Binomial Sampling Charts Revisited with Graphical and Analytical Arguments

Abstract

ABSTRACTConfidence interval estimation via binomial sampling charts is an important tool in the reliability field. The topic of reliability can be taught in engineering programmes at both the undergraduate and the graduate levels. It is demonstrated how to apply the binomial distribution-based belt curves to predict confidence intervals. Our demonstrated approach relies on charts that are readily available for typical confidence levels, such as, 80%, 90%, 95%, or 99%. It is the proposition of this paper that understanding the basis for the graphical confidence interval prediction method is significantly easier to appreciate if the formal analysis, which can be found in more advanced texts on reliability, is combined with visual representations for the connections between two distributions: the discrete binomial distribution and continuous partial beta distribution. The paper is presented using a combination of analytical and graphical arguments that leads to the expressions that reproduce the belt curves consistent with the “gold standard” of the Clopper–Pearson (C&P) 1934 model. The detail is sufficient to generate belt curves using a math software package. Examples illustrating the technique for predicting confidence limits with confidence belt curves are included. Students’ assessment data are also provided to support the effectiveness of the combined approach.