climit {spc4sts}

Control Limit and Diagnostic Threshold Construction

Description

Establish control limits (for local defects and/or global changes) and diagnostic thresholds (for local defects) from the given Phase I images. climit is used for the first time. climit2 can update the control limits and diagnostic thresholds given the output of climit. See Warning. To plot histograms of the Phase I monitoring statistics, use plot.climit.

Usage

climit(imgs, fa.rate, model, type, stat = c("ad", "bp"), w = 5,
       nD = 10, no_cores = 1, verbose = FALSE)
climit2(cl, fa.rate, nD)

Arguments

imgs

a 3-dimensional array containing all Phase I in-control images.

fa.rate

the false alarm rate, which asserts the rate of in-control images that are falsely alarmed as out-of-control. This can be a vector, in which case several levels of the control limit are returned.

model

the object returned by surfacemodel.

type

for local defects, type = 1; for global changes, type = 2; for both, type = 1:2.

stat

for local defects only. The statistic used in the spatial moving statistics. Must be either "ad" (default) or "bp".

w

for local defects only. The dimension of the spatial (square) moving window. Must be an odd number >= 3.

nD

for local defects only. The parameter to construct the diagnostic threshold. It is the average number of highlighted pixels in the diagnostic image for an in-control image.

no_cores

if > 1, parallely compute Phase I monitoring statistics using no_cores processors.

verbose

if TRUE, show the computing progress.

cl

the object returned by climit or climit2.

Value

An object of class climit. See climit.object.

Author(s)

Anh Bui

References

Bui, A.T. and Apley., D.W. (2018a) "A Monitoring and Diagnostic Approach for Stochastic Textured Surfaces", Technometrics, 60, 1-13.

Bui, A.T. and Apley, D.W. (2018b) "Monitoring for changes in the nature of stochastic textured surfaces", Journal of Quality Technology, 50, 363-378.

See Also

monitoringStat, diagnoseLD

Examples

## build the in-control model
img <- sarGen(m = 50, n = 50, border = 50) # training image
model <- surfacemodel(img, nb = 1, keep.residuals = TRUE)

## after that, generate Phase I images
imgs <- array(0, c(50,50,3))
for (j in 1:dim(imgs)[3])
  imgs[,,j] <- sarGen(phi1 = .6, phi2 = .35, m = 50, n = 50, border = 50)

## establish control limits and diagnostic thresholds
# construct control limits (for both local defects and global changes)
# and diagnostic thresholds (for local defects) for the first time
cl <- climit(imgs, fa.rate = .05, model, type = 1:2, stat = "ad", w = 5, nD = 50)
cl
# update new control limit and diagnostic threshold
cl2 <- climit2(cl, fa.rate = .01, nD = 5)
# plots histograms of Phase I monitoring statistics
plot(cl2)

## after that, monitor a Phase II image as follows:
# create a new image with a local defect
img2 <- sarGen(phi1 = .6, phi2 = .35, m = 50, n = 50, border = 50) # simulate a new image
img3 <- imposeDefect(img2)$img # add a local defect to this image
ms3 <- monitoringStat(img = img3, model = model, cl = cl2) # computing monitoring statistics
# now create a new image with parameters reduced by 5% (representing a global change)
img4 <- sarGen(phi1 = .6*.95, phi2 = .35*.95, m = 50, n = 50, border = 50)
ms4 <- monitoringStat(img = img4, model = model, cl = cl2) # computing monitoring statistics

## diagnose for local defect regions in img3
bimg <- diagnoseLD(ms3, dth = 9, plot.it = FALSE) # use climit() to find dth

#par(mfcol = c(1, 2))
#par(mar = c(2, 0.5, 1, 0.5))
image(xaxt = 'n', yaxt = 'n', as.matrix(t(apply(img3 , 2, rev))),
      col = gray((0:32)/32), xlab = '', ylab = '', asp = 1, bty = 'n')
image(xaxt = 'n', yaxt = 'n', as.matrix(t(apply(bimg , 2, rev))),
      col = gray(c(1, .5)), xlab = '', ylab = '', asp = 1, bty = 'n')

#
# NOTE: The above example is just for quick illustration. To obtain a good
# control limit, the training image should be representative (e.g., set
# m = 250, n = 250, and border = 200). The number of Phase I images also
# needs to be large (e.g., 100 images or more).
#
# For real images in a textile application, use the R data package "textile".
#