Adaptive Exponential Smoothing Models for Reliability Estimation

Four methods are discussed for determining the smoothing parameters in an adaptive exponential smoothing model which is used to assess reliability of a complex system tested in stages. The adaptive model is defined as Ri = ¿iri + (1 - ¿i)Ri-1, i = 2,...k, where Ri-1 is the assessed reliability at stage (i -1), ri is the ratio of the number of successes to the number of trials at stage i. Among the four procedures given here for determining the smoothing parameters xi two empirical methods and an empirical Bayes procedure are considered in some detail including a numerical example in which these techniques are compared.