# mult.chart: Multivariate Control Chart In MSQC: Multivariate Statistical Quality Control

## Description

It computes several multivariate control charts: Hotelling, Chi-squared, MEWMA, MCUSUM and Generalized Variance chart.

## Usage

 ```1 2 3``` ```mult.chart(type = c("chi", "t2", "mewma", "mcusum", "mcusum2"), x, Xmv, S, colm, alpha = 0.01, lambda = 0.1, k = 0.5, h = 5.5, phase = 1, method = "sw", ...) ```

## Arguments

 `type` refers to the name of the type of chart e.g. type="chi", type="t2", type="mewma" or type="mcusum" `x` matrix or array of the quality characteristics. `Xmv` is the mean vector. It is only specified for Phase II or when the parameters of the distribution are given. `S` is the sample covariance matrix. It is only used for Phase II or when the parameters of the distribution are known. `colm` is the number of samples (m). It will only be used for the Hotelling control chart (Phase II). `alpha` it is the significance level (0.01 for default). `lambda` is the smoothing constant for the MEWMA chart. Only the value 0.1, 0.2,...,0.9 are allowed. `k` is a constant used in MCUSUM chart. Frequently k = 0.5. `h` is a constant used in MCUSUM chart. Usually h = 5.5. `phase` Refers to the Phase, say phase = 1 or 2. It is used to select the type of UCL. `method` is the method employed to compute the covariance matrix for the case of individual observations. Two methods are used "sw" for compute it according to Sullivan and Woodall (1996) and "hm" to compute it using Holmes and Mergen (1993) approach. `...` other parameters

## Author(s)

Edgar Santos-Fernandez

## References

Bodden, K.M., Rigdon, S.E.: A Program for Approximating the In Control ARL for the MEWMA Chart. Journal of Quality Technology 31,(1999)

Borror, C.M., Montgomery, D.C., Runger, G.C.: Robustness of the EWMA control chart to non normality. Journal of Quality Technology 31(3), (1999)

Camil Fuchs, R.K.: Multivariate Quality Control: theory and applications. Chapman and Hall/CRC, (1998)

Crosier, R.B.: Multivariate Generalizations of Cumulative Sum Quality Control Schemes. Technometrics 30(3),(1988)

Healy, J.D.: A Note on Multivariate CUSUM Procedures. Technometrics 29(4), (1987)

Holmes, D.S., Mergen, A.E.: Improving the performance of T square control chart. Quality Engineering 5(4), (1993)

Hotelling, H.: The Generalization of Student's Ratio. Institute of Mathematical Statistics, (1931)

Hotelling, H.: Multivariate Quality Control. McGraw Hill, (1947)

Jackson, J.E.: Quality Control Methods for two Related Variables. Industrial Quality Control 12 (1956)

Jackson, J.E.: Quality Control Methods for Several Related Variables. Technometrics 1 (1959)

Jackson, J.E.: A User Guide to Principal Components. John Wiley & Sons, New York (1991)

Lowry, C.A., Montgomery, D.C.: A review of multivariate control charts. IIE Transactions 27(6), (1995)

Lowry, C.A., Woodall, W.H., Champ, C.W., Rigdon, S.E.: A Multivariate Exponentially Weighted Moving Average Control Chart. Technometrics 34(1), (1992)

Mason, R., Tracy, N., Young, J.: Monitoring a multivariate step process. Journal of Quality Technology 28,(1996)

Mason, R.L., Tracy, N.D., Young, J.C.: Decomposition of T square for multivariate control chart interpretation. Journal of Quality Technology 27, (1995)

Mason, R.L., Young, J.C.: Multivariate Statistical Process Control with Industrial Application, 1 ed. Society for Industrial and Applied Mathematics, (2001)

Montgomery, D.C.: Introduction to Statistical Quality Control, 5 ed. John Wiley & Sons, (2005)

Pignatiello, J., Runger, G.: Comparisons of Multivariate CUSUM Charts. Journal of Quality Technology 22(3), (1990)

Prabhu, S.S., Runger, G.C.: Designing a multivariate EWMA control chart. Journal of Quality Technology 29, (1997)

Runger, G.C., Alt, F.B., Montgomery, D.C.: Contributors to a multivariate SPC chart signal. Communications in Statistics: Theory and Methods 25, (1996)

Sullivan, J.H., Woodall, W.H.: A Comparison of Multivariate Quality Control Charts for Individual Observations. Journal of Quality Technology 28(4) (1996)

Tracy, N., Young, Mason, R.: Multivariate Control Charts for Individual Observations. Journal of Quality Technology 24 (1992)

Woodall, W.H., Ncube, M.M.: Multivariate CUSUM Quality Control Procedures. Technometrics 3(3), (1985)

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24``` ```data(dowel1) mult.chart(dowel1, type = "chi", alpha = 0.05) #Phase I data(carbon1) mult.chart(type = "t2", carbon1) #Phase II Xmv <- mult.chart(carbon1, type = "t2") \$Xmv S <- mult.chart(carbon1, type = "t2") \$covariance colm<-nrow(carbon1) data(carbon2) mult.chart(carbon2, type = "t2", Xmv = Xmv, S = S, colm = colm) # (MEWMA) in Phase II Xmv <- mult.chart(carbon1, type = "t2") \$Xmv S <- mult.chart(carbon1, type = "t2") \$covariance mult.chart(type = "mewma", carbon2, Xmv = Xmv, S = S) #Multivariate Cumulative Sum (MCUSUM) in Phase I mult.chart(type = "mcusum", carbon2) mult.chart(type = "mcusum2", carbon2) ```

MSQC documentation built on May 29, 2017, 11:51 a.m.