Editing Tolerance interval (section)

{{Short description|Type of statistical probability}}
{{distinguish|Engineering tolerance}}

A '''tolerance interval''' ('''TI''') is a [[statistical interval]] within which, with some [[confidence level]], a specified [[sampling (statistics)|sampled]] [[proportion of a population]] falls. "More specifically, a {{math|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)."<ref>D. S. Young (2010), Book Reviews: "Statistical Tolerance Regions: Theory, Applications, and Computation", TECHNOMETRICS, FEBRUARY 2010, VOL. 52, NO. 1, pp.143-144.</ref> "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."<ref name=Krishnamoorthy2011>Krishnamoorthy, K. and Lian, Xiaodong(2011) 'Closed-form approximate tolerance intervals for some general linear models and comparison studies', Journal of Statistical Computation and Simulation, First published on: 13 June 2011 {{doi|10.1080/00949655.2010.545061}}</ref> "A (p, 1−α) upper '''tolerance limit''' (TL) is simply a 1−α upper [[confidence limit]] for the 100 ''p'' [[percentile]] of the population."<ref name=Krishnamoorthy2011/>