Multivariate CUSUM Quality- Control Procedures

It is a common practice to use, simultaneously, several one-sided or two-sided CUSUM procedures of the type proposed by Page (1954). In this article, this method of control is considered to be a single multivariate CUSUM (MCUSUM) procedure. Methods are given for approximating parameters of the distribution of the minimum of the run lengths of the univariate CUSUM charts. Using a new method of comparing multivariate control charts, it is shown that an MCUSUM procedure is often preferable to Hotelling's TZ procedure for the case in which the quality characteristics are bivariate normal random variables.

[1]  H. Hotelling,et al.  Multivariate Quality Control , 1947 .

[2]  W. A. Wallis,et al.  Techniques of Statistical Analysis. , 1950 .

[3]  E. S. Page.  CONTINUOUS INSPECTION SCHEMES , 1954 .

[4]  J. Jackson,et al.  An Application of Multivariate Quality Control to Photographic Processing , 1957 .

[5]  J. Edward Jackson,et al.  Quality Control Methods for Several Related Variables , 1959 .

[6]  K. W. Kemp,et al.  Sampling inspection of continuous processes with no autocorrelation between successive results , 1960 .

[7]  Douglas C. Montgomery,et al.  Economic Design of T2 Control Charts to Maintain Current Control of a Process , 1972 .

[8]  D. A. Evans,et al.  An approach to the probability distribution of cusum run length , 1972 .

[9]  G. B. Wetherill,et al.  Quality Control and Industrial Statistics , 1975 .

[10]  Raymond F. Woods.  Effective, Economic Quality Through the Use of Acceptance Control Charts , 1976 .

[11]  J. E. Jackson,et al.  Control Procedures for Residuals Associated With Principal Component Analysis , 1979 .

[12]  J. Edward Jackson,et al.  Principal Components and Factor Analysis: Part I - Principal Components , 1980 .

[13]  A. G. Munford.  A Control Chart Based on Cumulative Scores , 1980 .

[14]  Robert S. Elder,et al.  Reviews of Standards and Specifications: United States Department of Agriculture CUSUM Acceptance Sampling Procedures , 1981 .

[15]  James M. Lucas,et al.  Combined Shewhart-CUSUM Quality Control Schemes , 1982 .

[16]  W. Deming.  Quality, productivity, and competitive position , 1982 .

[17]  William H. Woodall,et al.  The Distribution of the Run Length of One-Sided CUSUM Procedures for Continuous Random Variables , 1983 .

[18]  W. Woodall.  On the Markov Chain Approach to the Two-Sided CUSUM Procedure , 1984 .

[19]  William H. Woodall,et al.  The Statistical Design of Quality Control Charts , 1985 .

[20]  I. Jolliffe.  Principal Component Analysis and Factor Analysis , 1986 .