Estimation of the lot fraction defective in a finite lot of products with auxiliary quality characteristics

Abstract

Many companies use sampling plans for the acceptance or rejection of lots of products. The final outcome of this decision-making process is based on the inspection of a sample of products selected from a lot under inspection, where a quality characteristic is observed. An important parameter of interest related to acceptance sampling for attributes is the proportion of defective items. This parameter is unknown for a given lot of products, but it can be estimated from the aforementioned sample information. Additional quality characteristics can be observed at the inspection stage. We propose to use this auxiliary information to obtain more accurate estimators of the lot fraction defective at the estimation stage. Various relevant applications of this process are described. For possible scenarios that may arise in practice, the empirical properties of the suggested estimation methods are investigated using Monte Carlo simulations, and desirable results are obtained when there is a strong relationship between the quality characteristic of interest and the auxiliary quality characteristic.

Keywords:

• distribution function
• lot fraction defective
• Monte Carlo simulation
• operating characteristic curve
• quality control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

Datasets and all the analyses are open and reproducible. We used a Rmarkdown document to explain statistical computing concepts and provide the R scripts used in this article. This supplemental material for reproducibility can be seen at the OSF repository (see the file “186DataSetsRcodesProportions.html” in Muñoz et al. (2023)).

Additional information

Funding

This research is part of the project PID2022-136235NB-I00, supported by the Spanish State Research Agency (AEI) / Ministry of Science and Innovation (MCIN/AEI 10.13039/501100011033) and the European Regional Development Fund (ERDF A way of making Europe).

Notes on contributors

Juan Francisco Muñoz-Rosas

Juan Francisco Muñoz-Rosas is a Professor in the Department of Quantitative Methods in Economics and Business at the University of Granada. His research is about the estimation of parameters and the applications of these estimation procedures to various disciplines and areas related to economics and business, including statistical quality control. Some of his more recent publications appeared in Quality and Reliability Engineering International, Total Quality Management & Business Excellence, Journal of Official Statistics, Journal of Applied Statistics, and Social Indicators Research.

Francisco Javier Blanco-Encomienda

Francisco Javier Blanco-Encomienda is an Associate Professor in the Department of Quantitative Methods in Economics and Business at the University of Granada and a PhD holder in Economic and Business Sciences from the same university. He is a member of the Research Group ‘Probabilistic Models Applied to Social Sciences’. His lines of research include quantitative techniques and statistical quality control. He has published several articles in high-impact journals.

Encarnación Álvarez-Verdejo

Encarnación Álvarez-Verdejo is an Associate Professor in the Department of Quantitative Methods in Economics and Business at the University of Granada. She is especially interested in the use of statistical methods for the estimation of parameters in social sciences. Some of her most recent publications are included in Quality and Reliability Engineering International, Journal of Applied Statistics, and Social Indicators Research.

Ferran Vendrell-Herrero

Ferran Vendrell-Herrero is an Associate Professor at the University of Edinburgh Business School, specializing in international business and the economic analysis of organizations. He has developed expertise in various areas, including the servitization of manufacturing, Industry 4.0, technological innovation, organizational learning, exporting, and subsidiary management. His contributions to these fields are evident through publications in prestigious academic journals such as the Journal of International Business Studies, Journal of World Business, Journal of Product Innovation Management, International Journal of Operations and Production Management, and Long Range Planning. He has also served as a co-guest editor for special issues in leading journals like Regional Studies. His research has influenced the thinking and actions of private companies, as demonstrated by a REF-2021 impact case with the BBC. Additionally, he is the founder and scientific director of the international conference on business servitization, available at www.servitization.org.