Statistical Process Control for Latent Quality Characteristics Using the Up-and-Down Test

ABSTRACT

In many applications, the quality characteristic of a product is continuous but unobservable, for example, the critical electric voltage of electro-explosive devices. It is often important to monitor a manufacturing process of a product with such latent quality characteristic. Existing approaches all involve specifying a fixed stimulus level and testing products under that level to collect a sequence of response outcomes (zeros or ones). Appropriate control charts are then applied to the collected binary data sequence. However, these approaches offer limited performance. Moreover, the collected dataset provides little information for troubleshooting when an out-of-control signal is triggered. To overcome these limitations, this article introduces the up-and-down test for collecting data and proposes a new control chart based on this test. Numerical studies show that the proposed chart is able to detect any shifts effectively and is robust in many situations. Finally, an example involving real manufacturing data is given to demonstrate the use of our proposed chart.

KEYWORDS:

• Binary data
• Censored data
• Control chart
• Latent quality characteristics
• Latent variable
• SPC
• Up-and-down test

Acknowledgments

The authors thank the Editor, the Associate Editor, and two referees for many constructive comments and suggestions, which have greatly improved the quality of the article. This work was supported by National Science Fund of China (No. 11501209, 11571113, 11271135, 71402133, 71602155), the Postdoctoral Science Foundation of China (2015M570348), Shanghai Rising Star Program (16QA1401700), the Fundamental Research Funds for the Central Universities and the 111 Project (B14019), The International Postdoctoral Exchange Fellowship Program (20160089), Program of Shanghai Subject Chief Scientist (14XD1401600), RGC General Research Fund (619913) and the Project of Shanghai Universities to enhance the competition and innovation “collaborative innovation of modern statistical methods and theory.”