DISTRIBUTION OF RUN-LENGTH FOR MULTIVARIATE CONTROL CHARTS WITH RULES USING EMBEDDED FINITE MARKOV CHAIN
0
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
A multivariate control chart that observes various charac- teristics at the same time was proposed by Hotelling. However, Hotelling's control chart has the disadvantage of slowing the speed of detecting anomalies when very small changes in the process occur, so rules for mul- tivariate control charts have been proposed. In this paper, to increase the sensitivity of the Shewhart chart, which has the same shortcomings, the proposed rule, Western Electronic Company's rule, is applied to the multivariate chart to obtain the run-length distribution. The run-length distribution is calculated by recognizing that an abnormality occurs in the process when the mean vector of the process changes in the pro- duction process. The run-length distribution of the multivariate control chart obtained using the proposed runs rule and the embedded nite Markov chain con rmed that the mean of run-lengths decreased sharply when very small changes occurred in the process. This means the speed of detecting small changes in the process is fast. Therefore, this method is expected to be e ective when observing very small changes due to multivariate quality control problems.
Abstract
A multivariate control chart that observes various charac- teristics at the same time was proposed by Hotelling. However, Hotelling's control chart has the disadvantage of slowing the speed of detecting anomalies when very small changes in the process occur, so rules for mul- tivariate control charts have been proposed. In this paper, to increase the sensitivity of the Shewhart chart, which has the same shortcomings, the proposed rule, Western Electronic Company's rule, is applied to the multivariate chart to obtain the run-length distribution. The run-length distribution is calculated by recognizing that an abnormality occurs in the process when the mean vector of the process changes in the pro- duction process. The run-length distribution of the multivariate control chart obtained using the proposed runs rule and the embedded nite Markov chain con rmed that the mean of run-lengths decreased sharply when very small changes occurred in the process. This means the speed of detecting small changes in the process is fast. Therefore, this method is expected to be e ective when observing very small changes due to multivariate quality control problems.
참고문헌 (17)
- Aki, S, "Discrete distributions of order k on a binary sequence", Ann.Inst. Statist. Math, 37, pp.205~224 (1985)
- Balakrishnan, N, "Runs and Scans with Applications" (2002), John Wiley & Sons Inc
- Bissell, A. F, "An Attempt to Unify the Theory of Quality Control Procedures", Bulletin in Applied Statictics, 5, pp.113~128 (1978)
- Champ, C. W, "Exact results for Shewhart control charts with supplementary runs rules", Technometrics, 29, pp.393~399 (1987)
- Feller, W, "An Introduction to Probability Theory and Its Applications" (1968), John Wiley & Sons Inc
- Fu, J. C., "Distribution Theory of Runs : A Markov Chain Approach", Journal of the American Statistical Association, 89, pp.1050~1058 (1994)
- Fu, J. C., "Distribution theory of runs and patterns and its applications handbook" (2003), World Scientific Publishing Co
- Hotelling, H., "Multivariate Quality Control Illustrated by Air Testing of Sample Bombsights, Techniques of Statistical Analysis", pp.111~184 (1947), McGraw Hill
- Khoo, M. B. C., "Incorporating runs rules into Hotelling's control charts", Quality Engineering, 15, pp.671~675 (2003)
- Koutras, M. V., "On a waiting time distribution in a sequence of Bernoulli trials", Annals of the Institute of Statistical Mathematics, 48, pp.789~806 (1996)
- Nelson, L. S., "Notes on the Shewhart Control Chart", Journal of quality tech-nology, 31, pp.124~126 (1999)
- Page, E. S., "Continuous Inspection Scheme", Biometrika, 41, pp.100~115 (1954)
- Philippou, A. N, "Distribution and fibonacci polynomials of order k, longest runs, and reliability of consecutive-k-out-of-n F systems", pp.203~227 (1986), Reidel Publishing Co
- Roberts, S. W., "Control Chart Tests Based on Geometric Moving Averages", Technometrics, 1, pp.239~250 (1959)
- Shewhart, W. A., "Economic control of Quality of Manufactured Products" (1931), John Wiley & Sons Inc
- Shmueli, G., "Run-Length Distribution for Control Charts with Runs and Scans Rules", Communications in Statistics-Theory and Methods, 32, pp.475~495 (2003)
- Western Electric Company, "Statistical Quality Control Handbook" (1956), Western Electric Co