×

Drift time detection and adjustment procedures for processes subject to linear trend. (English) Zbl 1160.90389

Summary: This paper considers production processes when the mean of a quality characteristic is drifted linearly with time. First, it introduces a procedure to detect the drift time of the process mean as early as possible. Then, based on the estimate of the drift time, a new adjustment procedure based on the maximum likelihood estimate of the drift time is developed to keep the process mean on target. The paper analyses and compares the performance of the proposed estimator with cumulative sum (CUSUM) and exponentially moving average (EWMA) change point estimation procedures. It is observed that the proposed procedure indeed estimates the drift time effectively for moderate and large trend rates. However, there is a noticeable decrease in its ability to detect drift time at small trend rates. Furthermore, the performance of the new adjustment procedure is compared with EWMA controllers. It is shown that the new procedure is more stable through a wide range of trend rates and its performance does not depend on any parameters of the process.

MSC:

90B30 Production models
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] DOI: 10.1093/biomet/58.3.525 · Zbl 0224.62035 · doi:10.1093/biomet/58.3.525
[2] DOI: 10.2307/1268581 · doi:10.2307/1268581
[3] DOI: 10.1109/66.286855 · doi:10.1109/66.286855
[4] Del Castello E, IIE Trans. 31 pp 1157– (1999)
[5] Del Castello E, J. Qual. Tech. 33 pp 153– (2001)
[6] Fahmy HM, Report No. 014, in: Drift Time Detection and Adjustment Procedures for Processes Subject to Linear Trend (2005)
[7] DOI: 10.1214/aos/1176343000 · Zbl 0324.62015 · doi:10.1214/aos/1176343000
[8] DOI: 10.1093/biomet/57.1.1 · Zbl 0198.51501 · doi:10.1093/biomet/57.1.1
[9] DOI: 10.1093/biomet/56.3.495 · Zbl 0183.48505 · doi:10.1093/biomet/56.3.495
[10] DOI: 10.2307/2284220 · Zbl 0226.62068 · doi:10.2307/2284220
[11] DOI: 10.2307/2283203 · Zbl 0146.40506 · doi:10.2307/2283203
[12] Ingolfsson A, J. Qual. Tech. 25 pp 271– (1993)
[13] DOI: 10.2307/2346413 · doi:10.2307/2346413
[14] DOI: 10.2307/2286616 · Zbl 0387.62048 · doi:10.2307/2286616
[15] DOI: 10.1002/qre.4680080605 · doi:10.1002/qre.4680080605
[16] Page ES, Biometrics 41 pp 100– (1954)
[17] DOI: 10.1142/S0218539305001719 · doi:10.1142/S0218539305001719
[18] Pignatiello JJ, J. Qual. Tech. 33 pp 82– (2001)
[19] DOI: 10.1080/08982119808919166 · doi:10.1080/08982119808919166
[20] Shewhart WA, Economic Control of Quality of Manufactured Product (1931)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.