Abstract
In this study, we have proposed a model of the sliding window coherent system in case of multiple failures. The considered model consists of G linearly required multi-state elements and G number of parallel elements in A-within-B-from-D/G for each multi-state. The system fails if at least A group elements out of B consecutive of D consecutive multi-state elements have performance lower than the weight w. We have evaluated the signature reliability, expected value and system sensitivity on the basis of the extended universal generating function of the considered system.
Highlights
In the real life situation binary state system (BSS) depends on mainly two states namely completely working or total failure
Kumar and Singh (2017a, 2017b) studied the complex A-out-of-G coherent system and sliding window coherent system (SWCS) with i.i.d. elements and calculated various reliability measures such as signature, mean time to failure (MTTF), Barlow-Proschan index using universal generating function (UGF) technique. It is clear from the above discussions that many researchers computed the reliability, MTTF, cost of binary and multi-state systems with various techniques, but the signature of SWCS is yet to be studied. Keeping this fact in view, in the present work we propose to study the A-within-B-fromD/G SWCS with G parallel i.i.d. elements consisting of the multi-state element (MSE) of the system
From equation (1), we can evaluate the signature of the system having i.i.d. elements as sA pD Ts TA:G, where T is system lifetime and sA is the probability of the system failure
Summary
In the real life situation binary state system (BSS) depends on mainly two states namely completely working or total failure. Kumar and Singh (2017a, 2017b) studied the complex A-out-of-G coherent system and sliding window coherent system (SWCS) with i.i.d. elements and calculated various reliability measures such as signature, mean time to failure (MTTF), Barlow-Proschan index using UGF technique It is clear from the above discussions that many researchers computed the reliability, MTTF, cost of binary and multi-state systems with various techniques, but the signature of SWCS is yet to be studied. Keeping this fact in view, in the present work we propose to study the A-within-B-fromD/G SWCS with G parallel i.i.d. elements consisting of the multi-state element (MSE) of the system. The system reliability of the sets of B consecutive groups of D consecutive MSE
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