【摘要】：帶有貯備部件的串聯(lián)系統(tǒng)是可靠性研究中非常重要的一類系統(tǒng),也是工程上常見(jiàn)的一類系統(tǒng),其中貯備部件的優(yōu)化是一類備受關(guān)注的問(wèn)題。如何合理地選擇備件并將之貯備在系統(tǒng)中將對(duì)系統(tǒng)的可靠性具有較大影響。在一般的可靠性討論中,通常假設(shè)系統(tǒng)中部件之間是相互獨(dú)立的。然而,根據(jù)實(shí)踐分析可知,系統(tǒng)在工作時(shí)其工作部件之間具有一定的相依性。基于適當(dāng)?shù)腃opula函數(shù),根據(jù)部件的邊緣分布得到聯(lián)合分布,進(jìn)而得出整個(gè)系統(tǒng)的可靠性指標(biāo)具有實(shí)際意義。對(duì)于可修系統(tǒng),既通過(guò)馬爾可夫過(guò)程,又利用馬爾可夫更新過(guò)程和補(bǔ)充變量法等工具進(jìn)行可靠性分析,具有系統(tǒng)性。首先,本文對(duì)于帶有貯備部件的三部件串聯(lián)系統(tǒng)的備件優(yōu)化問(wèn)題做出了詳細(xì)討論。分別從貯備部件與工作部件同型和不同型的兩種情形討論了系統(tǒng)貯備部件基于可靠度的優(yōu)化問(wèn)題。在兩種情形下又分別對(duì)帶有冷貯備和溫貯備的系統(tǒng)進(jìn)行了分析,得出相應(yīng)的可靠度表達(dá)式,并通過(guò)MATLAB作圖得出最優(yōu)化結(jié)果。其次,對(duì)上述優(yōu)化結(jié)果中特定的帶有兩個(gè)冷貯備的三部件串聯(lián)系統(tǒng),在系統(tǒng)中部件相互獨(dú)立時(shí)和部件相依時(shí)的情形下分別進(jìn)行可靠性分析。部件相依時(shí)又引入了FGM Copula,AMH Copula和Clayton Copula三種不同的連接函數(shù)進(jìn)行對(duì)比研究。最后,本文針對(duì)帶有兩個(gè)冷貯備的三部件串聯(lián)系統(tǒng),研究了基于馬爾可夫過(guò)程和幾何過(guò)程的可靠性。對(duì)于馬爾可夫型系統(tǒng),通過(guò)一定的假設(shè),分析得到系統(tǒng)所有的狀態(tài),運(yùn)用馬可夫過(guò)程理論進(jìn)行分析求解。對(duì)于幾何過(guò)程的退化系統(tǒng),在假定系統(tǒng)中工作部件具有優(yōu)先維修權(quán),特定部件維修時(shí)間服從幾何過(guò)程等條件下,運(yùn)用補(bǔ)充變量法研究系統(tǒng)的可靠性。
[Abstract]:Series system with spare parts is a very important system in reliability research, and it is also a kind of common system in engineering. Among them, the optimization of spare parts is a kind of problem that attracts much attention. How to reasonably select spare parts and store them in the system will have a great impact on the reliability of the system. In general reliability discussions, it is generally assumed that the components of the system are independent of each other. However, according to the analysis of practice, the system has certain dependence on its working parts. Based on the proper Copula function, the joint distribution is obtained according to the edge distribution of the components, and the reliability index of the whole system is obtained. For repairable systems, reliability analysis is carried out by means of Markov process, Markov renewal process and supplementary variable method. Firstly, this paper discusses in detail the problem of spare parts optimization for three parts series system with spare parts. In this paper, the reliability optimization problem of the system storage components is discussed from the two cases of the same type and different types of the spare parts and the working parts, respectively. In both cases, the system with cold reserve and warm reserve is analyzed, the corresponding reliability expression is obtained, and the optimization result is obtained by MATLAB diagram. Secondly, the reliability analysis of the special three-component series system with two cold reserves in the above optimization results is carried out under the condition that the components are independent of each other and the components are dependent on each other. When components depend on each other, three different connection functions, FGM Copula Copula and Clayton Copula, are introduced for comparative study. Finally, this paper studies the reliability of Markov process and geometric process for the three-component series system with two cold reserves. For Markov systems, all the states of the system are obtained through some assumptions, and the Markov process theory is used to solve the problem. For the degenerate system of geometric process, the reliability of the system is studied by means of supplementary variable method under the assumption that the working part has the priority maintenance right in the system and the maintenance time of the specific component is dependent on the geometric process.
【學(xué)位授予單位】：南昌大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O213.2

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