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Cusum Control Chart for Monitoring Process Variance  

Lee, Yoon-Dong (Department of Applied Statistics, Konkuk University)
Kim, Sang-Ik (Department of Applied Statistics, Konkuk University)
Publication Information
Journal of Korean Society for Quality Management / v.33, no.3, 2005 , pp. 149-155 More about this Journal
Abstract
Cusum control chart is used for the purpose of controling the process mean. We consider the problem related to cusum chart for controling process variance. Previous researches have considered the same problem. The main difficulty shown in the related researches was to derive the ARL function which characterizes the properties of the chart. Sample variance, differently with sample mean, follows chi-squared type distribution, even when the quality characteristics are assumed to be normally distributed. The ARL function of cusum is described by a type of integral equation. Since the solution of the integral equation for non-normal distribution is not known well, people used simulation method instead of solving the integral equation directly, or approximation method by taking logarithm of the sample variance. Recently a new method to solve the integral equation for Erlang distribution was published. Here we consider the steps to apply the solution to the problem of controling process variance.
Keywords
CUSUM; Process Variance; Erlang Distribution;
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Times Cited By KSCI : 1  (Citation Analysis)
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1 Brook, D. and Evans, D. A.(1972). 'An Approach to the Probability Distributionb of Cusum Run Length', Biometriks, Vol. 59, pp. 539-549   DOI   ScienceOn
2 Lee, Y. D.(2004), 'Unified Solutions of Integral Equations of SPRT for exponential Random Variables', Commanicetions in Statistics, Series A, Theory and Method, Vol. 33, pp. 65-74
3 Stadje, W.(1987). 'On the SPRT for the Mean of an Exponential Distribution', Statistics & Probability Letters, Vol. 5, pp. 389-395   DOI   ScienceOn
4 Knoth, S.(1998), 'Exact Average Run Leng ths of CUSUM Schemes for Erlang Distribution' Sequentl Analysis, Vol. 17, pp. 173-184   DOI   ScienceOn
5 Crowder, S. V. and Hamilton, M. D.(1992), 'An EWMA for Monitoring a Process Standard Deviation', Journal of Quality Technology, Vol. 24, .pp 12-21   DOI
6 Chang, T. and Gan, F.(1995), 'A Cumulative Sum Control Chart for Monitoring Process Variance', Journal of Quality Technology, Vol. 25, pp. 109-119
7 Vardeman, S. and Ray, D.(1985), 'Average Run Lengths for CUSUM Schemes When Observations Are Exponentially Distributed', Technometrics, Vol. 27, pp. 145-150   DOI   ScienceOn
8 Gan, F. and Choi, K(1994), 'Computing Average Run Lengths for Exponential CUSUM Schemes',Journal of Quality Technology, Vol. 26,pp 134-139   DOI
9 이은경, 나명환, 이윤동(2005), '얼랑분포의 축자확률비 검정과 관련된 적분방정식의 해', '응용통계연구', 18권, pp.57-66   DOI
10 Page, E. S.(1954), 'Continuous Inspection Schemes', Biometrika, Vol. 41, pp. 100-115   DOI
11 Kohlruss, D.(1994), 'Exact Formulas for the OC and the ASN Functions of the SPRT for Erlang Fistributions', Sequential Analysis, Vol. 13, pp. 53-62   DOI   ScienceOn