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Robustness of measures of common cause sigma in presence of data correlation. (English) Zbl 1060.62136

Summary: Process monitoring in the presence of data correlation is one of the most discussed issues in statistical process control literature over the past decade. However, the attention to retrospective analysis in the presence of data correlation with various common cause sigma estimators is lacking in the literature. H. D. Maragah et al. [ibid. 40, No. 1–2, 29–42 (1992)], in an early paper on the retrospective analysis in presence of data correlation, addresses only a single common cause sigma estimator. This paper studies the effect of data correlation on retrospective \(X\)-charts with various common cause sigma estimates in stable periods of AR(1) processes. This study is carried out with the aim of identifying suitable standard deviation statistic/statistics which is/are robust to the data correlation. This paper also discusses the robustness of common cause sigma estimates for monitoring the data following other time series models, namely ARMA(1,1) and AR\((p)\). Further, the bias characteristics of robust standard deviation estimates have been discussed for the above time-series models.
This paper further studies the performance of retrospective X-charts on forecast residuals from various forecasting methods of AR(1) processes. The above studies were carried out through simulating the stable period of AR(1), AR(2), stable and invertible periods of ARMA(1,1) processes. The average number of false alarms have been considered as a measure of performance. The results of simulation studies have been discussed.

MSC:

62P30 Applications of statistics in engineering and industry; control charts
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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[1] DOI: 10.1080/03610929208830829 · Zbl 0800.62636 · doi:10.1080/03610929208830829
[2] DOI: 10.2307/1391421 · doi:10.2307/1391421
[3] Bissell A. F., Applied Statistics 11 pp 305– (1984)
[4] Box G. E. P., Time Series Analysis: Forecasting and control (1994) · Zbl 0858.62072
[5] DOI: 10.2307/1270028 · doi:10.2307/1270028
[6] Brown R. G., Smoothing, Forecasting, and Prediction of Discrete Time Series (1963)
[7] Cox D. R., Journal of the Royal Statistical Society 23 pp 414– (1961)
[8] DOI: 10.1016/0360-8352(90)90117-5 · doi:10.1016/0360-8352(90)90117-5
[9] Kamat A. R., Biometrika 40 pp 116– (1953) · Zbl 0050.35804 · doi:10.1093/biomet/40.1-2.116
[10] DOI: 10.2307/2985323 · doi:10.2307/2985323
[11] Kennedy J. B., Basic Statistical Methods for Engineers and Scientists (1976)
[12] DOI: 10.1080/00949659208811363 · Zbl 0775.62283 · doi:10.1080/00949659208811363
[13] Montgomery D. C., Introduction to Statistical Quality Control (1991) · Zbl 0997.62503
[14] Montgomery D. C., Journal of Quality Technology 23 pp 179– (1991)
[15] DOI: 10.1080/03610919208813068 · Zbl 04510682 · doi:10.1080/03610919208813068
[16] Prasad S. S. R., International Journal of Quality, Reliability and Safety Engineering
[17] Roes K. C. B., Journal of Quality Technology 25 pp 188– (1993)
[18] Ryan Thomas, P., Statistical Methods for Quality Improvement (1989) · Zbl 0941.62129
[19] Tseng S., Communications in Statistics Simulation and Computation pp 187– (1994)
[20] DOI: 10.2307/1270407 · Zbl 0871.62087 · doi:10.2307/1270407
[21] Vasilopoulos A. V., Journal of Quality Technology 10 pp 20– (1978)
[22] DOI: 10.1214/aoms/1177731677 · Zbl 0060.29911 · doi:10.1214/aoms/1177731677
[23] DOI: 10.2307/1269191 · Zbl 0800.62671 · doi:10.2307/1269191
[24] Wheeler D. J., Understanding Statistical Process Control. (1986)
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