Effect of Estimation on Simple Linear Profile Monitoring under Non-normality

Year 2019, Volume: 23 Issue: 1, 251 - 262, 01.04.2019

Burcu Aytaçoğlu Özlem Türker Bayrak

https://doi.org/10.19113/sdufenbed.506918

Abstract

In
recent years, many control charts have been proposed to monitor profiles where
the quality of a process/product is expressed as function of response and
explanatory variable(s). The methods mostly assume that the in control
parameter values are known in Phase II analysis and innovations are normally
distributed. However, in practice, the parameters are estimated in Phase I
analysis and innovations may be non-normal. In this study, the performance of T²,
EWMA-R and EWMA-3 methods for monitoring simple linear profiles is examined via
simulation where the parameters are estimated and innovations have Student’s
t-distribution. As a
performance measure, both the average and standard deviation of the run length is
considered. Finally,
some recommendations for practitioners are summarized in a table.    

Keywords

Control chart, Run length, Exponentially weighted moving average, Profile monitoring, Statistical process control

Normal Olmayan Dağılımlar Altında Tahminin Basit Doğrusal Profil İzleme Üzerine Etkisi

Abstract

Son
yıllarda, bir ürün veya sürecin kalitesinin tepki ve açıklayıcı değişken(ler)
arasındaki ilişkinin fonksiyonu ile ifade edildiği profillerin izlenmesi için
pek çok kalite şeması önerilmiştir. Bu yöntemlerin çoğu Faz II analizlerinde
kontrol parametre değerlerinin bilindiğini ve artıkların normal dağıldığını
varsaymaktadır. Oysaki uygulamada parametreler Faz I analizlerinde tahmin
edilir ve artıklar normal olmayabilir. Bu çalışmada simülasyon ile artıkların t
dağıldığı ve parametrelerin tahmin edildiği durumlarda basit doğrusal
profillerin izlenmesi için önerilen T², EWMA-R ve EWMA-3
yöntemlerinin performansları değerlendirilmiştir. Performans ölçüsü olarak hem
ortalama koşu uzunluğu hem de koşu uzunluğu standart sapması dikkate
alınmıştır. En sonunda uygulayıcılar için bazı öneriler tablo halinde
özetlenmiştir.    

Keywords

Kontrol şeması, Koşu uzunluğu, Üstel ağırlıklı hareketli ortalama, Profil izleme, İstatistiksel süreç kontrol

References

• [1] Woodall W.H., Spitzner D.J., Montgomery D.C., Gupta S. 2004. Using control charts to monitor process and product quality profiles. Journal of Quality Technology, 36(2004), 309-320. DOI: 10.1080/00224065.2004.11980276
• [2] Noorossana R., Saghaei A., Amiri A. 2011. Statistical Analysis of Profile Monitoring (eds). John Wiley & Sons: Hoboken, NJ.
• [3] Woodall W.H., Montgomery D.C. 1999. Research issues and ideas in statistical process control. Journal of Quality Technology, 31(1999), 376-386. DOI: 10.1080/00224065.1999.11979944
• [4] Woodall W.H., Montgomery D.C. 2014. Some current directions in the theory and application of statistical process monitoring. Journal of Quality Technology, 46(2014), 78-94. DOI: 10.1080/00224065.2014.11917955
• [5] Mahmoud M.A. 2012. The performance of Phase II simple linear profile approaches when the parameters are estimated. Communications in Statistics - Simulation and Computation, 41(2012), 1816-1833. DOI: 10.1080/03610918.2011.621570
• [6] Aly A.A., Mahmoud M.A., Woodall W.H. 2015. A comparison of the performance of Phase II simple linear profile control charts when parameters are estimated. Communications in Statistics - Simulation and Computation, 44(2015), 1432-1140. DOI: 10.1080/03610918.2013.821484
• [7] Kang L., Albin S.L. 2000. On-line monitoring when the process yields a linear profile. Journal of Quality Technology, 32(2000), 418-426.
• [8] Kim K., Mahmoud M.A., Woodall W.H. 2003. On the monitoring of linear profiles. Journal of Quality Technology, 35(2003), 317-328.
• [9] Mahmoud M.A., Morgan J.P., Woodall W.H. 2010. The monitoring of simple linear regression profiles with two observations per sample. Journal of Applied Statistics, 37(2010), 1249-1263. DOI: 10.1080/02664760903008995
• [10] Mahmoud M.A., Woodall W.H. 2004. Phase I analysis of linear profiles with calibration applications. Technometrics, 46(2004), 380-391. DOI: 10.1198/004017004000000455
• [11] Noorossana R., Vaghefi A., Dorri M. 2011. Effect of non-normality on the monitoring of simple linear profiles. Quality and Reliability Engineering International, 27(2011), 425-436. DOI: 10.1002/qre.1125
• [12] Noorossana R., Saghaei A., Dorri M. 2010. Linear profile monitoring in the presence of non-normality and autocorrelation. International Journal of Industrial Engineering and Production Research, 21(2010), 221-230.
• [13] Williams J.D., Birch J.B., Woodall W.H., Ferry N.M. 2007. Statistical monitoring of heteroscedastic dose-response profiles from high-throughput screening. Journal of Agricultural, Biological and Environmental Statistics, 12(2007), 216-235. DOI: 10.1198/108571107X197779
• [14] Vaghefi A., Tajbakhsh S.D., Noorossana R. 2009. Phase II monitoring of nonlinear profiles. Communications in Statistics: Theory and Methods, 18(2009), 1834-1851. DOI: 10.1080/03610920802468707
• [15] Lucas J.M., Saccucci M.S. 1990. Exponentially weighted moving average control schemes: properties and enhancements. Technometrics, 32(1990), 1-29. DOI: 10.2307/1269835
• [16] Montgomery D.C. 2009. Introduction to Statistical Quality Control (6th edn). John Wiley & Sons: Hoboken, NJ, p702.