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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)."
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 ...
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 ...
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.
the statistical confidence interval or tolerance interval of the initial measurement; the number of significant figures of the measurement; the intended use of the measurement, including the engineering tolerances; historical definitions of the units and their derivatives used in old measurements; e.g., international foot vs. US survey foot.
A cascade chart is an alternative way from the traditional damage tolerance analysis (DTA) methodology for determining a reliable inspection interval. It uses the scatter from crack growth simulations, uncertainty in material properties, and probability of detection distribution to determine the NDI interval, given a desired cumulative ...
It is remarkable that the sum of squares of the residuals and the sample mean can be shown to be independent of each other, using, e.g. Basu's theorem.That fact, and the normal and chi-squared distributions given above form the basis of calculations involving the t-statistic:
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