TY - JOUR
T1 - On Designing an Optimal SPRT Control Chart with Estimated Process Parameters under Guaranteed In-control Performance
AU - Teoh, Jing Wei
AU - Teoh, Wei Lin
AU - Boon Chong Khoo, Michael
AU - Castagliola, Philippe
AU - Moy, W. H.
N1 - Funding Information:
This work was supported by the Ministry of Higher Education (MOHE) Malaysia and Heriot-Watt University Malaysia under Fundamental Research Grant Scheme (FRGS), no. FRGS/1/2021/STG06/HWUM/02/1.
Publisher Copyright:
© 2022 Elsevier Ltd
PY - 2022/12
Y1 - 2022/12
N2 - 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.
AB - 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.
KW - Average extra quadratic loss
KW - Guaranteed in-control performance
KW - Markov chain
KW - Parameter estimation
KW - SPRT control chart
KW - Statistical process control
UR - http://www.scopus.com/inward/record.url?scp=85145591967&partnerID=8YFLogxK
U2 - 10.1016/j.cie.2022.108806
DO - 10.1016/j.cie.2022.108806
M3 - Article
SN - 0360-8352
VL - 174
JO - Computers and Industrial Engineering
JF - Computers and Industrial Engineering
M1 - 108806
ER -