CAJ | 학술논문

针对具有一定拓扑结构的元件相依复杂系统的可靠性分析问题，提出了一类新的元件相依系统———空间相依圆形可修系统。该系统由若干个排列成圆形的元件组成，并且每个元件的运行依赖于空间上与之相邻的元件（“邻居”）。采用马尔可夫过程描述系统的运行过程，定义了四元件和五元件空间相依圆形可修系统的状态，得到了系统的状态转移率矩阵。运用Laplace变换方法，给出了系统的可用度。通过数值示例说明了结论的应用，并把上述2个系统的可用度与元件独立马尔可夫可修系统的可用度进行了对比。
침대구유일정탁복결구적원건상의복잡계통적가고성분석문제，제출료일류신적원건상의계통———공간상의원형가수계통。해계통유약간개배렬성원형적원건조성，병차매개원건적운행의뢰우공간상여지상린적원건（“린거”）。채용마이가부과정묘술계통적운행과정，정의료사원건화오원건공간상의원형가수계통적상태，득도료계통적상태전이솔구진。운용Laplace변환방법，급출료계통적가용도。통과수치시례설명료결론적응용，병파상술2개계통적가용도여원건독립마이가부가수계통적가용도진행료대비。
Aim.The introduction of the full paper reviews a number of papers on reliability models with dependent units in the open literature and proposes what we believe to be a new model mentioned in the title.The core of Sec-tion 1 consists of:( 1) we present the assumptions of the circular Markov repairable systems with spatial depend-ence;( 2) we put forward the Markov processes associated with the 4-unit and 5-unit circular Markov repairable systems with spatial dependence and define their states as indicated in Fig.1 and Fig.2.Section 2 analyzes the state transitions of the 4-unit and 5-unit systems and obtains the state transition rate matrices corresponding to them.Sec-tion 3 discusses the instantaneous and asymptotic availabilities of the 4-unit and 5-unit systems, which are given by equations (3)-(5).Section 4 presents the numerical examples of the 4-unit and 5-unit systems.The curves of in-stantaneous availabilities are shown in Fig.5 and Fig.6.We obtain the conclusions that:(1) the system with inde-pendent units is more reliable than the circular Markov repairable system with spatial dependence;(2) the 5-unit circular Markov repairable system is more reliable than the 4-unit system.