政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/51205

政大機構典藏-National Chengchi University Institutional Repository(NCCUR):Item 140.119/51205

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题名:	新的加權平均損失管制圖 A new weighted average loss control chart
作者:	歐家玲 Ou, Chia Ling
贡献者:	楊素芬 Yang,Su Fen 歐家玲 Ou, Chia Ling
关键词:	統計製程管制加權平均損失適應性管制圖馬可夫鏈最佳化技術 EWMA手法 Statistical process control Weighted average loss Adaptive control chart Markov chain Optimization technique EWMA scheme
日期:	2010
上传时间:	2011-10-05 14:32:01 (UTC+8)
摘要:	近幾年來，有一些研究提出了只用單一一個管制圖即可同時偵測平均數和變異數。根據此目的，我們提出了加權平均損失管制圖，此管制圖是利用加權平均損失所建立的，在一個製成的目標值和平均數不一定相等時，它可同時監控一個製成的平均數和變異數。此加權平均損失統計量是應用一個加權因子，去調整製程平均和目標值的平方差和變異數的損失比重，所以此管制圖的效能比未經由加權因子調整過的管制圖還好。我們不只建立了固定管制參數(FP)加權平均損失管制圖，也建立了適應性加權平均損失管制圖，包括變動抽樣間隔(VSI)、變動樣本數與抽樣間隔(VSI)、變動管制參數(VP)；我們利用平均連串長度(ARL)來衡量固定管制參數管制圖的偵測績效，利用馬可夫鏈的方法計算偵測出異常訊息所需的平均時間(ATS)來衡量適應性管制圖的績效，並且做比較，我們發現適應性管制圖比固定管制參數管制圖的效能還要好。我們也利用最佳化技術建立最加適應性管制圖，當製成失控時，此最佳化管制圖能使ATS1最小。此外，當平均數和變異數的偏移幅度很小時，我們利用指數加權移動平均法(EWMA)建立EWMA加權平均損失管制圖，使其有較好的偵測力。這些我們所提出的管制圖，是只根據單一一個統計量所建立的，和X bar-S管制圖相比，有較好的效能，且和使用兩個管制圖同時偵測平均數和變異數相比，比較輕易理解且容易執行。 In recent years, a few researchers had proposed different types of single charts that jointly monitor the process mean and the variation. In this project, we use the weighted average loss (WL) to construct WL control charts for monitoring the process mean and variance simultaneously while the target value may be different from the in-control mean. This statistic WL applied a weighted factor to adjust the weights of the loss due to the square of the deviation of the process mean from the target and the variance change. So the WL charts are more effective than unadjusted loss function charts. We not only construct the fixed parameters (FP) WL chart but also the adaptive WL charts which included variable sampling interval (VSI) WL chart, variable sample size and sampling interval (VSSI) WL chart and variable parameters (VP) WL chart. We calculate the average run length (ARL) for FP WL chart and using Markov chain approach to calculate the average time to signal (ATS) for adaptive WL charts to measure the performance and compare each other. From the comparison, we find the adaptive WL charts are more effective than the FP WL chart. We also proposed the optimal adaptive WL charts using an optimization technique to minimize ATS1 (ARL1) when the process was out-of-control. In addition, in order to detect the small shifts of the process mean and variance effectively, we construct the WL charts using the EWMA scheme. The proposed charts are based on only one statistic and are more effective than the X bar-S chart. And the WL charts are easy to understand and apply than using two charts for detecting the mean and variance shifts simultaneously.
參考文獻:	[1] Chan, L. K. and Cheng, S. W. (1996), “Semicircle control chart for variable data,” Quality Engineering, 8, 441-446. [2] Chen, G. and Cheng , S. W. (1998), “Max chart: combining X-bar chart and S chart,“ Statistica Sinica, 8, 263-271. [3] Chen, G., Cheng , S. W. and Xie, H. (2004), “A new EWMA control chart for monitoring both location and dispersion,” Quality Technology & Quantitative Management, 2, 217-231. [4] Chengular, I. N., Arnold, J. C. and Reynold, M. R., JR. (1989), “Variable sampling intervals for multiparameter Shewhart charts,” Communications in Statistic-Theory and Methods, 18, 1769-1792. [5] Costa A. F. B. (1999b), “ charts with variable parameters,” Journal