vMask-package: Detect Small Changes in Process Mean using CUSUM Control...

In vMask: Detect Small Changes in Process Mean using CUSUM Control Chart by v-Mask

Description

The V-mask chart is a visualization method to detect both increases and decreases in the mean on the Cumulative Sum (CuSum) control chart. The vMask package for R provides several algorithms for detecting small changes in mean by putting a V-mask on the face of the CUSUM control chart. This traditional method, named V-mask method, is considered based on the variety of situations/information by different functions in vMask Package.

Author(s)

Abbas Parchami

References

Montgomery, D.C. (1985) Introduction to Statistical Quality Control, John Wiley and Sons, New York.

Goel, A. L. (2011) Cumulative sum control charts, In Handbook of Methods and Applications of Statistics: Engineering, Quality Control, and Physical Sciences, N Balakrishnan (ed.). John Wiley and Sons: New York, 120-129.

Goel, A. L. (1982) Cumulative Sum Control Charts, Encyclopedia of Statistical Sciences. S. Kots and N. L. Johnson, Eds, Vol. 2, John Wiley and Sons, New York, 233-241.

Examples

### Example 1:  V-Mask CUSUM chart with vectored data based on the real data from:
#   https://www.itl.nist.gov/div898/handbook/pmc/section3/pmc323.htm

# In this applied example We are going to quickly detect a shift in mean as large as one 
# sigma by CUSUM chart.

Data = c( 324.925, 324.675, 324.725, 324.350, 325.350, 325.225, 
          324.125, 324.525, 325.225, 324.600, 324.625, 325.150, 
          328.325, 327.250, 327.825, 328.500, 326.675, 327.775, 
          326.875, 328.350 )
n = 4
mean(Data)
sd(Data)
sd(Data)/sqrt(n)

vMask.method3( data=Data, mu0=325, k=1, alpha=.0027, beta=.01, s="PressEnter" )



### Example 2:  V-Mask CUSUM chart based on a data matrix.
# A wood products company manufactures charcoal briquettes for barbecues. It packages these 
# briquettes in bags of various sizes, the largest of which is supposed to contain 40 lbs.
# The weights of bags from 16 different samples, each of size n=4 are given in below. 

n = 4
m = 16
mu0 = 40
sigma = .5

Data = c( 40.77, 39.95, 40.86, 39.21,  
          38.94, 39.70, 40.37, 39.88,  
          40.43, 40.27, 40.91, 40.05,  
          39.55, 40.10, 39.39, 40.89,  
          41.01, 39.07, 39.85, 40.32,  
          39.06, 39.90, 39.84, 40.22,  
          39.63, 39.42, 40.04, 39.50,  
          41.05, 40.74, 40.43, 39.40,  
          40.28, 40.89, 39.61, 40.48,  
          39.28, 40.49, 38.88, 40.72,  
          40.57, 40.04, 40.85, 40.51,  
          39.90, 40.67, 40.51, 40.53,  
          40.70, 40.54, 40.73, 40.45,  
          39.58, 40.90, 39.62, 39.83,  
          40.16, 40.69, 40.37, 39.69,  
          40.46, 40.21, 40.09, 40.58 )  

M = matrix(Data, ncol=n, byrow=TRUE)
M

# X.bar Control Chart: 
( LCL = mu0 - 3*sigma/sqrt(n) )
( UCL = mu0 + 3*sigma/sqrt(n) )
plot(1:16,rowMeans(M), col=3, pch=16, ylim=c(LCL-.2,UCL+.2))
abline(h=c(mu0, LCL, UCL), col=2, lty=c(3,1,1))

# Three different strategies for putting v-mask on CUSUM Control Chart:
cumsum(rowMeans(M)-mu0)

vMask.method2( data=M, mu0=40, d=5.6, h=1, s=0 )
vMask.method6( data=M, mu0=40, mu1=40.3, sigma=.5, h=1, w=2, sl="PressEnter" )
vMask.method5( data=M, mu0=40, mu1=40.3, alpha=.1, beta=.01, sl=0 )

vMask documentation built on May 1, 2019, 10:21 p.m.