Nonparametric Estimation of the Limiting Interval Reliability

In many practical situations, one may be interested in knowing the extent to which the system will survive an interval of duration after it has been run for a long time. In such situation, the limiting interval reliability may be used as an appropriate measure for system effectiveness. Also, since it is difficult to obtain closed form expressions for the interval reliability, except for few simple cases, in the literature more attention is being paid to its limiting measure. The limiting interval reliability is the limiting value of the interval reliability, ( , ) R x t , as t → ∞ . In this chapter, we consider the nonparametric estimation of the limiting interval reliability when the failure and repair times form a bivariate sequence of i.i.d. random variables.