On the reduction in remaining system time above a specific state due to a jump downwards of a component in nonrepairable multistate strongly coherent systems

Abstract

In the present paper results given in Natvig (1990) are generalized to a multistate, strongly coherent, nonrepairable system of independent components by considering the reduction in remaining system time above a certain state due to a jump downwards of a component. This reduction also equals the increase in remaining system time above a certain state due to a minimal repair of the component at its time of jump downwards. The expected value of the sum of such reductions/increases for the di erent possible jumps downwards of the component is the building block of the Natvig measure of the importance of the component in the multistate case. Hence, now the whole distributions of these reductions/increases are arrived at, not only the expectations, then throwing more light on the consequences for the system of the deterioration of the components.