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http://dx.doi.org/10.7232/iems.2016.15.4.432

Designing Statistical Test for Mean of Random Profiles  

Bahri, Mehrab (Department of Industrial Engineering, Tehran Science and Research Branch, Islamic Azad University,)
Hadi-Vencheh, Abdollah (Department of Mathematics, Isfahan (Khorasgan) Branch, Islamic Azad University)
Publication Information
Industrial Engineering and Management Systems / v.15, no.4, 2016 , pp. 432-445 More about this Journal
Abstract
A random profile is the result of a process, the output of which is a function instead of a scalar or vector quantity. In the nature of these objects, two main dimensions of "functionality" and "randomness" can be recognized. Valuable researches have been conducted to present control charts for monitoring such processes in which a regression approach has been applied by focusing on "randomness" of profiles. Performing other statistical techniques such as hypothesis testing for different parameters, comparing parameters of two populations, ANOVA, DOE, etc. has been postponed thus far, because the "functional" nature of profiles is ignored. In this paper, first, some needed theorems are proven with an applied approach, so that be understandable for an engineer which is unfamiliar with advanced mathematical analysis. Then, as an application of that, a statistical test is designed for mean of continuous random profiles. Finally, using experimental operating characteristic curves obtained in computer simulation, it is demonstrated that the presented tests are properly able to recognize deviations in the null hypothesis.
Keywords
Random Profile; Profile Monitoring; Functional Approach; Designing Statistical Test; Operating Characteristic Curve;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Zhang, H. and Albin, S. (2009), Detecting outliers in complex profiles using a ${\chi}^2$ control chart method, IIE Transactions (Institute of Industrial Engineers), 41(4), 335-345.   DOI
2 Zou, C., Tsung, F., and Wang, Z. (2007), Monitoring general linear profiles using multivariate exponentially weighted moving average schemes, Technometrics, 49(4), 395-408.   DOI
3 Zou, C., Zhang, Y., and Wang, Z. (2006), A control chart based on a change-point model for monitoring linear profiles, IIE Transactions (Institute of Industrial Engineers), 38(12), 1093-1103.   DOI
4 Chicken, E., Pignatiello Jr, J. J., and Simpson, J. R. (2009), Statistical process monitoring of nonlinear profiles using wavelets, Journal of Quality Technology, 41 (2), 198-212.   DOI
5 Ding, Y., Zeng, L., and Zhou, S. (2006), Phase I analysis for monitoring nonlinear profiles in manufacturing processes, Journal of Quality Technology, 38 (3), 199-216.   DOI
6 Gupta, S., Montgomery, D. C., and Woodall, W. H. (2006), Performance evaluation of two methods for online monitoring of linear calibration profiles, International Journal of Production Research, 44(10), 1927-1942.   DOI
7 Jensen, W. A., Birch, J. B., and Woodall, W. H. (2008), Monitoring correlation within linear profiles using mixed models, Journal of Quality Technology, 40 (2), 167-183.   DOI
8 Mahmoud, M. A. (2008), Phase I analysis of multiple linear regression profiles, Communications in Statistics: Simulation and Computation, 37(10), 2106-2130.   DOI
9 Kang, L. and Albin, S. L. (2000), On-line monitoring when the process yields a linear profile, Journal of Quality Technology, 32(4), 418-426.   DOI
10 Li, Z. and Wang, Z. (2010), An exponentially weighted moving average scheme with variable sampling intervals for monitoring linear profiles, Computers and Industrial Engineering, 59(4), 630-637.   DOI
11 Mahmoud, M. A., Parker, P. A., Woodall, W. H., and Hawkins, D. M. (2007), A change point method for linear profile data, Quality and Reliability Engineering International, 23(2), 247-268.   DOI
12 Mahmoud, M. A. and Woodall, W. H. (2004), Phase I analysis of linear profiles with calibration applications, Technometrics, 46(4), 380-391.   DOI
13 Mestek, O., Pavlik, J., and Suchanek, M. (1994), Multivariate control charts: Control charts for calibration curves, Fresenius Journal of Analytical Chemistry, 350(6), 344-351.   DOI
14 Noorossana, R., Eyvazian, M., and Vaghefi, A. (2010), Phase II monitoring of multivariate simple linear profiles, Computers and Industrial Engineering, 58 (4), 563-570.   DOI
15 Stover, F. S. and Brill, R. V. (1998), Statistical quality control applied to ion chromatography calibrations, Journal of Chromatography A, 804(1/2), 37-43.   DOI
16 Subramani, J. and Balamurali, S. (2016), A Modified Single Sampling Plan for the Inspection of Attribute Quality Characteristics, Industrial Engineering and Management Systems, 15(1), 41-48.   DOI
17 Woodall, W. H., Spitzner, D. J., Montgomery, D. C., and Gupta, S. (2004), Using control charts to monitor process and product quality profiles, Journal of Quality Technology, 36(3), 309-320.   DOI
18 Kim, K., Mahmoud, M. A., and Woodall, W. H. (2003), On the monitoring of linear profiles, Journal of Quality Technology, 35(3), 317-328.   DOI
19 Vaghefi, A., Tajbakhsh, S. D., and Noorossana, R. (2009), Phase II monitoring of nonlinear profiles, Communications in Statistics-Theory and Methods, 38(11), 1834-1851.   DOI
20 Woodall, W. H. (2007), Current research on profile monitoring, Producao, 17(3), 420-425.   DOI