and transition states, given that process has started in state i (Fig. 1), where these inspections are scheduled in such a way that the expected risk of transition A(o) between any two consecutive inspections is constant. The probability of transition of the sub-system ,(i,j,m) and its expected time (i,j,m), during the mth inspection interval T(i,m), T(i,m+l) (Fig. 2), given that the following set of conditions exists, which hereafter will be called set 1 conditions: (i) the sub-system has entered in state i, at time TL(i), which contains inherited defects with a probability of Inspection points (constant base interval risk) To(i) T(i,2) T(i,5) T(i,6) Tim( T(i, 1) T(i,3) T(i,4) L Fig. 1. Joint probability density functions of the transition process for an initial state j = 1 and transition states j=2(-),j=3(-)andj=4( ). T(i,l) T(i,l + 1) T(i,m) (c3,)l(,j,- ). (,m) Tt(i,m- 1)1 T(i,m + 1) Tt(i,rn)l L 6a(i,m) l z,(i,j,;l,).: Ts(i, j, m) T,(i,m) , (i,j,m- 1) (i,j,m- 1) , Tu(i,m- 1) ,1 Fig. 2.The probability density functions for delay time ( ) and inspection error (- - -) and expected transition times for an inherited fault. A delay time multi-level on-condition preventive maintenance inspection model 825 P(i), (ii) it has delay time in a small interval x, +Ax), the probability of this event being i,j,x)dx, and (iii) the sub-system will make the next transition to state j, respectively, are 5: :T(i.m + 1) al(id.m ) = Pi(i)|r,.m (ij.x)dx (2) and T(i.m + 1) fPi(i) / hd2(ij,x)dx) 3T(i,m) i 2l(ij,m) = -i-, - (3) for l-m-n-1, iN and ijeN. The probability of transition of the subsystem, Al(ij,m,l) and its expected time T(ij,m,l) (Fig. 3), during the ruth inspection interval T(i,m), T(i,m+l), provided the following set of conditions exists, which hereafter will be called set 2 conditions: (i) the sub-system has entered in state i, at time TL(i), (ii) the fault will be initiated within the lth inspection interval T(i,l), T(i,l+l) in a small interval y, y+Ay), with a probability of g(id,y)Ay, has delay time in a small interval y+h, y+h+Ah, the probability of this event being id,h)dh, and (iii) the sub-system will make the next transition to state j, respectively, are 5: A(idml):.r(i.l) IJT(i,m,-y dp(idh)dhlg(iy)dy (4) and T(i.m + l)-y . hdp( id,h )dh. r(,+ ,) |Jlr(,m)-yl | (i,)d Tl(idml)=jr(i.t ) Y+ lJ g Y Y (5) for l-m, l-m-n-l, T(i,l)_yT(i,l+l), ieN and ije where n-I m Ml(ij,m) + Al(ij,m,l) = 1. m=l l=l (6) t- i: , , , _ I v .IV hl ,IAh.- I r T(i,l) T(i,l + 1) T(i,m) T(i,m + 1) 1, 2 rlIi,j,I .71(i,j,m - ,l!j rl(i,j,m,O Ta(i,m - 1) ,I T,(i,m) t6aCi,m) I - (,j,) n(i,j,m 1,1) -I . ,I T,(i,rn- 1) ,I T,(,m) , Fig. 3. The probability density functions for fault initiating times, (-), delay time ( (- - -) and expected transition times for a deterioration fault. 