Abstract
Quality management and improvement involves time in a number of ways. To monitor systems in their inter-temporal perspective, it is necessary to develop models which represent the process of change and which can be used to measure and monitor a process. Measurements (through sampling, control charts and any other method) may then be used to track and detect variations which may be unexpected, and which would require special attention. In Chapter 6, we noted that the approach underlying the application of control charts was the ‘search for observations deviating from expectations’. To do so, we presumed that processes were stable and sought to devise ‘tests’, ‘probability assessments’, etc. which will reject our presumption that the process or variable being charted were stable. In fact, non-stationarities of various sorts, poor representation of the underlying process, collinearity over time etc. make it necessary to represent the temporal dependence such processes exhibit. Models of various sorts can then be devised to better represent and analyse shifting patterns of data over time, using available statistical means. There are many approaches and methods we can use in such circumstances.To this end, we introduce some basic notions of filtering theory and control charts of processes such as moving average charts, EWMA (exponentially weighted moving average) and ARIMA (Auto regressive and Moving Average Models) and related models.
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References
AFNOR X08–031.3 (1993) Carte de Controle des Sommes Cumulées (Doc. written by MM. Daudin and Palsky), September.
Alwan L.C. and H.V. Roberts (1988) Time series modeling for statistical process control, Journal of Business and Economic Statistics, 6, 87–95.
Antelman G.R., and I.R. Savage (1965) Surveillance problems: Wiener processes, Naval Research Log. Quarterly, 12, 1, 35–55.
Barnard G.A. (1959) Control charts and stochastic processes, Journal of the Royal Statistical Society, Series B, 21 239–271.
Basseville M. (1988) Detecting changes in signals and systems-A survey, Automatica, vol 24 no. 3, 309–326.
Basseville M. and A. Benveniste (eds) (1986) Detection of Abrupt Changes in Signals and Dynamic Systems, Lecture Notes in Control and Information Sciences, vol 77, Berlin, Springer Verlag.
Bather J.A. (1963) Control charts and the minimization of costs J. of Royal Stat. Society, B, 25, 1 49–70.
Bather.A. (1971) Free boundary problems in the design of control charts, Transactions of the 6th Prague Conference on Information Theory, Statistical Decision Functions and Random processes, 89 106.
Benveniste A., M. Basseville and G. Moustakides (1987) The asymptotic local approach to change detection and model validation, IEEE Trans. on Automatic Control, AC-32, no. 7, 583–592, July.
Box G.E.P. and G.M. Jenkins (1976) Time Series Analysis, Forecasting and Control, Second edition, Holden Day, San Francisco.
British Standards Institution (1981) Guide to Data Analysis and Control Using Cusum Techniques, BS5703.
Chow, Y.S., H. Robbins and D. Siegmund (1971) The Theory of Optimal Stopping, Dover Publications, New York.
Crowder S.V. (1987) A simple method for studying run length distributions of exponentially weighted moving average charts, Technometrics, 29 401–407.
Crowder S.V. (989) Design of exponentially weighted moving average schemes, Journal of Quality Technology, 21, 3, 155–162.
Feller W. (1951) The asymptotic distribution of the range of sums of independent random variables, Ann. Math. Stat., 22 427–432.
Hunter J.S. (1986) The exponentially weighted moving average, Journal of Quality Technology, 18 19–25.
Imhof J.P. (1992) A construction of the brownian path and its inverse process, Annals of Probability, 13, 1011–1017.
Jazwinsky.H. (1970) Stochastic Processes and Filtering Theory, Academic Press, New York.
Kalman R.E. and R. Bucy (1961) New results in linear filtering and prediction theory, Trans ASME, J. Basic Engineering, vol 83D 95–108, March.
Moustakides G.V. (1986) Optimal stopping times for detecting changes in distributions, Ann. Stat. 13 1379–1387.
Page E.S. (1954) Continuous inspection schemes, Biometrika, 41 100–114.
Patton R.J., P.M. Frank and R.N. Clark (Eds.) (1989) Fault Diagnosis in Dynamic Systems: Theory and Applications, Prentice Hall International,UK.
Pollak M. (1987) Average run lengths of an optimal method of detecting a change in distribution, Ann. Stat., 15 2, 749–779.
Robinson, B.P. and T.Y. Ho (1978) Average run lengths of geometric moving average charts, Technometrics, 20 85–93.
Sage A.P. and J.L. Melsa (1971) Estimation Theory: with Applications to Communications and Control, New York, McGraw Hill Book Co.
Siegmund D. (1985) Sequential Analysis, Tests and Confidence Intervals, Springer. Verlag, Berlin
Tapiero C.S. (1977) Managerial Planning: An Optimum and Stochastic Control Approach, Gordon Breach, New York (2 volumes).
Tapiero C.S. (1977a) Optimization of information measurement with inventory applications, Infor, 15 50–61.
Tapiero C.S. (1987) Production learning and quality control, IIE Transactions, 19, no. 4 362–370.
Tapiero C.S. (1988) Applied Stochastic Models and Control in Management, Amsterdam, North-Holland, Publ. Co.
Tapiero C.S., A. Reisman and P. Ritchken (1987) Product Failures, Manufacturing Reliability and Quality Control: A Dynamic Framework, INFOR (Canadian Journal of Operations Research).
Vallois P., On the range process of a bernoulli random walk, Proceedings of the Sixth International Symposium on Applied Stochastic Models and Data Analysis, vol. II Editors, J. Janssen and C.H. Skiadas, World Scientific, 1020–1031.
Vallois P. and C.S. Tapiero (1995a) Moments of an amplitude process in a random walk and approximations: Computations and applications, RAIRO, 1-6.
Vallois P. and C.S. Tapiero (1995b) The range process in random walks: Theoretical results and applications, Working Paper, ESSEC, Cergy Pontoise, France.
Willsky Alan S. (1976) A survey of design methods for failure detection in dynamic systems, Automatica, 12 601–611.
Willsky A.S. (1986) Detection of abrupt changes in dynamic systems, in detection of Abrupt Changes in Signals and Dynamical Systems, M. Basseville and A. Benveniste (Eds.), Lecture Notes in Control and Information Sciences, LNCIS 77, Springer Verlag, 27–49.
Willsky A.S. and H.L Jones (1976) A generalized likelihood ratio approach to the detection and estimation in linear systems of jumps in linear systemsIEEE Trans. on Automatic Control, 21, 108–112.
Yaschin E. (1993) Performance of CUSUM control schemes for serially correlated observations Technometrics, 35 37–52.
Yaschin E. (1993) Statistical control schemes: Methods, applications and generalizations, International Statistical Review, 61 41–66.
Zehnwirth B. (1985) Linear filtering theory and recursive credibility estimation, Astin Bull., 19–36.
Zhang Q., M. Basseville and A. Benveniste (1992) Early warning of slight changes in systems and plants with application to condition based maintenance, IRISA, Working Paper no. 671, July.
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© 1996 Charles S. Tapiero
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Tapiero, C.S. (1996). The control of quality in a temporal setting. In: The Management of Quality and its Control. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-2055-9_9
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DOI: https://doi.org/10.1007/978-1-4615-2055-9_9
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