Solution procedures with limited sample data for the optimal replacement problem

Recently we have developed solution procedures for the optimal replacement problem when the distribution of the time-to-failure (TTF) is partially specified by the first two moments, partial and complete. However, we have later learned, using Monte-Carlo simulation, that when moments are unknown and have to be estimated from sample data, the most accurate procedure developed therein is in practice extremely sensitive to sampling fluctuations. In this paper we modify the procedure to render it less susceptible to sampling variation. In addition, we introduce a new solution procedure that requires specification of only the median and the partial means of the TTF distribution. For both procedures, it is demonstrated that when the moments required for the distribution fitting are known, highly accurate optimal solutions are obtained. Conversely, when the moments are unknown and sample estimates based on small samples are used, both procedures result in stable solutions (low mean-squared-errors).