rbcc_opt {rbcc}

Optimized Risk-based Univariate Control Charts

Description

Calculate Optimized Risk-based Univariate Control Chart

Usage

rbcc_opt(X, UC, C, n, type=c("xbar", "R", "S"),confidence_level=0.9973,
K_init=0,LKL=-5,UKL=5)

Arguments

X

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

UC

vector of measuerement error (numeric vector).Either can be simulated using data_gen or defined by using available previous information.

C

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

n

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

type

a character string specifying the type of Shewhart control chart. Available types are; "Xbar", "R"and "S".

confidence_level

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

K_init

a correction component (default value is 0).

LKL

Lower limit of K parameter (default value is -5)

UKL

Upper limit of K parameter (default value is -5)

Value

cost0

Total cost of a monitoring process

cost1

Total cost of correct acceptance related to a process monitoring

cost2

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

cost3

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

cost4

Total cost of correct reject related to a process monitoring

LCLx

Lower Control Limit of a Shewhart univariate 'type' chart for a given data

UCLx

Upper Control Limit of a Shewhart univariate 'type' chart for a given data

LCLy

Lower Control Limit of an Optimal Risk-based univariate 'type' chart for a given data

UCLy

Upper Control Limit of an Optimal Risk-based univariate 'type' chart for a given data

real

Real values of plotting statistic for a given data

Observed

Observed plotting statistic for a given data with measurement errors

par

Optimal 'K' parameter of risk-based univariate 'type' chart

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, rbewmacc, rbewmacc_opt, rbmacc, rbmacc_opt, rbmcc, rbmcc_opt, plot.rbcc, summary.rbcc.

Examples

# Data Generation and Xbar chart.

## Example for generation of data vector X and measuremenet error vector UC.
obs <- 200                 # Total number of observations of a process.
mu_X <- c(0)               # Define data mean.
va_X  <- c(1)              # Define data standard deviation.
sk_X <- c(0)               # Define data skewness.
ku_X <- c(3)               # Define data kurtosis.
mu_UC <- c(0)              # Define mean of measurement errors.
va_UC <- c(1)              # Define standard deviation of measurement errors.
sk_UC <- c(0)              # Define skewness of measurement errors.
ku_UC <- c(3)              # Define kurtosis of measurement errors.

 # Simulation of 200 obervations of 1 variable.
X <- data_gen (obs, mu_X, va_X, sk_X, ku_X)
# Simulation of 200 muasurement erros related to 1 variable.
UC <- data_gen(obs,mu_UC, va_UC, sk_UC, ku_UC)

# Construction of risk-based Xbar chart with default vector of decision costs
C <- c(1,1,1,1)                                 # vector of decision costs
H <- rbcc(X, UC, C, n=3, type="xbar")           # for subgroups of size 3
summary(H)                                      # summarize the results
plot(H)                                         # plot RBCC

# optimal risk-based xbar control chart
H_opt <- rbcc_opt(X, UC, C, n=3, type="xbar")

# Data Generation and multivariate T2 chart.

# Data generation for a 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.

# Example for generation of data matrix X of 200 obervations of 3 variables.
X <- data_gen (obs, mu_X, va_X, sk_X, ku_X)

# 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 of 3 variables.
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
summary(H)                     # summarize the results
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