On-line algorithms for attribute sampling

Abstract

Acceptance sampling is an important field of statistical quality control. This thesis proposed online algorithms to construct hypergeometric sampling plans using Chebyshev polynomials. The recurrence relationship of Chebyshev polynomials significantly reduces the combinatorial computations for hypergeometric distributions. This property can be extended to compute binomial probabilities. The online tables generated by the proposed algorithms are easy to use and precise compared with the Odeh and Owen (1983)'s table. One can readily check the required sample size and acceptance number for pre-specified producer's risk; consumer's risk, proportion defective, and/or lot size for hypergeometric and binomial samplings. The algorithms also cover the confidence limits for hypergeometric and OC curve for binomial sampling. The programs written in R language are appended to show the implementation for the algorithms proposed.