Browse > Article

The Z-CUSUM Control Chart for the Process with Recurring Cycles or Frequent Small Shifts  

강해운 (한양대학교 산업공학과)
강창욱 (한양대학교 산업공학)
백재원 (한양대학교 산업공학과)
Publication Information
Journal of Korean Society for Quality Management / v.32, no.2, 2004 , pp. 132-153 More about this Journal
Abstract
CUSUM control charts are widely used to monitor processes with small shifts. CUSUM control charts are, however, less effective in detecting for recurring cycles or frequent small shifts in the processes. With Shewhart control charts, we have applied the variety of run rules to check the stability of process in addition to the situations that some points fall outside the control limits. In this paper, we propose the Z -CUSUM control chart for monitoring the process with recurring cycles or frequent small shifts by use of the zone concept as like the Shewhart control charts.
Keywords
recurring cycle; small shifts; Z -CUSUM control chart;
Citations & Related Records
연도 인용수 순위
  • Reference
1 Abdellatif M.A. and E.I. Shabrawy A.Z.(1996), 'The economic design of cumulative sum charts used to maintain current control of non normal process means', Computers & Industrial Engineering, Vol. 31, pp. 783-790   DOI   ScienceOn
2 Hawkins, D. M.(1992), 'A Fast Accurate Approximation for Average Run Lengths of CUSUM Control Charts', Journal of Quality Technology, Vol.24. pp. 37-43   DOI
3 Hawkins, D. M.(1993), 'Cumulative Sum Control Charting: An Underutilized SPC Tool', Quality Engineering, Vol.25. pp. 463-477
4 Luceno, A.(1999), 'Average Run Len gths and Run Legth Probability Distributions for Cuscore Charts to Control Normal Mean', Computational Statistics and Data Analysis, Vol. 32, pp. 177-195   DOI   ScienceOn
5 Page, E. S.(1961), 'Cumulative Sum Charts', Technometrics, Vol. 3, pp. 1-10   DOI   ScienceOn
6 Page, E. S.(1962), 'Cumulative Sum Schemes Using Gauging', Technometrics, Vol. 4, pp. 97-109   DOI   ScienceOn
7 Rahim E. S. and Lashkari R. S. (1982), 'An Economic Design of cusum Charts to Control Non- Normal Process Means', Computers & Industrial Engineering, Vol. 6, pp. 1-18   DOI   ScienceOn
8 Rowlands, R. J., Nix, A. B., Abdollian, M. A. and Kemp, K. W.(1982), 'Snub -nosed V-mask Control Schemes', The Statistician, Vol. 31, pp. 133-142   DOI   ScienceOn
9 Woodall, W. H.(1984), 'One the Markov Chain Approach to the Two-sided CUSUM Procedure', Technometrics, Vol. 26, pp. 41-46   DOI   ScienceOn
10 Chiu, W. K.(1974), 'The Economic Design of CUSUM Charts for Controlling Nomal Means', Applied Statistics, Vol. 23, pp. 420-433   DOI   ScienceOn
11 Lu, C. W. and Reynolds, M. R.(2001), 'CUSUM charts for monitoring an autocor related process', Journal of Quality Technology, Vol. 33, pp. 316-335   DOI   ScienceOn
12 Goel, A. L. and Wu, S. M. (1973), 'Economically Optimum Design of CUSUM Charts', Management Science, Vol. 19, pp. 1271-1282   DOI   ScienceOn
13 Woodall, W. H.(1986), 'The Design of CUSUM Quality Control Charts', Journal of Quality Technology, Vol. 18, pp. 99-102   DOI
14 Woodall, W. H.(1983), 'The Distribution of the Run Length of One-sided CUSUM Procedures for Continuous Random Variables', Technometrics, Vol. 25, pp. 295-301   DOI   ScienceOn
15 Lucas, J. M.(1982), 'Conbined Shewh art CUSUM Quality Control Schemes', Journal of Quality Technology, Vol. 14, pp. 51-59   DOI   ScienceOn
16 Nelson, L S..(1984), 'The Shewhart Control Chart Tests for Special Causes', Journal of Quality Technology, Vol. 14, pp. 237-239
17 Bissell, A. F(1979), 'A Semi parabolic Mask for Cusum Charts', The Statistician, Vol. 28, pp. 1-7   DOI   ScienceOn
18 Yshchin, E.(1985), 'One the Markov Chain Approach to the Two-sided CUSUM Procedure', Technometrics, Vol. 26, pp. 41-46   ScienceOn
19 Johnson, N. L. and Leone, F. C.(1962), 'Cumulative Sum Control Charts: Mathema tical Principles Applied to Construction and Use', Industrial Quality Control, Vol. 18, pp. 15-21
20 Gan, F. F.(1993), 'The Run Length Distribution of a Cumulative Sum Control Chart', Journal of Quality Technology, Vol. 25, pp. 205-215   DOI
21 Luceno, A. and Puig-Pey, J.(2000), 'Evaluation of the Run Length Probability Distribution for CUSUM Charts: Assessing Chart Performance', Technometrics, Vol. 42, pp. 411-416   DOI   ScienceOn
22 Woodall, W. H.(1985), 'The Statistical Design of Quality Control Charts', The Statistician, Vol. 34, pp. 155-160   DOI   ScienceOn
23 Lucas, J. M. and Crosier, R. B. (1982), 'Fast Initial Response for CUSUM Quality Control Schemes', Technometrics, Vol. 24, pp. 199-205   DOI   ScienceOn
24 Montgomery, D. C.(2001), INTRO- DUCTION TO STATISTICAL QUALITY CONTROL, Wiley, pp. 166-177 & pp. 406-430
25 Besterfield, D. H.(2001), Quality Control, Prentice Hall, pp. 179-206
26 Champ, C. W. and Woodall, W. H. (1987), 'Exact Results for Shewhart Control Charts with Supplementary Run Rules', Technometrics, Vol. 29, pp. 393-399   DOI   ScienceOn
27 Lucas, J. M(1973), 'A Modified 'V' Mask Control Schemes', Technometrics, Vol. 15, pp. 833-847   DOI   ScienceOn
28 Atienza, O. O., Tang, L.C. and Ang, B. W.(2002), 'A CUSUM scheme for auto correlated observations', Journal of Quality Technology, Vol. 34, pp. 187-200   DOI   ScienceOn
29 Taylor, H. M.(1968), 'The Economic Design of Cumulative Sum Control Charts', Technometrics, Vol. 10, pp. 479-488   DOI   ScienceOn
30 Luceno, A. and Puig-Pey, J.(2000a), 'Computing the Run Length Probability Distribution for CUSUM Charts', Journal of Quality Technology, Vol. 34, pp. 209-214
31 Waldmann, K. H.(1996), 'Design of double CUSUM quality control schemes', European Journal of Operational Research, Vol. 95, pp. 641-648   DOI   ScienceOn
32 Ewan, W. D.(1963), 'When and How to Use CUSUM Charts', Technometrics, Vol. 5, pp. 1-22   DOI   ScienceOn
33 Deming, W. E.(1982), Quality, Productivity, and Competitive Position Massa chusetts Institute of Technology
34 Gibra, I. N.(1975), 'Recent Developments in Control Chart Techniques', Journal of Quality Technology, Vol. 7, pp. 183-192   DOI   ScienceOn