Abstract




 
   

IJE TRANSACTIONS A: Basics Vol. 29, No. 4 (April 2016) 514-523   

downloaded Downloaded: 231   viewed Viewed: 2372

  SIMULTANEOUS MONITORING OF MULTIVARIATE PROCESS MEAN AND VARIABILITY IN THE PRESENCE OF MEASUREMENT ERROR WITH LINEARLY INCREASING VARIANCE UNDER ADDITIVE COVARIATE MODEL (RESEARCH NOTE)
 
M. Maleki, A. Amiri and R. Ghashghaei
 
( Received: October 11, 2015 – Accepted in Revised Form: April 14, 2016 )
 
 

Abstract    In recent years, some researches have been done on simultaneous monitoring of multivariate process mean vector and covariance matrix. However, the effect of measurement error, which exists in many practical applications, on the performance of these control charts is not well studied. In this paper, the effect of measurement error with linearly increasing variance on the performance of ELR control chart for simultaneous monitoring of multivariate process mean vector and covariance matrix is investigated. The multiple measurement approach is also extended to reduce this effect. Also, the performance of the proposed multiple measurement approach is evaluated in terms of average run length (ARL) and standard deviation run length (SDRL). Finally, the application of the proposed monitoring method is illustrated by a real data in manufacturing industry.

 

Keywords    measurement error, multiple measurements, linearly increasing variance, additive covariate model, simultaneous monitoring

 

چکیده    در سال‌های اخیر تحقیقاتی روی پایش همزمان بردار میانگین و ماتریس کوواریانس در فرایندهای نرمال چند متغیره انجام شده است. لیکن اثر خطای اندازه گیری که در بسیاری از کاربردهای عملی وجود دارد روی عملکرد این نوع نمودارهای کنترل به خوبی بررسی نشده است. در این مقاله اثر خطای اندازه‌گیری با واریانس خطی افزایشی روی عملکرد نمودار کنترل ELR برای پایش همزمان بردار میانگین و ماتریس کوواریانس فرایند‌های نرمال چند متغیره نشان داده شده است. همچنین روش چند بار اندازه‌گیری برای کاهش اثر خطا توسعه داده شده است. همچنین برای ارزیابی عملکرد روش چندبار اندازه‌گیری از دو معیار متوسط و انحراف استاندارد طول دنباله استفاده شده است. در نهایت با استفاده از داده‌های واقعی در صنعت ساخت کاربرد روش پیشنهادی نشان داده شده است.

References   

1.     Khoo, M. B., Teh, S. and Wu, Z., "Monitoring process mean and variability with one double ewma chart", Communications in Statistics—Theory and Methods,  Vol. 39, No. 20, (2010), 3678-3694.

2.     Guh, R.-S., "Simultaneous process mean and variance monitoring using artificial neural networks", Computers & Industrial Engineering,  Vol. 58, No. 4, (2010), 739-753.

3.     Ostadsharif Memar, A. and Niaki, S. T. A., "The max ewmams control chart for joint monitoring of process mean and variance with individual observations", Quality and Reliability Engineering International,  Vol. 27, No. 4, (2011), 499-514.

4.     Teh, S., Khoo, M. B. and Wu, Z., "Monitoring process mean and variance with a single generally weighted moving average chart", Communications in Statistics-Theory and Methods,  Vol. 41, No. 12, (2012), 2221-2241.

5.     Tasias, K. A. and Nenes, G., "A variable parameter shewhart control scheme for joint monitoring of process mean and variance", Computers & Industrial Engineering,  Vol. 63, No. 4, (2012), 1154-1170.

6.     Sheu, S.-H., Huang, C.-J. and Hsu, T.-S., "Maximum chi-square generally weighted moving average control chart for monitoring process mean and variability", Communications in Statistics-Theory and Methods,  Vol. 42, No. 23, (2013), 4323-4341.

7.     Chowdhury, S., Mukherjee, A. and Chakraborti, S., "A new distributionfree control chart for joint monitoring of unknown location and scale parameters of continuous distributions", Quality and Reliability Engineering International,  Vol. 30, No. 2, (2014), 191-204.

8.     Khoo, M. B., "A new bivariate control chart to monitor the multivariate process mean and variance simultaneously", Quality Engineering,  Vol. 17, No. 1, (2004), 109-118.

9.     Hawkins, D. M. and Maboudou-Tchao, E. M., "Multivariate exponentially weighted moving covariance matrix", Technometrics,  Vol. 50, No. 2, (2008), 155-166.

10.   Niaki, S. T. A. and Memar, A. O., "A new statistical process control method to monitor and diagnose bivariate normal mean vectors and covariance matrices simultaneously", The International Journal of Advanced Manufacturing Technology,  Vol. 43, No. 9-10, (2009), 964-981.

