Colombian statisticians working on better monitoring of industrial quality

A researcher from Universidad del Valle (Univalle) and international collaborators explored how to improve the performance of a statistical tool used worldwide in the monitoring and control of product manufacturing quality.

"A control chart is a statistical tool designed to monitor the behavior of a critical quality variable in a process. For example: length, diameter, strength, adhesiveness or any other variable that measures the quality of the product," explained professor Jaime Mosquera Restrepo, director of the Escuela School of Statistics at the Faculty of Engineering at Univalle.

In a paper called Guaranteeing acceptable in-control and out-of-control performance of joint X ̅-S control charts with estimated parameters published in the journal Quality Technology & Quantitative Management, Professor Mosquera and his collaborators demonstrate that when the user of such a control chart does not know the parameters of the probability distribution of the quality variable, mean and variance, and instead uses an estimate based on the results of a sample, the performance of the chart can deteriorate substantially.

In practice, the above exposes the user to experience noticeable delays in detecting an undesired change in the behavior of the quality variable, under which the production of nonconforming units increases.

"We are helping companies to deliver products to the community with the agreed quality conditions," Professor Mosquera said. 

Photo: A control chart. Credit: Andrew James/NCC-FI/Univalle

The Research

In his office, Professor Mosquera explained the problem using the example of a screw factory, making screws that must produce screws with diameters between 5 and 6 millimeters. In this case, the X-S control chart is designed to detect situations in which thick (more than 6 cms) or thin (less than 5 millimeters) screws are produced.

"If the X-S control chart is not well calibrated, it can happen that when an anomalous situation arises that leads to the production of very large screws, the chart takes a long time to detect the change," the professor said, adding that in turn, late detection of the situation leads to the production of a high quantity of nonconforming screws.

"A control chart itself is very simple because it works visually," Professor Mosquera said.

As a contribution to the industry, to ensure early detection of anomalous situations, the authors solve a statistical/mathematical optimization problem under which they determine the minimum sample size that should be employed for the calibration of the limits of the X-S control chart.

"These results will contribute to providing companies with a much more effective monitoring tool, with which they can provide greater assurance to the community that their products meet the agreed quality conditions," Professor Mosquera said.

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Photo: Professor Jaime Mosquera Restrepo Credit: Andrew James/NCC-FI/Univalle

International Collaboration

Dr. Eugenio Kahn Epprecht, an associate professor at the Pontificia Universidad Católica de Río de Janeiro in Brazil and co-author of the paper, said that "undoubtedly" the academic collaboration with Professor Mosquera contributed to his academic development.

"The Department of Industrial Engineering at my institution (Pontifical Catholic University of Rio de Janeiro) highly values high-level publications and international collaboration," Professor Epprecht said.

Francisco José Aparisi García, from the Universitat Politècnica de València in Spain and a co-author of the paper, said that the work was of great complexity, and without the great contribution of Professor Mosquera it would not have been carried out.

Professor Aparisis added that for the Universitat Politècnica de València, publishing in high impact journals contributes to the rise in international quality indexes.

"Although I originally had the original idea of using zones to study the deviations produced by errors in the estimation phase, the development of the work was largely produced by Professors Mosquera and Epprecht," Profesor Aparisi said.

"Professor Mosquera attended a Master's course at the Polytechnic University of Valencia and during the course I taught him I saw his excellent performance, I proposed him to direct the final Master's thesis and later we continued collaborating with him in what was his doctoral thesis," Profesor Aparisi said.

If you would like to contact the researcher or learn more about the project, please write to the Communications Office, Faculty of Engineering: comunicaingenieria(at)correounivalle.edu.co.

Banner Photo: Professor Jaime Mosquera Restrepo Credit: Andrew James/NCC-FI/Univalle