Analysis of lognormal survival data

The failure rate and the mean residual life function (MRLF) of a lognormal distribution are known to be nonmonotonic. It is of interest to study the point at which the monotonicity changes (the change point). In this article we study the change points of the failure rate and the MRLF for the lognormal distribution. It is shown that the change points are the solutions of certain nonlinear equations. We apply these results to estimate the change points for survival data on guinea pigs given by Bjerkedal. The standard deviation of the estimate is obtained using bootstrap and jackknife methods. Finally confidence bands for the failure rate and the MRLF are also provided to illustrate the behavior of the estimates.