data_gen {rbcc}

Data Generator for Risk-based Control Charts

Description

data_gen function simulate the data set from a specified distribution used in the risk based control charts.

Usage

data_gen(obs, mu, va, sk, ku)

Arguments

obs

The total number of observations of a process( a numeric value).

mu

The means of p characteristics/measurement errors (a numeric vector).

va

The variances of p characteristics/measurement errors (a numeric vector).

sk

The skewness of distribution of p characteristics/measurement errors (a numeric vector).

ku

The kurtosis of distribution of p characteristics/measurement errors (a numeric vector).

Value

Return the data vector/matrix and the measurement error vector/matrix used in the risk-based control charts functions.

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

rbcc, rbcc_opt, 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
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 with 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
plot(H)                        # plot RBMCC

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

# 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