A tolerance interval is a statistical construct for population-level uncertainty quantification. It specifies a range that, with a specified confidence level (1-alpha), contains at least a specified proportion (p) of the underlying population distribution. Parameters: (1) the confidence level — the probability that the interval covers the specified proportion, (2) the coverage proportion — the fraction of the population to be contained, (3) sample statistics (mean, standard deviation) used to compute the interval bounds. Persistence mechanism: mathematical formula applied to sample data to produce interval bounds that account for both sampling variability and population spread, documented in statistical practice and software implementations. [formal: interval tolerance | substrate: mind | horizon: a moment | explicit: yes | epoch: 0.01]
Accepted ontology entry
tolerance interval
A tolerance interval is a statistical construct for population-level uncertainty quantification. It specifies a range that, with a specified confidence level (1-alpha), contains at least a specified proportion (p) of the underlying populat…
Definition
Why it is in scope
A tolerance interval is a human-made statistical construct that quantifies uncertainty in a population: it specifies a range that, with a stated confidence level, contains at least a specified proportion of the population distribution. Unlike confidence intervals (which estimate population parameters) or prediction intervals (which bound single future observations), tolerance intervals jointly specify both coverage proportion and confidence — making them a distinct construct for population-level uncertainty statements. It persists through mathematical formulation and statistical practice.
Names and aliases
- tolerance intervalen · CANONICAL
Relations from this entry
- cmsddehj003sp3vv3r6h06pb8INSTANCE_OF →
A tolerance interval IS a specific kind of statistical method. It is a method that constructs an interval guaranteed to contain a specified proportion of a population with a given confidence level. Direction: specific→general per Law 9. A competent speaker would call a tolerance interval a type of statistical method.
- cmrxj3acr03cmsoacx73fal1oDEPENDS_ON →
A tolerance interval is a statistical confidence interval that estimates a range containing a specified proportion of a population with given confidence. Remove statistics — remove confidence intervals, sampling theory, and population inference — and the tolerance interval concept ceases to operate. The removal test is operational, not meta-level: the concept's machinery collapses without its statistical framework.
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Record identity
- Created
- Aug 8, 2026, 3:24 PM UTC
- Content hash
- b0dcffda241e4499467693af34694e184884b4eba6af61b4de0f2154b791063a