Estudo sobre planos de inspeção mistos baseados no índice Cpk

Abstract

The development of sampling plans for evaluating product batches is one of the topics present in statistical process control. Several articles dedicated to mixed sampling plans using the sampling estimator 𝐶̂𝑝𝑘, from the process capability index Cpk, constituted the object of study of this research. In mixed sampling plans, a sample is initially subjected to an inspection by attributes and, depending on the results, it is also subjected to an inspection by variables. When submitting a sample to inspection by attributes and after that, subjecting it to inspection by variables, the distribution of the quality characteristic X becomes truncated, making it difficult to obtain the distribution of 𝐶̂𝑝𝑘 and, consequently, of the risks α and β. In the literature, some authors did not pay attention to this issue. In addition, they used an incorrect expression for the cumulative distribution function of the 𝐶̂𝑝𝑘 estimator. Through Monte Carlo simulations, it was discovered that the optimal sampling plans presented by these authors lead to very high risks of acceptance of poor quality lots, greatly harming the buyer. It was necessary to redo all the optimization of the sampling plans, truly respecting the α and β risks. During the investigations, it was observed that the sample estimator 𝐶̂𝑝𝑘 does not necessarily need to be a function of the specification limits. By using a new test statistic that is unrelated to the specifications, the optimization of sampling plans now has one more degree of freedom, leading to a reduction in the average number of items inspected per lot.