On upper bounds for the variance of functions of the inactivity time

چکیده مقاله

In this article, we obtain an upper bound for the variance of a function of inactivity time X(t) = (t − X|X < t). Since one of the most important types of system structures is the parallel structure, we give an upper bound for the variance of a function of random variable Φrn (X; t) = (t − Xr:n|Xn:n ≤ t) for n identical and independent components. We have shown that when the components of the system have decreasing reversed hazard then, the variance inactivity time of the system increases with respect to time, under suitable conditions. It is shown that the underlying distribution function F can be recovered from the proposed expected inactivity time and variance inactivity time. Moreover,weshow that the variance inactivity time of the components of the system is not necessarily a decreasing function of r, unlike their expected inactivity time.