Uncertainty Bounds for a Monotone Multistate System
نویسندگان
چکیده
We consider a monotone multistate system with conditionally independent compo nents given the component reliabilities and random component reliabilities Upper and lower bounds are derived for the moments of the random reliability function extending results for binary systems The second moment of the reliability function is given spe cial attention as this quantity is used to calculate the standard deviation of the system availability estimate key words monotone multistate system reliability function uncertainty association Introduction We shall consider a multistate monotone system with n components as de ned and studied for example in Gri th and Natvig For i n let Xi denote the state of the ith component the set of possible states being Si f Mig We assume that the states in each Si are linearly ordered with denoting the worst state complete failure and Mi being the best state perfect functioning The state vector of the system is X X Xn with possible values in S S Sn We furnish S with the componentwise partial order de ned by x x xn y y yn xi yi for i n For convenience we shall later write x y to mean that x y and xi yi for at least one i In multistate reliability theory one de nes a structure function S f Mg with x denoting the state of the system when the components are in states x see e g Here M denotes the perfect system state and states are then ordered down to which corresponds to complete system failure The function is assumed to be increasing with respect to the partial order on S i e
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