Richards, Dale O. (1992, ASQC) Brigham Young University, Provo, UT 84602
The author discusses several characteristics that determine confidence intervals with respect to mean time to failure, reliability at a specified time, and survival time.
Equal tail intervals, including equations for population mean, population variance/standard deviation, and ratio of variances, can calculate a confidence interval for parameters of a normal distribution from a representative sample. Minimum length intervals calculate from the same equations as equal-tail intervals, but produce tails of unequal length (due to the Snedecor F- and chi square distributions). The author provides a list of additional papers listing the most accurate tabular values for variance, standard deviation, or ratio of variances. Finally, he describes parameters and reliability of the exponential distribution for discovering confidence intervals. Parameter equations can be used by replacing the equal tail chi-square with appropriate values from a different table.
If minimal confidence intervals for the reliability of an exponentially distributed random variable are sufficient, use equal tail interval limits for theta under a particular value, and minimum length limits for theta over that value. He also demonstrates that both location and length of interval are important. One should carefully consider all of these factors before deciding on a technique for calculating confidence intervals.
Chi-square statistics,Confidence limits,Reliability,Statistics,Standard deviation