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.

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Recently, with the wide application of tolerance intervals (TIs), especially in quality management, the construction of TIs has attracted increasing attention. However, TIs applied to record data have not been well established as they have been for complete data. In many industrial stress tests, only record data are stored instead of complete data, which leads to the fact that the developments of methods based on record data are as important as those based on complete data. In this paper, we propose the exact two-sided TIs for the exponential distribution based on record values from the frequentist and Bayesian perspectives. The accuracy of each type of TIs is quantified. The results show that the Bayesian approach is superior to the frequentist approach in terms of the accuracy. A real data example is used to illustrate the constructions and implementations of the proposed TIs.