On Designing an Optimal SPRT Control Chart with Estimated Process Parameters under Guaranteed In-control Performance

Jing Wei Teoh, Wei Lin Teoh, Michael Boon Chong Khoo, Philippe Castagliola, W. H. Moy

Research output: Contribution to journalArticlepeer-review

Abstract

Being one of the most sophisticated control charts, the sequential probability ratio test (SPRT) chart possesses fast detection ability across a broad range of process shifts. The SPRT chart has the advantage of sampling only a modest number of observations. Thus far, the SPRT chart has been developed under the assumption that the process parameters are known. As process parameters are often unknown in practice, this article reveals that parameter estimation from a limited amount of Phase-I data, leads to excessive false alarms and unstable chart’s performances. To counter these problems, this article advocates the use of adjusted control limits to ensure that a sufficiently high proportion of the in-control conditional average time to signal value, is greater than a pre-specified level. This increasingly prevalent design of control charts is known as Guaranteed In-Control Performance (GICP). In this article, we propose an optimization design for the SPRT chart with estimated process parameters, by minimizing the expected value of the average extra quadratic loss under the GICP framework. Theoretical derivations by means of the Markov chain approach are developed in this article to evaluate the run-length properties of the SPRT chart with estimated process parameters. Results show that the overall performance of the proposed optimal SPRT chart is almost twice as good as the optimal CUSUM chart over a given range of process mean shifts. Finally, an implementation of the proposed optimal SPRT chart is demonstrated with real industrial data obtained from an epitaxial process.
Original languageEnglish
Article number108806
JournalComputers and Industrial Engineering
Volume174
Early online date10 Nov 2022
DOIs
Publication statusPublished - Dec 2022

Keywords

  • Average extra quadratic loss
  • Guaranteed in-control performance
  • Markov chain
  • Parameter estimation
  • SPRT control chart
  • Statistical process control

ASJC Scopus subject areas

  • Computer Science(all)
  • Engineering(all)

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