37-6-D ) and inspection error 826 G.B. Williams and R. S. Hirani Thus, for an initial state i 5, the expected total constant base interval risk of transition A(m), in any ruth interval irrespective of destination state and the nature of the fault, is: A(m) = P(i s(i,m) + A,(ij,m,l . (7) j=i+l 1=1 Let the condition or state of the sub-system be taken as a function of multiple parameters. Some of these parameters can be measured directly, whereas others cannot. Thus a fault already present or initiated is reflected in the parameter, which is the measure of its exist- ence with the probability of 7/. Imperfect inspection may, therefore, detect only the reflected fault with a probability of . Once a fault is detected, inspection detects the status of the transition state with a probability q, and its transition time with an accuracy of _+ in fraction of the width of the forthcoming inspection interval. Thus the upper and lower error limits, T,(i,m) and Tl(i,m) for the estimation of a transition time T(i,m)T-T(i,m+l), at the time of the ruth inspection (Fig. 2 and Fig. 3), are: T,(i,m) = T+ T(i,m + 1)-T(i,m) (8) and Tl(i,m) = T- T(i,m + 1)- T(i,m) (9) for l n- i, i e Ig and ij n 1 -(m-O.2(ij,m) + 1 -.z(ij,m).4(ij,m)q 1 -Pf(j) + (1 -q)Pf(); for 1 = m = n-l, iel and ije 1 - m- 1).2(ij,m) + 1 -.l(id,rn) s4(id,m) + .5(i,m),(id,m) m 1-Pf() + (1-q)Pf(j);for 1 = mn-1, iEl and ije. K=I 1 -K-l),s(id,m- 1) 1 -s,(ij,rn- 1) + .3(id,rn) + 1 -,(id,m)s4(ij,m) + ss(id,m),(id,m)q 1-Pf(j) + (1-q)Pf(j); for 1ren-1, iel and ije 1 - - I).s(id,m- 1) 1 -,(id,rn- 1) + ,3(id,m) + 1 -s(id,m),4 (ij,m)g 1-Pf(j) + (1-q)Pf(j);for l n-I, i and ije rff l-(-t-)A2(ij,m,l) + 1-Az(id,m,l)A4(id,m,l)q 1 -PdJ) + 1-q Pf(j); for l + 1 = m = n-l,i and ije 1 - (-t- )A2( iJ,m,l) + 1 -A( i,j,m,l) A4( ij,m,l) + As( ij,m,l)A.( ij,m,l) Iq1-Pf(j) + (1-q)Pf(j);for l + 1 = mn-1, iN and ije rl K=I+ 1 1 -(-t-)As(ij,m- 1,/) 1 -A,(ij,m- 1,l) + A3(ij,m,l) + 1 -A(ij,m,l)A4(ij,m,l) + As(ij,m,l)Au(ij,m,l)q 1 -Pf() + (1-q)Pf(j);for l + lmn-1, iER and ij 1 1-(-z-)As(ij,m- 1,/) 1 -A,(ij,m- 1,/) + A3(ij,m,l) + 1 -Al(ij,m,l) K=l+l A4(ij,m,i)q1-Pf(j) + (1-q)Pf(j);for I + lm = n-l, iR and ijE (11) Let a penalty be charged at a uniform rate of Cl(i) per unit production time lost due to unavailability of the sub-system in state i, independent of the transition state j and the cause of unavailability. The inspection cost ci(i) per inspection is paid in agi(i) instalments, where the instalment is equal to pi(v,i), a fraction of q(i). This is paid at time Y(v,i) from the time of the inspection. Thus the net present value (NPV) of the expected single step costs of the inspection plus penalty paid during the time of the inspection Ti, Ci(i), is: Ci(i ) = t. -lIs(ij ) A(ij 1) i + P(iJ)m- 1 ,m + l ,m, j= 1 -1 l=1 = 1 E ci(i)pi(P,i)(VIV2) trL(i) + r(i,K)-I-(K-,;.1 + YI vi) k= l v= l + cl(i)Ti(ViV2)trL(i) + i,)+ (,-0.5)Ti (12) for