Monotonic change-point estimation of multivariate Poisson processes using a multi-attribute control chart and MLE

References

• Abbasi, B., S. T. A. Niaki, and S. E. Seyedan. 2011. “A Simple Transformation Method in Skewness Reduction.” International Journal of Engineering Transactions A: Basics 24: 169–175.
   Google Scholar
• Aebtarm, S., and N. Bouguila. 2010. “An Optimal Bivariate Poisson Field Chart for Controlling High-quality Manufacturing Processes.” Expert Systems with Applications 37: 5498–5506.
   Web of Science ®Google Scholar
• Atashgar, K., and R. Noorossana. 2012. “Diagnosing the Source(s) of a Monotonic Change in the Process Mean Vector.” International Journal of Advanced Manufacturing Technology 60: 1175–1183.
   Web of Science ®Google Scholar
• Ayer, M., H. D. Brunk, G. M. Ewing, W. T. Reid, and E. Silverman. 1955. “An Empirical Distribution Function for Sampling with Incomplete Information.” Annals of Mathematical Statistics 26: 641–647.
   Google Scholar
• Best, M. J., and N. Chakravarti. 1990. “Active Set Algorithms for Monotonic Regression: A Unifying Framework.” Mathematical Programming 47: 425–439.
   Web of Science ®Google Scholar
• Cario, M. C., and B. L. Nelson. 1997. Modeling and Generating Random Vectors with Arbitrary Marginal Distributions and Correlation Matrix. Technical Report, Department of Industrial Engineering and Management Sciences, Northwestern University, USA.
   Google Scholar
• Chiu, J. E., and T. I. Kuo. 2008. “Attribute Control Chart for Multivariate Poisson Distribution.” Communications in Statistics-Theory and Methods 37: 146–158.
   Web of Science ®Google Scholar
• Fahmy, H. M., and E. A. Elsayed. 2006. “Drift Time Detection and Adjustment Procedures for Processes Subject to Linear Trend.” International Journal of Production Research 44: 3257–3278.
   Web of Science ®Google Scholar
• Famoye, F. 2010. “A New Bivariate Generalized Poisson Distribution.” Statistica Neerlandica 64: 112–124.
   Web of Science ®Google Scholar
• Fernando, W. T. P. S., and D. D. S. Kulatunga. 2007. “On the Computation and Some Applications of Multivariate Isotonic Regression.” Computational Statistics & Data Analysis 52: 702–712.
   Web of Science ®Google Scholar
• Francisco, A., A. Gerardo, and S. Jose. 2006. “Techniques to Interpret T2 Control Chart Signals.” IIE Transactions 38: 647–657.
   Web of Science ®Google Scholar
• Hansohm, J., and X. Hu. 2012. “A Convergent Algorithm for a Generalized Multivariate Isotonic Regression Problem.” Statistical Papers 53: 107–115.
   Web of Science ®Google Scholar
• Ho, L. L., and A. F. B. Costa. 2009. “Control Charts for Individual Observations of a Bivariate Poisson Process.” International Journal of Advanced Manufacturing Technology 43: 744–755.
   Web of Science ®Google Scholar
• Jarque, C. M., and A. K. Bera. 1987. “A Test for Normality of Observations and Regression Residuals.” International Statistical Review 55: 163–172.
   Web of Science ®Google Scholar
• Johnson, R. A., and D. W. Wichern. 2007. Applied Multivariate Statistical Analysis. 6th ed. New Jersey, NJ: Prentice Hall.
   Google Scholar
• Karlis, D., and L. Meligkotsidou. 2007. “Finite Mixtures of Multivariate Poisson Distributions with Application.” Journal of Statistical Planning and Inference 137: 1942–1960.
   Web of Science ®Google Scholar
• Laungrungrong, B. 2010. “Multivariate Charts for Multivariate Poisson-distributed Data.” Dissertation, Arizona State University, USA.
   Google Scholar
• Li, Y., and F. Tsung. 2012. “Multiple Attribute Control Charts with False Discovery Rate Control.” Quality and Reliability Engineering International 28: 857–871.
   Web of Science ®Google Scholar
• Lowry, C. A., and D. C. Montgomery. 1995. “A Review of Multivariate Control Charts.” IIE Transactions 27: 800–810.
   Web of Science ®Google Scholar
• Lu, X. S., M. Xie, T. N. Goh, and C. D. Lai. 1998. “Control Chart for Multivariate Attribute Processes.” International Journal of Production Research 36: 3477–3489.
   Web of Science ®Google Scholar
• Mason, R. L., N. D. Tracy, and J. C. Young. 1997. “A Practical Approach for Interpreting Multivariate T2 Control Chart Signals.” Journal of Quality Technology 29: 396–406.
   Web of Science ®Google Scholar
• Montgomery, D. C. 2005. Introduction to Statistical Quality Control. 5th ed. New York, NY: John Wiley.
   Google Scholar
• Montgomery, D. C., and C. M. Mastrangelo. 1991. “Some Statistical Process Control Methods for Autocorrelated Data.” Journal of Quality Technology 23: 179–204.
   Web of Science ®Google Scholar
• Niaki, S. T. A., and B. Abbasi. 2007a. “Skewness Reduction Approach In Multi-attribute Process Monitoring.” Communications in Statistics-Theory and Methods 36: 2313–2325.
   Web of Science ®Google Scholar
• Niaki, S. T. A., and B. Abbasi. 2007b. “On the Monitoring of Multi-attributes High-quality Production Processes.” Metrika 66: 373–388.
   Web of Science ®Google Scholar
• Niaki, S. T. A., and B. Abbasi. 2008. “Generating Correlation Matrices for Normal Random Vectors in Norta Algorithm Using Artificial Neural Networks.” Journal of Uncertain Systems 2: 192–201.
