Volume- 2
Issue- 1
Year- 2014
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Dr. Shobha Dutta Deka , Dr. B. Gogoi
Various control charts are already developed for the problem of detecting any shift in the mean/median of a sequence of observations from a specified control value taken from some process. Some of them for detecting small shift(s) from the target values are Cumulative Sum (CUSUM), Cumulative Score (CuScore) and recently developed nonparametric charts. Various authors have already worked on CUSUM control charts and found suitable results. Another chart is Cuscore chart, which is also suitable for this situation. Another test is nonparametricCUSUM charts based on nonparametric test statistic. One of the efficient procedure is the Cumulative Sum Control chart (CSCC) originally introduced by Page [1]. The properties of CSCC procedure are usually derived under the assumption that the observations are independent and identically distributed normal random variables, another control chart based on Cumulative Scores developed by Munford [2]. The ARL of this scheme are simpler to compute than those of CSCC. Recently a new control chart is developed based on the nonparametric chart which is preferable from the robustness point of view. Few of the workers on nonparametric CSCC are Parent [3], Reynolds [4, 5], Mcgilchrist and Woodyer [6], Bakir and Reynolds [7] etc. In this paper we want to study the performance of CSCC, CuScore and Nonparametric CUSUM control Chart in detecting the mean/median shift from the specified (target) values. For this purpose we computed the ARL by the simulation method for both in control and under control situations of the process. Results obtained are displayed in various tables using different shift parameters and under different distributions. Results are also shown in graph for easy visual comparison.
[1] Page, E.S. (1954): Continuous Inspection Schemes, Biometrika, vol. 41,pp.100-114.
[2] Munford, A.G. (1980): A control Chart based on Cumulative Scores, Appl. Statist.,29, No.3, pp.252-258.
[3] Parent, E.A., Jr. (1965): Sequential ranking Procedures, Technical report no.80, Dept.of Statistics, Stanford University, Stanford, California.
[4] Reynolds, M. R. Jr. (1972): A Sequential Nonparametric Test for Symmetry with Application to Process Control, Technical report no.148, Dept. of Operations Research and Dept. of Statistics, Stanford University, Stanford, California.
[5] Reynolds, M. R. Jr.(1975): Approximation to the Average run Length in CUSUM control charts, Technometrics, Vol. 17, 1,pp.65-71.
[6] McGilchrist, C.A and Woodyer, k.D., Note on Distribution- free Cusum Technique, Technometrics, Vol. 17,pp.321-325.
[7] Bakir, S.T. and Reynolds, M.R. Jr. (1979): A nonparametric procedure for process control based on within-group ranking, Technometrics, vol. 21,pp.175-183.
[8] Evan, W.D. and Kemp, K.W. (1960): Sampling Inspection of Continuous Process with no autocorrelation between Successive results, Biometrika, 47,pp.363-380.
[9] Bissel l, A.F. (1969): Cusum techniques for quality control, Appl. Statist.,18,pp.1-25
[10] Roberts, S.W. (1959): Control Chart Tests Based on Geometric Moving Average, Techometrics, vol.3,pp.239-250.
[11] Roberts, S.W. (1966): A Comparison of Some Control Chart Procedures, Technometrics, Vol. 8,pp.411-430.
[12] Lucas, J.M. and Succucci, M.S. (1990a): Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements (with discussion), Tech. 32(1),pp.1-29.
[13] Box, G.E.P., and Jenkins, G.M. (1966): Models for Prediction and Control: VI Diagnostic Checking, Technical Report No. 99, Department of Statistics, university of Wisconsin-Madison.
[14] Page, E.S. (1962): Cumulative Sum Schemes using Gauging, Technometrics,Vol.4, No.1,pp97-109.
[15] Amin, R.W., Reynolds, M. R.Jr. and Bakir, S. (1995): Nonparametric Quality Control Charts based on the Sign Statistic, Commun. Statist.-Theory Meth., 24(6),pp. 1597-1623.
[16] Van Dobben de Bruyn, C.S., (1968): Cumulative Sum Tests, Hefner, New York.
[17] Lucas, J.M. and Succucci, M.S (1990b): Average Run lengths for EWMA Schemes using the Markov Chain approach, Jrnl. Qual. Tech. 22, pp. 154-162.
[18] Box, G.E.P and Muller, M.E. (1958): A Note on the Generation of Random Normal Deviates, The Annals of Math.Statist., vol. 29, pp.610-611. [19] Montgomery, D. C. (2004): Introduction to Statistical Quality Control, 4th Edition John Willy Sons – New York
Department of Statistics, D.H.S.K College, Dibrugarh, Assam, India, Mobile No.9707911163,(e-mail: shobha.998@rediffmail.com)
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