The design of the mixed repetitive sampling plans based on the Cpk index

• Published in: The International journal of quality & reliability management 2024-01, Vol.41 (2), p.674-697
• Main Authors: Marques, Rafaela Aparecida Mendonça, Maciel, Aline Cristina, Costa, Antonio Fernando Branco, Santos, Kleber Roberto da Silva
• Format: Article
• Language: English
• Subjects: Inspection; Monte Carlo simulation; Sample size; Sampling
• ISSN: 0265-671X; 1758-6682
• DOI: 10.1108/IJQRM-07-2022-0231

PurposeThis study investigates the repetitive mixed sampling (MRS) plan based on the Cpk index that was proposed by Aslam et al. (2013a). They were the first to study the MRS plan, but they did not pay attention to the fact that submitting to the variable inspection a sample that was first submitted to the attribute inspection, truncates the X observations. In addition, they did not work with an accurate expression to calculate the probabilities of the Cpk statistic.Design/methodology/approachThe authors presented the results based on their original sampling plan through Monte Carlo simulation and defined the theoretical results of their plan when the sample submitted to the variable inspection is no longer the same one submitted to the attribute inspection.FindingsThe β risks of the optimum sampling plans presented by Aslam et al. (2013a) are pretty high, exceeding 46%, on average – this same problem was also observed in Saminathan and Mahalingam (2018), Balamurali (2020) and Balamurali et al. (2020), where the β risks of their proposed sampling plans are yet higher.Originality/valueIn terms of originality, the authors can declare the following. It is not a big deal to propose new sampling plans, if one does not know how to obtain their properties. The miscalculations of the sampling plans risks are dangerous; imagine the situation where the acceptance of bad lots exceeds 50% just because the sampling plan was incorrectly designed. Yes, it is a big deal to warn that this type of problem is arising in a growing number of papers. The authors of this study are the pioneers to discover that many studies focusing on the sampling plans need to be urgently revised.