   Google Scholar
• Niaki, S. T. A., and B. Abbasi. 2009. “Monitoring Multi-attribute Processes Based on NORTA Inverse Transformed Vectors.” Communications in Statistics-Theory and Methods 38: 964–979.
   Web of Science ®Google Scholar
• Niaki, S. T. A., and M. Khedmati. 2012. “Detecting and Estimating the Time of a Step-change in Multivariate Poisson Processes.” Scientia Iranica: Transactions E 19: 862–871.
   Web of Science ®Google Scholar
• Niaki, S. T. A., and M. Khedmati. 2013. “Estimating the Change Point of the Parameter Vector of Multivariate Poisson Processes Monitored by a Multi-attribute T2 Control Chart.” International Journal of Advanced Manufacturing Technology 64: 1625–1642.
   Web of Science ®Google Scholar
• Niaki, S. T. A., and M. Nafar. 2008. “An Artificial Neural Network Approach to Monitor and Diagnose Multi-attribute Quality Control Processes.” Journal of Industrial Engineering International 4: 10–24.
   Google Scholar
• Niaki, S. T. A., and S. A. Nasaji. 2011. “A Hybrid Method of Artificial Neural Networks and Simulated Annealing in Monitoring Auto-correlated Multi-attribute Processes.” International Journal of Advanced Manufacturing Technology 56: 777–788.
   Web of Science ®Google Scholar
• Noorossana, R., and A. Shadman. 2009. “Estimating the Change Point of a Normal Process Mean with a Monotonic Change.” Quality and Reliability Engineering International 25: 79–90.
   Web of Science ®Google Scholar
• Noorossana, R., A. Saghaei, K. Paynabar, and S. Abdi. 2009. “Identifying the Period of a Step Change in High-yield Processes.” Quality and Reliability Engineering International 25: 875–883.
   Web of Science ®Google Scholar
• Perry, M. B., and J. J. Pignatiello. 2005. “Estimation of the Change Point of the Process Fraction Nonconforming in SPC Applications.” International Journal of Reliability, Quality and Safety Engineering 12: 95–110.
   Google Scholar
• Perry, M. B., and J. J. Pignatiello. 2006. “Estimation of the Change Point of a Normal Process Mean with a Linear Trend Disturbance.” Quality Technology and Quantitative Management 3: 101–115.
   Google Scholar
• Perry, M. B., J. J. Pignatiello, and J. R. Simpson. 2006. “Estimating the Change Point of a Poisson Rate Parameter with a Linear Trend Disturbance.” Quality and Reliability Engineering International 22: 371–384.
   Web of Science ®Google Scholar
• Perry, M. B., J. J. Pignatiello, and J. R. Simpson. 2007a. “Change Point Estimation for Monotonically Changing Poisson Rates in SPC.” International Journal of Production Research 45: 1791–1813.
   Web of Science ®Google Scholar
• Perry, M. B., J. J. Pignatiello, and J. R. Simpson. 2007b. “Estimating the Change Point of the Process Fraction Non-conforming with a Monotonic Change Disturbance in SPC.” Quality and Reliability Engineering International 23: 327–339.
   Web of Science ®Google Scholar
• Pignatiello, J. J., and T. R. Samuel. 2001. “Estimation of the Change Point of a Normal Process Mean in SPC Applications.” Journal of Quality Technology 33: 82–95.
   Web of Science ®Google Scholar
• Robertson, T., F. T. Wright, and R. L. Dykstra. 1988. Order Restricted Statistical Inference. New York: Wiley.
   Google Scholar
• Samuel, T. R., and J. J. Pignatiello. 1998. “Identifying the Time of a Change in a Poisson Rate Parameter.” Quality Engineering 10: 673–681.
   Google Scholar
• Samuel, T. R., and J. J. Pignatiello. 2001. “Identifying the Time of a Step Change in the Process Fraction Non-conforming.” Quality Engineering 13: 357–365.
   Google Scholar
• Samuel, T. R., J. J. Pignatiello, and J. A. Calvin. 1998a. “Identifying the Time of a Step Change with X-bar Control Charts.” Quality Engineering 10: 521–527.
   Google Scholar
• Samuel, T. R., J. J. Pignatiello, and J. A. Calvin. 1998b. “Identifying the Time of a Step Change in a Normal Process Variance.” Quality Engineering 10: 529–538.
   Google Scholar
• Sasabuchi, S., M. Inutsuka, and D. D. S. Kulatunga. 1983. “A Multivariate Version of Isotonic Regression.” Biometrika 70: 465–472.
   Web of Science ®Google Scholar
• Sasabuchi, S., M. Inutsuka, and D. D. S. Kulatunga. 1992. “An Algorithm for Computing Multivariate Isotonic Regression.” Hiroshima Mathematical Journal 22: 551–560.
   Google Scholar
• Skinner, K. R., G. C. Runger, and D. C. Montgomery. 2006. “Process Monitoring for Multiple Count Data Using a Deleted-Y Statistic.” Quality Technology and Quantitative Management 3: 247–262.
   Google Scholar
• Topalidou, E., and S. Psarakis. 2009. “Review of Multinomial and Multi-attribute Quality Control Charts.” Quality and Reliability Engineering International 25: 773–804.
   Web of Science ®Google Scholar
• Yahav, I., and G. Shmueli. 2012. “On generating Multivariate Poisson Data in Management Science Applications.” Applied Stochastic Models in Business and Industry 28: 91–102.
   Web of Science ®Google Scholar
• Zamba, K. D., and D. M. Hawkins. 2009. “A Multivariate Change-point Model for Change in Mean Vector and/or Covariance Structure.” Journal of Quality Technology 41: 285–303.
   Web of Science ®Google Scholar