A Note on Point Estimation of System Reliability Exemplified for the Log-Logistic Distribution

Point estimation constitutes the heart of statistics. In this paper the corresponding methods are looked at from the viewpoint of a user and it is shown that point estimation procedures not only have major conceptual deficiencies, but that the corresponding methods offered and recommended in textbooks and journal articles are often confusing and misleading. To exemplify these claims reliability estimation assuming the log-logistic distribution is used. The reliability function is viewed as a parametric function. For certain values of the shape parameter, the scale parameter is estimated and used to obtain reliability estimates.