of Quality Technology, 31, 408-416. [6] Costa A. F. B. and De Magalhaes M. S. (2007), “An adaptive chart for monitoring the process mean and variance,” Quality and Reliability Engineering international, 23, 821-831. [7] Costa A. F. B. and Rahim M. A. (2006), “A single EWMA chart for monitoring process mean and process variance,” Quality Technology & Quantitative Management, 3, 295-305. [8] Cyrus, D. (1997), Statistical aspects of quality control, Academic press, London, UK. [9] Imhof, J. P. (1961), “Computing the distribution of quadratic forms in normal variables,” Biometrika, 48(3 and 4), 419-426. [10] Khoo, M. B. C., Wu, Z. and Chen, C. H. (2010), “Using one EWMA chart to jointly monitor the process mean and variance,” Comput Stat, 25, 299-316. [11] Lucas, J. M. and Saccucci, M. S. (1990), “Average run length for exponentially weighted moving average control schemes using the Morkov chain approach,” Journal of Quality Technology, 22, 154-162. [12] Moschopoulous, P. G. and Canada, W. B. (1984), “The distribution function of a linear combination of chi-square,” Comp. & Maths, with Appls, 10, 383-386. [13] Patnaik, P. B. (1949), “The non-central and F-distribution and their Applications,” Biometrika, 36, 202-232. [14] Pearson, E. S. (1959), “Note on an approximation to the distribution of non-central ,” Biometrika, 46, 364-365. [15] Reynolds, M. R. JR., Amin, R. W., Arnold, J. C. and Nachlas, J. A (1988), “ charts with variable sampling intervals,” Technometrics, 30(2), 181-192. [16] Taguchi, G (1986). Introduction to Quality Engineering. Asian Productivity Organization, Tokyo. [17] Wu, Z. and Tian. Y. (2006), “Weighted-loss-function control charts,” Int J Adv Manuf Technol, 31, 107-115. [18] Wu, Z., Tian. Y. and Zhang, S. (2005), “Adjusted-loss-function charts with variable sample sizes and sampling intervals,” Journal of Applied statistics, 32, No.3, 221-242. [19] Wu, Z., Wang, P. and Wang, Q. (2009), “A loss function-based adaptive control chart for monitoring the process mean and variance,” Int J Adv Manuf Technol, 40, 948-959. [20] Wu, Z., Zhang, S. and Wang, P. (2007), “A CUSUM scheme with variable sample sizes and sampling intervals for monitoring the process mean and variance,” Quality and Reliability Engineering international, 23, 157-170. [21] Yang, S. and Chen, W., 2010, "Monitoring and diagnosing dependent process steps using VSI control charts," Journal of Statistical Planning and Inference, 141, 1808-1816. [21] Yang, S., Ko, C. and Yeh, J. (2010),” Using VSI Loss Control Charts to Monitor a Process with Incorrect Adjustment”, Communications in Statistics-Simulation and Computation, 39, 736-749. [22] Yang, S., Lin, D, Hung, T., (2008), "Improvement consistency of the metallic film thickness of computer connectors(in press)," Journal of process control. [22] Yang, S and Lin, J. (2009), Variable parameters loss function control chart, SSS 2009, Cape town, South Africa. [23] Yang, S. and Su, H. (2007), ”Adaptive control schemes for dependent process steps,” International Journal of loss prevention in the process industries, 20, 15-25. [24] Zhang, S. and Wu, Z. (2006), “Monitoring the process mean and variance using a weighted loss function CUSUM scheme with variable sampling intervals,” IIE Transactions, 38,377-387.
描述:	碩士國立政治大學統計研究所 98354023 99
資料來源:	http://thesis.lib.nccu.edu.tw/record/#G0098354023
数据类型:	thesis
显示于类别:	[統計學系] 學位論文

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