# Tolerance interval

## Type of statistical probability / From Wikipedia, the free encyclopedia

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A **tolerance interval** (**TI**) is a statistical interval within which, with some confidence level, a specified sampled proportion of a population falls. "More specifically, a 100×*p*%/100×(1−α) tolerance interval provides limits within which at least a certain proportion (*p*) of the population falls with a given level of confidence (1−α)."^{[1]} "A (*p*, 1−α) tolerance interval (TI) based on a sample is constructed so that it would include at least a proportion *p* of the sampled population with confidence 1−α; such a TI is usually referred to as p-content − (1−α) coverage TI."^{[2]} "A (p, 1−α) upper **tolerance limit** (TL) is simply a 1−α upper confidence limit for the 100 *p* percentile of the population."^{[2]}