An analysis of online quality control by attributes with an imperfect classification system and inspections with samples of size n

Abstract

In this article we propose a new online control system aiming to lower the instants in which the production process migrates from being in- to out-of-control state, which generates an increase in the non-conformity rates. As shifts from in- to out-of-control are non-deterministic, a sample of size n is collected, for each m or L units produced, and each element from the sample is imprecisely classified as conform or non-conform (that is, there may be classification errors). If the amount of conform units from the sample is equal or greater than a, the process would not be adjusted and another sample would be collected after m units produced. If the quantity of conform units is inferior to a, the process would be adjusted and another sample would be collected after L units produced, given that L > m. A genetic algorithm is proposed to approximately find the values of a, n, m, and L that minimize all costs involved in the process being controlled. All procedures are illustrated through a detailed numerical example that attests the efficacy and efficiency of the proposed online control system.

Keywords:

• Online control by attributes
• Classification errors
• Economic planning
• Genetic algorithms

MATHEMATICS SUBJECT CLASSIFICATION:

• 62P30
• 60J05
• 60J20
• 60J10

Acknowledgment

The authors would like to acknowledge the suggestions from the anonymous reviewer, which greatly contributed to the readability of this article.

Diclosure statement

The founder had no role in the study design, data collection and analysis, decision to publish, or preparation of the manuscript. The authors declare that there are no conflicts of interest regarding the publication of this article.

Availability of data and material

The data used to support the findings of this study are included within the article.

Code availability

The proposed algorithms can be encoded in the reader's favorite programming language. MATLAB® macros can be obtained from the authors upon request.

Authors' contributions

All authors, LFB, RCQ, FRBC, and ARP contributed equally to the design and implementation of the research, to the analysis of the results, and to the final writing of the manuscript.

Classification code

An Analysis of Online Quality Control by Attributes with an Imperfect Classification System and Inspections with Samples of Size n.

Additional information

Funding

The authors would like to acknowledge CNPq (Conselho Nacional de Desenvolvimento Científico e Tecnológico, grants 479199/2013-2 and 305515/2018-7) and FAPEMIG (Fundação de Amparo à Pesquisa do Estado de Minas Gerais, grants APQ-02888-15 and CEX-PPM-00564-17) for partial financial support.