Likelihood adjustment: a simple method for better forecasting from small samples

Abstract

New methods developed by the authors improve data analysis and reliability prediction accuracy when using maximum likelihood estimates (MLE) particularly for small samples. The Fulton factor (FF) modifies the likelihood ratio test to reduce nonconservative bias when measuring difference between designs. The reduced bias adjustment (RBA) factor decreases bias in distribution parameter estimates for better reliability and lifetime predictions. Finally, a postulated relationship designated the justified likelihood function (JLF) reduces confidence contour bias for better confidence interval estimates and for use in graphical comparison of design alternatives. Monte Carlo simulation provides the basis for these conclusions. The results herein apply to complete samples, but also work well with suspensions using failure quantity only as the sample size. Additional research into data with suspensions is desirable.