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  本文選題：幾何過程 + 預(yù)防維修策略��； 參考：《西南交通大學(xué)》2012年碩士論文

【摘要】：可修系統(tǒng)是可靠性理論中討論的一類重要系統(tǒng),也是可靠性數(shù)學(xué)的主要研究對象之一。在系統(tǒng)的維修策略研究中,帶有故障小修的周期預(yù)防維修策略是最基本的維修策略之一,對于維修計劃的制定和提高系統(tǒng)的可用度具有現(xiàn)實的意義。 本文研究的是以可靠性,安全性為中心的預(yù)防維修計劃,提出了對系統(tǒng)部件進(jìn)行周期小修預(yù)防維修計劃的優(yōu)化方法。 首先,本文假設(shè)在系統(tǒng)部件修舊非新的條件下,基于幾何過程不考慮小修時間的預(yù)防維修策略(R,N),預(yù)防維修周期是變化的,由可靠度來確定,當(dāng)系統(tǒng)可靠度下降到一定值就對系統(tǒng)部件進(jìn)行預(yù)防維修。當(dāng)系統(tǒng)部件失效時就進(jìn)行小修,小修只能恢復(fù)系統(tǒng)部件的工作狀態(tài),小修時間不計,當(dāng)預(yù)防維修次數(shù)達(dá)到N時就進(jìn)行更換,進(jìn)而推導(dǎo)出了系統(tǒng)長期運行單位時間內(nèi)的最小花費,在此基礎(chǔ)上并建立了費用維修的預(yù)防維修策略模型,并給出算例對模型求解,得出最優(yōu)的預(yù)防維修策略。 其次,本文研究的是基于幾何過程考慮小修時間的預(yù)防維修策略(R,N),預(yù)防維修周期也是由可靠度來確定,系統(tǒng)失效時進(jìn)行小修,這里的小修時間不是忽略不計而是假設(shè)每個周期內(nèi)每次小修時間變量獨立同分布,每個周期之間的小修時間是服從隨機遞增的幾何過程,當(dāng)系統(tǒng)預(yù)防維修N次時就進(jìn)行更換。最后給出系統(tǒng)的平均花費的表達(dá)式,通過算例對模型求解,得出最優(yōu)的預(yù)防維修策略。 再次,本文研究的是基于幾何過程的周期小修的預(yù)防維修策略(cd,N),考慮到具有嚴(yán)重安全性以及環(huán)境性故障后果的機械系統(tǒng)零部件,它們要求在預(yù)防維修周期內(nèi)安全可靠性相對來說比較高,比如像航空系統(tǒng)對系統(tǒng)部件的安全性就要求的比較高,所以在這里系統(tǒng)的預(yù)防維修周期是由安全工作時間來確定的,當(dāng)系統(tǒng)的安全工作時間達(dá)到一定值時就對系統(tǒng)進(jìn)行預(yù)防維修。同樣給出了算例對模型求解,得出最優(yōu)的預(yù)防維修策略。 最后由模型一和模型二比較可得小修時間確實影響到最優(yōu)維修策略的制定,而且考慮小修時間的模型得到的最小維修費用大于不考慮小修時間的最小維修費用,這是合理的,因為考慮小修時間就是相當(dāng)于考慮了因為小修而產(chǎn)生的停工損失,這樣就會使得費用變大。由模型二和模型三比較可得,模型二更優(yōu),但模型三的維修策略適合對安全性要求比較高,對費用要求相對不高的維修系統(tǒng)。
[Abstract]:Repairable system is a kind of important system discussed in reliability theory, and it is also one of the main research objects of reliability mathematics.In the research of system maintenance strategy, periodic preventive maintenance strategy with minor fault repair is one of the most basic maintenance strategies, which has practical significance for making maintenance plan and improving the availability of the system.In this paper, the preventive maintenance plan centered on reliability and safety is studied, and the optimization method of periodic minor repair preventive maintenance plan for system components is put forward.First of all, this paper assumes that the preventive maintenance strategy based on geometric process does not take minor repair time into account under the condition that the system components are repaired old and not new. The preventive maintenance period is variable and is determined by reliability.When the reliability of the system drops to a certain value, preventive maintenance of the system components is carried out.Minor repairs are carried out when the system components fail, and minor repairs can only restore the working state of the system components. The minor repair time is not taken into account. When the preventive maintenance times reach N, the minimum cost per unit time of the system is deduced.On this basis, the preventive maintenance strategy model of cost maintenance is established, and an example is given to solve the model, and the optimal preventive maintenance strategy is obtained.Secondly, the preventive maintenance strategy based on geometric process considering minor repair time is studied in this paper. The preventive maintenance period is also determined by reliability, and minor repairs are carried out when the system fails.The minor repair time here is not ignored but assumed that each minor repair time variable in each cycle is distributed independently. The minor repair time between each cycle is a geometric process of random increment and is replaced when the preventive maintenance of the system is N times.Finally, the expression of the average cost of the system is given, and the optimal preventive maintenance strategy is obtained by solving the model with an example.Thirdly, this paper studies the preventive maintenance strategy of periodic minor repair based on geometric process, considering the mechanical system components with serious safety and environmental failure consequences.They require a relatively high level of safety and reliability during the preventive maintenance cycle, such as the relatively high requirements for the safety of system components in aviation systems, so the preventive maintenance cycle of the system is determined by safe working hours here.When the safe working time of the system reaches a certain value, preventive maintenance of the system is carried out.At the same time, an example is given to solve the model, and the optimal preventive maintenance strategy is obtained.Finally, compared with model 1 and model 2, the minimal repair time can really affect the formulation of the optimal maintenance strategy, and the minimum maintenance cost of the model considering the minor repair time is larger than the minimum maintenance cost without considering the minor repair time, which is reasonable.Because considering minor repair time is equivalent to taking into account the damage caused by minor repairs, this will increase the cost.Compared with model 2 and model 3, model 2 is better than model 2, but the maintenance strategy of model 3 is suitable for maintenance systems with high security requirements and relatively low cost requirements.
【學(xué)位授予單位】：西南交通大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2012
【分類號】：TH17

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