Reliability Analysis Of 1-dimensional And 2-dimensional Consecutive-k-out-of-n System

In the past researches on system reliability,most scholars supposed that system components are independent and identical distributed at the components level.In recent years,more and more scholars have considered the independent and non-identical distri-bution,first-order homogeneous Markov dependence,and first-order non-homogeneous Markov dependence of system components which were more in line with the actual en-gineering background.Repairability,multi-state and weights of components are also common assumptions in recent years.At the system structure level,the consecutive-k-out-of-n system is a popular research topic.This kind of system is widely applied in the fields of integrated circuit design,satellite relay communication system,telephone sound reinforcement system and aircraft airborne navigation equipment.Consecutive-k-out-of-n system is divided into fail(F)system and good(G)system.Consecutive-k-out-of-n:F system fails if consecutive k components are not functional.Consecutive-k-out-of-n:G system is in operation if continuous k components work.It is important to analyze the reliability of such systems for the safety of various industrial equipment.This article focuses on the consecutive-k-out-of-n:F system with components having random weights and conditional consecutive-(r,s)-out-of-(m,n):F system.Analyzing the reliability of these two types of systems,and obtaining the accurate expression of reliability is of great significance to system design and control.In this article,we first consider the consecutive-k-out-of-n:F system with compo-nents having random weight.According to the requirements of system structure and weights,This system is subdivided into two types of systems.If the summation weight-s of the failed components is greater than or equal to a fixed constant c or at least k components are invalid,then system fails which denoted by system S1;If the sum-mation of consecutive failed components' weights is greater than or equal to c or the number of failed components reaches k,system stops working which is recorded as system S2.We first assume that all the components are independent and non-identical distributed.The reliability of system S1 and S2 are estimated by Monte-Carlo simu-lation,and the curve of system reliability varying with time is obtained.In addition,we obtain a clear expression of the system reliability and give a proof,and we show the variety characteristics with each parameter of the reliability of system S1 and S2 through some numerical examples.Secondly,we suppose that the components are non-homogeneous Markov dependent,and also analyze the reliability of the two systems,and give the variation of the system reliability with the parameters k,c.Finally,we de-fine the weighted importance of the consecutive-k-out-of-n:F system with components having random weight.The expression of classic Birnbaum reliability importance is also given.For the theoretical results of system reliability and components importance,we give corresponding algorithms.Next,we use a new method to study the conditional consecutive-(r,s)-out-of-(m,n):F system and a new algorithm with lower complexity is proposed.If the failed components forms a(r,s)sub-matrix that is a matrix concluding failed components on-ly or if the quantity of failed components is more than or equal to 2rs then the system fails.This type of system is mainly used in the X ray disease diagnosis,pattern detec-tion and so on.Based on the number of failed components in the system,we discuss the arrangement of the failed components in the system,and obtain the expression of system signature and reliability of the system,and analyze the influence of the system scale and component lifetime distribution by numerical examples.Meanwhile we study the random order relationship between the lifetime and the signature of two systems of the same size.