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 Most products are produced by several process steps and have more than one interested quality characteristics. If each step of the process is independent, and the observations taken from the process are also independent then we may use Shewhart control chart at each step. However, in many processes, most production steps are dependent and the observations taken from the process are correlated. In this research, we consider the process has two dependent steps and the observations taken from the process are correlated over time. We construct the individual residual control chart to monitor the previous process and the cause-selecting control chart to monitor the current process. Then simulate all the states occur in the process and present the individual residual control chart and the cause-selecting control chart of the simulations. Furthermore compare the proposed control charts with the Hotelling T2 control chart. At last, we give an example to illustrate how to construct the proposed control charts. From the proposed control charts, we can determine which step of the process is out of control easily. If there is a signal in the individual residual control chart, it means the previous process is out of control. If there is a signal in the cause-selecting control chart, it means the current process is out of control. The Hotelling T2 control chart only indicate the process is out of control but does not detect which step of the process is out of control.
 TABLE OF CONTENTS 1. INTRODUCTION……………………………………………………………..……………….1 2. THE PROCESS MODEL………………………………………………………………...…….4 2.1Assumptions and Notation……………………….…………………………………….……..4 2.2The Possible Distribution of Xt and Yt ……………………….…………………………..….6 2.3Process Control for the Previous and Current process…………………….………………..22 2.3.1 Establish the Individual Residual Chart to Monitor the Previous Process…………….22 2.3.2 Establish the Cause-Selecting Control Chart to Monitor the Current Process………...23 2.4 Type I, Type II Error Probabilities and the Power of the Propose Control Chart…………..26 3. Simulation Study and An Empirical Example………………………………………………...42 3.1 Simulate 9 Process States…………………………………………………………………..42 3.1.1 Simulate state 1 in the process……………………………………………………..……42 3.1.2 Simulate state 2 in the process……………………………………………………..……57 3.1.3 Simulate state 3 in the process……………………………………………………..……59 3.1.4 Simulate state 4 in the process……………………………………………………..……61 3.1.5 Simulate state 5 in the process……………..……………………………………………63 3.1.6 Simulate state 6 in the process…………………………………….…………………….65 3.1.7 Simulate state 7 in the process………………….……………………………….………67 3.1.8 Simulate state 8 in the process…………….…………………………………….………69 3.1.9 Simulate state 9 in the process…………….……………………………………….……71 3.2 An Empirical Example…………………………………………………………………….73 3.3 Comparison the proposed control chart and Hotelling T2 control chart…………………..90 4. CONCLUSION………………………………………………………………………………..91 5.REFERENCES………………………………………………………………………………...92 6.APPENDICES…………………………………………………………………………………94 Appendix 1 (the empirical data to build the proposed charts)……………...…………………..94 Appendix 2 (the empirical data to build the proposed charts)……………………….………....95 Appendix 3 (the S-plus program to count ARL for the simulated 9 states data)……………….96
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