Methods of Evaluating One-Sided Tolerance Limit (A- and B-Basis Values) of Combined Sample Sets

概要

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Methods of evaluating the one-sided tolerance limit (A- and B- basis values) of combined sample sets are derived. The A- and B- basis values are statistically calculated numbers that respectively indicate that at least 99 and 90 percent of the population is expected to equal or exceed the statistically calculated value with a confidence of 95 percent, and they are used to determine strength tolerance limits in aerospace designs. The A- and B-basis values tend to be underestimated when the sample size is small and the conventional methods are used. Our novel methods improve the basis values by combining multiple sample sets from normally (Gaussian) distributed populations. We extended analysis of variance (ANOVA) to evaluate the A- and B- basis values by using non-central t-distribution under the condition of equality of variances. In addition, we derive coefficients for the basis values under the condition of non-equality of variances by using a Monte-Carlo method. Numerical examples show that both methods, i.e., equality and non-equality of variance cases, increase the A- and B-basis values.