Sample size determination strategies for normal tolerance intervals using historical data

摘要

Purpose:To propose strategies for the determination of minimum required sample size when using normal tolerance intervals along with historical data.Summary:The significance of using random sample in the construction of statistical tolerance interval with a required confidence level is discussed. Use of an optimal sample (minimum) size is always expected when using tolerance intervals subject to a required precision and confidence level. Under the Faulkenberry-Weeks (Ref. 1) approach for sample size determination of parametric tolerance intervals, the user is expected to specify a set of rule-of- thumb values for characterizing the desired precision of the tolerance interval. Most occasions the use of historical data and its underlying distribution play a key role in sample size determination. Accordingly, in the article presents a strategy for specifying the precision quantities in the Faulkenberry-Weeks approach that utilizes both historical data and the required specification limits. Both classical and Bayesian normal tolerance intervals are considered and the findings are numerically demonstrated. (36 refs.)Results:Use of an optimal (minimum) sample size is very important in many statistical applications such as the construction of statistical tolerance intervals. A statistical tolerance interval is constructed based on a random sample so that it includes at least a specified proportion of sampled population with a given confidence level.