i e and j e , where V V2 are the annual time value or discount factor and the annual net inflation factor, respectively 7. Let the OCPM cost co(i), be paid in Oo(i) instalments, where the instalment is equal to po(v,i) a fraction of co(i), which is paid at time Yo(v,i) from the time when pending failure is detected. Thus, the NPV of the expected single step costs of OCPM, plus penalty during the time required for OCPM To(i), regardless of transition state Co(i), is: Co(i) = L n-1 P(ij) Po(ij,m) + Po(ij,m,l) j=i+l m=l l=l i_ i c(i)O(Pi)(VI V2)TL(i) + T(im) + mTi + + cl(i)To(i)(Vs V2) trt.( + r(i.m) + mT i + 0.5To(i) (13) 828 G.B. Williams and R. S. Hirani for ilg and je. Minimal repair is performed at cost rate Cm(j) , whenever transition occurs to a non- functional state j, which takes time Tin(j). The cost is paid in agm(j) instalments, where the th instalment is equal to pm(Vd), a fraction of c(j). This is paid in at time Y,(vj) from the expected time of transition to a non-functional state, plus time taken by inspec- tion. Therefore, the NPV of the single-step expected cost of on-failure minimal repair plus the penalty Cm(i) is: Cm(i): 2 P(ij)1-P) m - (l-r/) + rl(1- 0- + r/(1-0 (*-) j=i+l 1 K=I 1 /Ore: (1-q) Sdl(ij,m) Cm(j)pm(PJ)(VIV2) TL(i) + mTi + l(ijm) + Ym(vJ) -1 4 Cl(i)Tm(j)(Vl V2) TL(i) + T(i,m) + mT i + l(i,m)+ 0.5Tinj) + T(1 _)(K-l)ql(ij,m ) (Om(/) s4(ij,m) E Cm(j)prn(Vd) (VlV2) rL(i) + mr, + fff4(ij,m)+ Ym(v,j) + c,(i)T,(j) v= 1 ( Vl V2 ) TL(i ) + T(i,m) +mT i + 2f4(ij.m) + 0.STm(J) .4. ( 1 - 7/) + 77( 1 - )(m-l) ,4. = K=I+ I I : 0(1 -(g-t-l)(1 -q) Al(ij,m,l) Cm(j)pm(lYJ)(V1V2) TL(i) + mTi + Tl(idml) + Ym(v) -1 +c,(i)Tm(j)(ViV2)TL(i)+T(i.m+mTi+Tl(id.m.l)+OSTm (j) -1- O:(l-)(K-l-l)qAl K=I+I o,.(/) (ij,m,l)A4(ij,m,l) l c. (j)pm(lyd)(V1V2) TL(i) + mr; + T4(id, m,l)+ Ym(vj) + cl(i)T.,(j ) .v= i (VlV2)TL(i)+T(i,m)+mTi+T4(ij.m,l)+O.STm(J) (14) for lmn-1, iR and j. ,6-1 n-1 j=i+l = + q(1 -)(-l)(1-q),l(ij,m) =l v=l Cm(j)pm ( vj)(V 1V2) TL(i) + mTi + l (id,m) + Yra (vd) + cl(i)Tm(J)(V 1V2)rL(i) * T(i,m) +mT i + l(id,m) + 0.STmJ) . fo.o #t ffi l = Cm(Jgpm( pd)(Vl V2) TL(1) +mT i + T4(id.m) + Ym(Vj) A delay time multi-level on-condition preventive maintenance inspection model 829 ) + CI( i) Tm(j)( VI V2) tr,:) + l(h,n) + mT i + tff4(id.m) + 0.STm(j) / + (1-) + ,(1-O(-A(ij,m,l) l = I cm 1 = (J)Pm( vj)(V I V2) TL(i) + mTi + TI (id,m.l) + Ym ( vj) + Cl + r(i.m) + ,T i + T, (ij,m,l) + O.STm(J) (i)Tm(j)( VI vy(,) J 05) for l=m-n-1, iR and ij. If the sub-system in state i makes a transition to any non-functional state j, or to any functional state jc, after OCPM, before the warranty period Tw(i), warranty recovery at the agreed rate is charged from the supplier/manufacturer 5. Let the NPV of such a single step expected warranty charge recovered be Cw(i); therefore, the net expected single step inspection cost, plus OCPM cost, plus on-failure minimal repair cost, minus warranty recovery Cs(i), is: Cs(i) = Ci(i) + Co(i) + Cm(i)-Cw(i). (16) Therefore, the total expected single-step time taken by inspection, OCPM, and minimal repair, plus the time utilised for production, irrespective of the transition state and nature of the fault, given that the initial state is state i, is: T(ij) = ,m) + o ,m, 1 I=l (P,.