Transformations Improving Maximum Likelihood Confidence Intervals for System Reliability

Transformations are devised to accelerate convergence to normality for maximum likelihood estimators of the reliability of complex systems. Improved confidence intervals follow from probability statements concerning the transformed estimator. Comparisons are made with intervals given by exact procedures and also by generating test results from a system of given reliability, enabling the confidence property of intervals obtained using the transformation to be assessed. Results using other methods, including the log odds transformation for binomial subsystem test data, are also given. The generality of the approach is illustrated by using the transformations to improve confidence intervals in cases where other methods are not appropriate.