= + + +

Suppose the manufacturer of a very sensitive instrument wants 99% of the instruments produced to operate within specified limits. To do this, it is necessary for each of three component parts of the instrument to operate within specified limits. The manufacturer samples the daily production of the parts and sets confidence limits on the variances of each part to determine if these variances are in compliance. In this case, 99% simultaneous confidence intervals are used for the set of three variances so that if each of the three confidence bounds is within its respective limit, the instrument will operate within the specified limits with probability 99%. In contrast, if one is interested in examining the variances of the three component parts separately and no single part or decision depends on the simultaneous performance of the three parts, then one-at-a-time confidence intervals should be used.