Abstract
In this study, we derive an asymptotic solution of the integral equation satisfied by the second moment function M2(t, a) . We first find the Laplace transform (M2)L(s, a) and then obtain M2(t, a) asymptotically by inversion. Further, we have derived the asymptotic expressions of M2(t, a) for some special lifetime distributions such as exponential, gamma, Weibull, lognormal and truncated normal. Finally, the asymptotic solution is compared with the numerical solution to evaluate its performance.