A new mixed repetitive group sampling plan based on the process capability index for product acceptance

Abstract

Purpose The purpose of this paper is to propose a new mixed repetitive group sampling (RGS) plan based on the process capability index, Cpk, where the quality characteristics of interest follow the normal distribution with unknown mean and unknown variance. Tables are constructed to determine the optimal parameters for practical applications for both symmetric and asymmetric fraction non-conforming cases. The advantages of this proposed mixed sampling plan are also discussed. The proposed sampling plan is also compared with other existing sampling plans. Design/methodology/approach In order to determine the optimal parameters of the proposed mixed RGS plan based on Cpk, the authors constructed tables for various combinations of acceptable and limiting quality levels (LQLs). For constructing tables, the authors followed the approach of two points on the operating characteristic (OC) curve. The optimal problem is formulated as a non-linear programming where the objective function to be minimized is the average sample number (ASN) and the constraints are related to lot acceptance probabilities at acceptable quality level and LQL under the OC curve. Findings The proposed mixed RGS plan will be a new addition to the literature of acceptance sampling. It is shown that the proposed mixed plan involves minimum ASN with desired protection to both producers and consumers compared to other existing sampling plans. The practical application of the proposed mixed sampling plan is also explained with an illustrative real-time example. Originality/value In this paper, the authors propose a new mixed RGS plan based on the process capability index Cpk, where the quality characteristic of interest follows the normal distribution with unknown mean and unknown variance. Tables are constructed to determine the optimal parameters for practical applications. The proposed mixed sampling plan can be used in all production industries. This kind of mixed RGS plan is not available in the literature.

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

“…The results were verified by simulation. Comparing the two cases a and b, we see that Saminathan and Mahalingam (2018) underestimated n 1 and n 2 , and also underestimated the average number of inspected items per lot (ψÞ.…”

“…The adoption of two different samples increases the ANI of the AMRS plan; in some cases, the increase is close to 100%. The mixed sampling plans proposed by Saminathan and Mahalingam (2018), Balamurali (2020) and Balamurali et al (2020) are examples of sampling plans where the sample submitted to the attribute inspection and the sample submitted to variable inspection are two different samples. They did not discuss the rationale behind the inspection of different samples.…”

“…In recent proposed mixed repetitive sampling plans, the sample submitted to the variable inspection is not the same sample submitted to the attribute inspection. Because of that, the X observations are no longer truncated; see, for instance, Saminathan and Mahalingam (2018), Balamurali (2020) and Balamurali et al (2020). In the literature of process control, several articles also consider the procedure of splitting the samples in two subsamples, where the items of the first subsample are submitted to the attribute inspection, and the items of the second subsample (2016) and Melo et al (2017).…”

Auto-encoder-based algorithm for the selection of key characteristics for products to reduce inspection efforts

“…Nakhaeinejad (2022) describes a model which includes a single sampling plan whose sample size is adapted according to the order quantity with the aim to optimize inventory management and quality control. Saminathan and Mahalingam (2018) develop a mixed sampling plan which uses the process capability index to reduce the sample size while securing quality. Cudney et al (2016) develop a model to determine sampling level products from component to assembly level.…”

A New Control Chart for Process Monitoring Based on the Unified Capability Index

“…Process capability indices (PCIs) are dimensionless measures based on process parameters and specifications that have been widely used to determine whether a manufacturing process is capable of producing items within a given specified tolerance set by the customer or MATTER: International Journal of Science and Technology ISSN 2454-5880 organization (Balamurali & Usha, 2018). Several capability indices have been proposed to measure process capability.…”