(ij ) P (ij l)Tm(i) + ,l + m ,m, l=1 + l(ij,m) + Al(ij,m,l mTi + Sgl(ij,m)Tl(ij,m) I=l m 0 + A,(ij,m,1)T,(ij,m, . 1=1 (17) The NPV of the cumulative expected cost of inspection, expected cost of OCPM, expected cost of on-failure minimal repair, minus warranty recovery until the sub-system is in set , is: /3-i /3-2 B- C(i) = C(i) + P(ij)C,(j)(VIV2)tL (J) + P(ij)P(j,k)C j=i+l jfil kffij+l (k)(VlV2)T,(id) + r(i,k) + E E E P(ij)P(j,k)P(k,l)C, j=i+lk=j+l l=k+l (I)(V1V2) tL(i) + rs(Jk) + Ts(kl) + . + P(ij)P(j,k).P(3-2,3-1)C(/3-1) (VV2)tr,) + . + r,(/3-2./3-,1 (18) for ioC_jl. n-l, iRandijE f t(1-7) + 7711- + */1-gl(-l(1-,)M,(i,j,m) + /1-1 (-1), K= K=I s,(id,m)sd4(id,m) 1-Pf(j)for m n- 1, illV and ij (1-71) + 71 1-m-lA(ij,m,l) 1-PRO) for/= m-n-1, i and ij(1-l)+B1-, (m-l) + 1-(-I-l)(1-q)Al(id,m,l) t=l+ l + 1-(-t-1)e.Al(id,m,l)A4(id,m,l)1-Pf(J) K=I+I for lm-n- 1, i E and ij (24) Since OCPM reduces the probability of transition to any non-functional state without changing the time of transition and the transition state, thus the net effective probabilities of transition of the sub-system in state i as a result of OCPM to any non-functional and functional states knf and kerry, are: P(i,k.f) = P.(id)P(i,k)m_ ,k,m) t rn ,k,m, J =l -1 1=1 (25) and ,(i,kf) = .P,(id)P(i,k)m_ 1- ,k,m)+ Pm(j,k,m,l J =l -1 1=1 (26) for i oC_, j E N and k.f and kf So. Where P.(ij) represents the expected number of visits to state j, before it leaves the set R 7, given that the process has started in state i, the NPV of the expected cumulative capital cost of the sub-system at the time of the first transition to any state keb, irrespective of its status CM(i), is: L CM(i) = Cp(i)- Z P(i,kf)cp(kf) ,(k? Z pp(ls, kf)(Vl V2)TL(i) + T(i) + Yp(v, kf) l,=l %(kf) + Pe(i,knf)cp(knf) Z Pp(l,knf) v=l (V V2)trt i + r(o + v,(.k,# (27) for ieoCR, kf and knfe c. The expected availability of the sub-system U(i) and the NPV of the expected cost rate per unit cycle time Cr(i), until it makes transition to any state in the set , given that it is repaired or replaced in state ioC_, at time TL(i), are: ,.,): 1 TAi) + To(i) (28) and 832 G.B. Williams and R. S. Hirani ICe(i) + CM(i) C(i) = di) + T- j (29) for ieoC_N. Since both the criteria for optimisation may be functions of the state in which the sub- system is repaired or replaced, the number of inspection intervals, and the control state /3, the optimum purchase state i*, the optimum control state/3* and the optimum number of inspection intervals (n*-1) are those which result in the maximum expected availability of the sub-system U.