Utilize our free Tolerance Interval Calculator to determine the statistical range within which a specific proportion of your population is expected to fall, given a certain confidence level. Ideal for quality assurance, engineering, and data analysis, ensuring your products or processes meet critical specifications. Simply input your sample data to get precise upper and lower tolerance limits.
Formula:
The two-sided tolerance interval is calculated using the formula:
Lower Tolerance Limit (LTL): X̄ - K * s
Upper Tolerance Limit (UTL): X̄ + K * s
Where:
X̄is the Sample Meansis the Sample Standard DeviationKis the Tolerance Factor. This factor depends on the sample size (n), the desired proportion (P) of the population to be contained, and the confidence level (γ). For a normal distribution, K is derived from the inverse standard normal cumulative distribution function (CDF) and the inverse Chi-squared CDF. This calculator uses robust numerical approximations for these inverse functions to compute K.