Author(s): Chang, FMM (Chang, Fengming M.); Chen, LH (Chen, Long-Hui); Chen, YL (Chen, Yueh-Li); Huang, CY (Huang, Chien-Yu)
Title: Approximate distribution of demerit statistic - A bounding approach
Source: COMPUTATIONAL STATISTICS & DATA ANALYSIS, 52 (7): 3300-3309 MAR 15 2008
Language: English Document Type: Article
KeyWords Plus: STRATEGIES; CHARTS
Abstract: The traditional classical demerit control chart is used to plot the demerit statistic, a weighted sum of the number of defects in each category, on a control chart. The approximate normal method is usually used to obtain control limits though the distribution that depends on the values of the weights and the parameters of the Poisson distribution which may not always be normal. [Jones, L.A., Woodall, W.H., Conerly, M.D., 1999. Exact properties of demerit control charts. Journal of Quality Technology 31 (2), 207-216] used the characteristic function approach to determine the distribution of the demerit statistic. Unfortunately, the process that they used to determine the distribution needs complex integral evaluation via mathematical software packages or using the approximate truncated infinite series. Moreover, the characteristic function does not provide an accurate result easily. In this paper, a bounding approach is proposed to determine the approximate distribution of the demerit statistic. It is easy to implement and also the approximate error can be controlled to meet the desired accuracy. In addition, an example is demonstrated to illustrate the proposed method. The results indicate that the proposed approach is efficient and accurate. Finally, the performance among the approximate normal method, the characteristic function approach, and the
proposed bounding approach are discussed. (c) 2007 Elsevier B.V. All rights reserved.
Addresses: [Chang, Fengming M.] Asia Univ, Dept Informat Sci & Applicat, Taichung, Taiwan; [Chen, Long-Hui] Shu Te Univ, Dept Logist Management, Kaohsiung, Taiwan; [Chen, Yueh-Li] Cheng Shu Univ, Dept Ind Engn & Management, Kaohsiung, Taiwan; [Huang, Chien- Yu] Shu Te Univ, Dept Informat Management, Kaohsiung, Taiwan
Reprint Address: Chang, FMM, 500 Lioufeng Rd, Wufeng 41354, Taichung County, Taiwan.
E-mail Address: paperss@gmail.com; cyhuang@mail.stu.edu.tw
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Cited Reference Count: 17 Times Cited: 0
Publisher: ELSEVIER SCIENCE BV
Publisher Address: PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS ISSN: 0167-9473
DOI: 10.1016/j.csda.2007.10.029
29-char Source Abbrev.: COMPUT STAT DATA ANAL ISO Source Abbrev.: Comput. Stat. Data Anal.
Source Item Page Count: 10
Subject Category: Computer Science, Interdisciplinary Applications; Statistics & Probability ISI Document Delivery No.: 290TU