(i), or the minimum cost rate/unit cycle time Crr(i): U*(i)=max max maxU(i) (30) iE i E E 0 2 3 4 5 6 7 Control states /DExpeet0d data (n =2)IISimulatod data (n =2) 1 (n=3) msimlateu Uata (n =3) Lj The optimum policy selected by main programme and simulation was same within reasonable accuracy, where n = 2, 13 = 4, and policy no. 96 (which recommends purchase state 1, and replacement to state 1 for each transition state _ 13 Fig. 5. Optimum system availability. t._ 0 0 0 .Q cO .O 0 t,.,. Q. E _1 v 3 4 5 6 7 Transition states _ 13 IIExpected data(n = 3) IBSimulated data (n = 3) 11 V Fig. 6. The probability of transition to various states. A delay time multi-level on-condition preventive maintenance inspection model 835 A 1 U) 1 (9 . 1 (9 .Q t (9 E F- - 1 2 3 4 5 Initial states 6 oteclta(n_- 2)msimlated data(n 21 Fig. 7. Time available for a production cycle. and the supporting software, (iii) the main program determined the optimum results within a few minutes whereas simulation runs took longer, and (iv) different policies were selec- ted for different criteria because these decisions were data dependent (Figs 4 and 5). An industrial setup was modelled using the ProModel simulation package. To facilitate decision making, user-defined sub-routines were written in Turbo Pascal. The ProModel simulation was then run and identical results were obtained; this confirms the validity of the model and the supporting software. Capital recovery for a production system is taken to be equal to the drop in value considering inflation or deflation, which enables mature as well as premature replacement by the same or its alternative without additional investment. REFERENCES 1 G. B. Williams and R. S. Hirani, Multi-level maintenance model for parts of a production system with a self-announcing present state. Proceedings of ProModel Corporation Third An
外文翻譯--當(dāng)檢驗(yàn)檢測(cè)失敗時(shí),基于恒基區(qū)間風(fēng)險(xiǎn)的一個(gè)多級(jí)層次時(shí)間延遲來(lái)預(yù)防維修檢查模型【中英文文獻(xiàn)譯文】.zip |
壓縮包目錄 | 預(yù)覽區(qū) |
|
請(qǐng)點(diǎn)擊導(dǎo)航文件預(yù)覽
|
編號(hào):2484350
類(lèi)型:共享資源
大?。?span id="24d9guoke414" class="font-tahoma">1.25MB
格式:ZIP
上傳時(shí)間:2019-11-25
10
積分
積分
- 關(guān) 鍵 詞:
- 中英文文獻(xiàn)譯文 外文 翻譯 檢驗(yàn) 檢修 檢測(cè) 失敗 基于 區(qū)間 風(fēng)險(xiǎn) 一個(gè) 多級(jí) 層次 時(shí)間 延遲 預(yù)防 維修 檢查 模型 中英文 文獻(xiàn) 譯文
- 資源描述:
-
外文翻譯--當(dāng)檢驗(yàn)檢測(cè)失敗時(shí)基于恒基區(qū)間風(fēng)險(xiǎn)的一個(gè)多級(jí)層次時(shí)間延遲來(lái)預(yù)防維修檢查模型【中英文文獻(xiàn)譯文】,中英文文獻(xiàn)譯文,外文,翻譯,檢驗(yàn),檢修,檢測(cè),失敗,基于,區(qū)間,風(fēng)險(xiǎn),一個(gè),多級(jí),層次,時(shí)間,延遲,預(yù)防,維修,檢查,模型,中英文,文獻(xiàn),譯文展開(kāi)閱讀全文
裝配圖網(wǎng)所有資源均是用戶(hù)自行上傳分享,僅供網(wǎng)友學(xué)習(xí)交流,未經(jīng)上傳用戶(hù)書(shū)面授權(quán),請(qǐng)勿作他用。
鏈接地址:http://www.szxfmmzy.com/p-2484350.html