11.   Zhang, J., Li, Z. and Wang, Z., "A multivariate control chart for simultaneously monitoring process mean and variability", Computational Statistics & Data Analysis,  Vol. 54, No. 10, (2010), 2244-2252.

12.   Ramos, P. F., Morais, M. C., Pacheco, A. and Schmid, W., "Misleading signals in simultaneous schemes for the mean vector and covariance matrix of a bivariate process", in Recent developments in modeling and applications in statistics, (2013), Springer, 225-235.

13.   Wang, K., Yeh, A. B. and Li, B., "Simultaneous monitoring of process mean vector and covariance matrix via penalized likelihood estimation", Computational Statistics & Data Analysis,  Vol. 78, (2014), 206-217.

14.   Maleki, M. R. and Amiri, A., "Simultaneous monitoring of multivariate-attribute process mean and variability using artificial neural networks", Journal of Quality Engineering and Production Optimization,  (2015), 44-54.

15.   McCracken, A. and Chakraborti, S., "Control charts for joint monitoring of mean and variance: An overview", Quality Technology and Quantitative Management,  Vol. 10, No. 1, (2013), 17-36.

16.   Linna, K.W., Woodall, W. H. and Busby, K. L., "The performance of multivariate control charts in the presence of measurement error", Journal of Quality Technology,  Vol. 33, No. 3, (2001), 348-355.

 

17.   Huwang, L. and Hung, Y., "Effect of measurement error on monitoring multivariate process variability", Statistica Sinica, (2007), 749-760.

18.   Maravelakis, P. E., "Measurement error effect on the cusum control chart", Journal of Applied Statistics,  Vol. 39, No. 2, (2012), 323-336.

19.   Chakraborty, A. B. and Khurshid, A., "Measurement error effect on the power of control chart for the ratio of two poisson distributions", Economic Quality Control,  Vol. 28, No. 1, (2013), 15-21.

20.   Chakraborty, A. and Khurshid, A., "Measurement error effect on the power of control chart for zero-truncated poisson distribution", International Journal for Quality Research,  Vol. 7, No. 3, (2013), 411-419.

21.   Ding, G. and Zeng, L., "On the effect of measurement errors in regression-adjusted monitoring of multistage manufacturing processes", Journal of Manufacturing Systems,  Vol. 36, (2015), 263-273.

22.   Hu, X., Castagliola, P., Sun, J. and Khoo, M. B., "The effect of measurement errors on the synthetic x̄ chart", Quality and Reliability Engineering International,  Vol. 31, No. 8, (2015), 1769-1778.

23.   Haq, A., Brown, J., Moltchanova, E. and Al-Omari, A. I., "Effect of measurement error on exponentially weighted moving average control charts under ranked set sampling schemes", Journal of Statistical Computation and Simulation,  Vol. 85, No. 6, (2015), 1224-1246.

24.   Noorossana, R. and Zerehsaz, Y., "Effect of measurement error on phase II monitoring of simple linear profiles", The International Journal of Advanced Manufacturing Technology,  Vol. 79, No. 9-12, (2015), 2031-2040.

25.   Abbasi, S.A., "Exponentially weighted moving average chart and twocomponent measurement error", Quality and Reliability Engineering International, (2015).

26.   Montgomery, D. C. and Runger, G. C., "Gauge capability and designed experiments. Part I: Basic methods", Quality Engineering,  Vol. 6, No. 1, (1993), 115-135.

27.   Khati Dizabadi, A., Shahrokhi, M. and Maleki, M. R., "On the effect of measurement error with linearly increasingtype variance on simultaneous monitoring of process mean and variability", Quality and Reliability Engineering International, (2015).

28.   Cheng, S. W. and Thaga, K., "Multivariate max-CUSUM chart", Vectors,  Vol. 1, No. 2, (2005).

29.   Linna, K. W. and Woodall, W. H., "Effect of measurement error on shewhart control charts", Journal of Quality Technology,  Vol. 33, No. 2, (2001), 213-222.

30.   Cheng, S. W. and Mao, H., "A multivariate semicircle control chart for variables data", Quality Technology and Quantitative Management,  Vol. 5, No. 4, (2008), 331-337.

31.   Niaki, S. A., Houshmand, A. and Moeinzadeh, B., "On the performance of a multivariate control chart in multistage environment", International Journal of Engineering,  Vol. 14, No. 1, (2001), 49-64.

32.   Niaki, S. and Moeinzadeh, B., "A multivariate quality control procedure in multistage production systems", International Journal of Engineering,  Vol. 10, No. 4, (1997), 191-208.

33.   Owlia, M. and Fallahnezhad, M., "A new statistical approach for recognizing and classifying patterns of control charts (research note)", International Journal of Engineering-Transactions A: Basics,  Vol. 28, No. 7, (2015), 1040.-1048.





International Journal of Engineering
E-mail: office@ije.ir
Web Site: http://www.ije.ir