Comparison of Two Methods of Obtaining Approximate Confidence Intervals for System Reliability

Some specific comparisons are made in this note between the use of the asymptotic Chi-square distribution of the likelihood ratio and the asymptotic normality of the maximum likelihood estimates to obtain confidence interval for reliabilities of arbitrary systems when only failure data on the components is known. In all the comparisons made, using moderate samples and systems of average complexity, the asymptotic Chi-square appears to give much more accurate confidence intervals. Although the asymptotic Chi-square method requires more computation for most systems than does the method based on asymptotic normality, these examples indicate the Chi-square method would yield superior results in most practical instances.