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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)."
For example, if a shaft with a nominal diameter of 10 mm is to have a sliding fit within a hole, the shaft might be specified with a tolerance range from 9.964 to 10 mm (i.e., a zero fundamental deviation, but a lower deviation of 0.036 mm) and the hole might be specified with a tolerance range from 10.04 mm to 10.076 mm (0.04 mm fundamental ...
Tolerance analysis, the study of accumulated variation in mechanical parts and assemblies; Tolerance coning, a budget of all tolerances that affect a particular parameter; Tolerance, a measure of multicollinearity in statistics; Tolerance interval, a type of statistical probability; Tolerance relation, a reflexive and symmetric binary relation ...
One-sided normal tolerance intervals have an exact solution in terms of the sample mean and sample variance based on the noncentral t-distribution. [8] This enables the calculation of a statistical interval within which, with some confidence level, a specified proportion of a sampled population falls.
A confidence interval states there is a 100γ% confidence that the parameter of interest is within a lower and upper bound. A common misconception of confidence intervals is 100γ% of the data set fits within or above/below the bounds, this is referred to as a tolerance interval, which is discussed below.
A weaker three-sigma rule can be derived from Chebyshev's inequality, stating that even for non-normally distributed variables, at least 88.8% of cases should fall within properly calculated three-sigma intervals. For unimodal distributions, the probability of being within the interval is at least 95% by the Vysochanskij–Petunin inequality ...
His more conventional work led him to formulate the statistical idea of tolerance intervals and to propose his data presentation rules, which are listed below: Data have no meaning apart from their context. Data contain both signal and noise. To be able to extract information, one must separate the signal from the noise within the data.
Tolerance interval; This page was last edited on 2 September 2022, at 04:04 (UTC). Text is available under the Creative Commons Attribution-ShareAlike 4. ...