Exact two-sided tolerance interval controlling tail proportions for sample variances

Tolerance intervals (TIs) for variances are useful when we are interested in the precision of the quality characteristic. They can provide a deeper understanding of the process variability corresponding to process improvement and deterioration. In this paper, we consider the exact two-sided TI for sample variances that simultaneously controls the proportions in each of the two tails of the distribution. The minimum number of subgroups required to achieve a specified level of precision is also computed. Moreover, we minimize the width of the TI through adjusting the tolerance factors, and the performance of the adjusted TI shows some improvement, especially when the amount of reference data is small. Finally, a real application is used to illustrate the construction and implementation of the proposed TIs.