rbmcc {rbcc}

Risk-based Multivariate Control Chart

Description

Calculate Risk-based Multivariate Control Chart

Usage

rbmcc(X, UC, C, n=1 , confidence_level=0.99, K=0)

Arguments

X

matrix of variables (numeric matrix). Either can be simulated using data_gen or defined by using available data set.

UC

matrix of measuerement error (numeric matrix).

C

vector of decision costs (default value is vector of 1).

n

The sample size for grouping. For individual obervations use n=1).

confidence_level

The (1-alpha)percent confidence level (default value is 0.99)

K

Set correction component to 0 by default (default value is 0)

Value

cost0

Total cost of a monitoirng process

cost1

Total cost of correct acceptance related to a process monitoring

cost2

Total cost of decision error type 1 related to a process monitoring

cost3

Total cost of decision error type 2 related to a process monitoring

cost4

Total cost of correct reject related to a process monitoring

baselimit

UCL of T^2 chart for a given data

limit

UCL of optimized risk based multivariate control chart for a given data

real

Real values of T2 statistic for a given data

Observed

Observed T2 with measurement errors for a given data

Author(s)

Aamir Saghir, Attila I. Katona, Zsolt T. Kosztyan*

e-mail: [e-mail]

References

Kosztyán, Z. T., and Katona, A. I. (2016). Risk-based multivariate control chart. Expert Systems with Applications, 62, 250-262.

See Also

data_gen, rbcc, rbcc_opt, rbewmacc, rbewmacc_opt, rbmacc, rbmacc_opt, rbmcc_opt, plot.rbcc, summary.rbcc.

Examples

# Data generation for matrix X
mu_X <- c(0,1,2)               # vector of means.
va_X  <- c(1,2, 0.5)           # vector of standard deviation.
sk_X <- c(0,0.5, 0.8)          # vector of skewness.
ku_X <- c(3,3.5, 4)            # vector of kurtosis.
obs <- 200                     # Total number of observations of a process.

X <- data_gen (obs, mu_X, va_X, sk_X, ku_X) # generate data pints

# Data generation for measurement error matrix UC

mu_UC <- c(0,0,0)              # vector of means of measurement errors.
va_UC <- c(1,2, 0.5)           # vector of standard deviation of measurement errors.
sk_UC <- c(0,0,0)              # Vector of skewness of measurement errors.
ku_UC <- c(3,3,3)              # Vector of kurtosis of measurement errors.

# example for generation of measurement error matrix
UC <- data_gen(obs,mu_UC, va_UC, sk_UC, ku_UC)

# with default vector of decision costs
C <- c(1,1,1,1)                # vector of decision costs
H <- rbmcc(X, UC, C)           # for subgroups of size 1
plot(H)                        # plot RBMCC

H_opt <- rbmcc_opt(X, UC, C)   # optimal risk-based multivariate control chart

# with vector of proportional decision costs
C <- c(1, 5, 60, 5)        # vector of decision costs
H <- rbmcc(X, UC, C)           # for subgroups of size 1
H_opt <- rbmcc_opt(X, UC, C)   # optimal risk-based multivariate control chart

# with vector of proportional decision costs and sugbroup size 3
C <- c(1, 5, 60, 5)           # vector of decision costs
H <- rbmcc(X, UC, C, 3)           # for subgroups of size 3
H_opt <- rbmcc_opt(X, UC, C, 3)   # optimal risk-based multivariate control chart

# Plot of Hotelling's T2 and optimal risk based multivariate control charts

plot(H_opt)

# Example of considering the real sample

data("t2uc")                # load the dataset

X <- as.matrix(t2uc[,1:2])  # get optical measurements ar "real" values
UC <- as.matrix(t2uc[,5:6]) # get measurement errors
C <- c(1,20,160,5) # define cost structure

# Fit optimized RBT2 control chart
R <- rbmcc_opt(X, UC, C, 1,confidence_level = 0.99)
summary(R) # summarize the results
plot(R)    # plot the result