Approximate interval estimation methods for the reliability of systems using component data with exponential and Weibull distributions.

Abstract

Two approximate parametric interval estimation methods for system reliability using component test data are developed and evaluated. One method can be applied to any coherent system with components which have exponential failure times with possibly different failure rates and different mission operating times. This method estimates the ratios of component failure rates which are then used to develop the approximate lower confidence limit. These ratio estimates are developed with and without jacknife methods and the two results are compared. This procedure is very accurate and simple to compute, requiring the use of standard chi-square tables. This ratio method is subsequently extended to coherent systems with components whose failure times have a Weibull distribution. A nearly exact parametric lower confidence limit for P(X> x) is developed and evaluated where x is given and X has a normal distribution with unknown mean and variance. This procedure is also simple to evaluate and requires the use of Student t tables.