Asymptotical distributions, parameters and coverage probabilities of tolerance limits

In industries a tolerance limit of material quality is usually obtained by calculating the lower limit of a confidence interval for a percentile of the quality characteristic population. In this paper a single unified expression is given for tolerance limits from one-population model, one-way ANOVA model and linear regression model. Based on this expression the asymptotical normality and the probabilistic convergence are established, the formulas for the parameters and for the coverage probabilities are derived. A numerical study is then conducted on A-basis and B-basis that are widely used in aircraft composite material industry.