The mean wasted life time of a component of system

Kavlak K.

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, vol.305, pp.44-54, 2016 (SCI-Expanded) identifier identifier


A reliability inspection model in which a component of a technical system has lifetime X and inspection time S is considered. It is assumed that X and S are random variables with absolutely continuous joint distribution function F-x,F-s, and the joint probability density function f(x,s). Firstly, we consider mean residual life function of the component under two different setups of inspection. Secondly, we consider an inspection model where at the inspection time the component is replaced with its spare regardless of whether the component is alive or failed at this time. Under condition that 0 < t < S < X we are interested in expected value of X - S, which is the mean wasted time of intact at time t component in the case if it will not be failed at inspection time, but will be replaced with the new one. We derive formula for mean wasted life time expressed in terms of f(x,s) and partial derivatives of F-x,F-s. Some examples with graphical representations are also provided. (C) 2016 Elsevier B.V. All rights reserved.