Research on the Sampling Procedures for Inspection by Variables When Quality Characteristics Follow the Chi-Square Distribution

Abstract

In this paper sampling procedures for inspection by variables are discussed under the assumption that product quality characteristics are distributed by chi-square distribution. In the sampling procedure, due to the randomness of sampling, the judgment result may be inconsistent with the actual situation of product quality. That is, when the actual quality of the product is qualified, it is judged as unacceptable (at this time, a type of error in hypothesis testing is made, and we control it to make the probability of making a type of error less than or equal to 0.05). When the actual quality of the product is unqualified, it may be judged as acceptable (at this time, another type of error in hypothesis testing is made, and we control it to let the probability of making a type of error less than or equal to 0.1). In this paper the idea of nonlinear programming is adopted to determine the sampling procedure.