rbewmacc_opt {rbcc}

Optimized Risk-based EWMA Control Charts

Description

Calculate Optimized Risk-based Univariate exponentially weighted moving average Control Chart

Usage

rbewmacc_opt(X, UC, C, n=1, lambada=0.20, nsigmas=3, 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).

lambada

a weight or smoothing constant for EWMA control charts. The value is between (0,1). The defualt value is 0.20.

nsigmas

the charting multiplier(default value is 3)

K_init

Set correction component to 0 by default (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 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 a EWMA chart for a given data

limit

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

real

Real values of plotting statistic for a given data

Observed

Observed plotting statistic with measurement errors for a given data

Kopt

Optimal 'K' paramater of risk-based EWMA control chart 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, rbmacc, rbmacc_opt, rbmcc, rbmcc_opt, plot.rbcc, summary.rbcc.

Examples

# Data generation for vector X
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.
obs <- 200                 # Total number of observations of a process.

X <- data_gen (obs, mu_X, va_X, sk_X, ku_X)

# Data generation for measurement error vector UC

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.

UC <- data_gen(obs,mu_UC, va_UC, sk_UC, ku_UC)

C <- c(1,1,1,1)                           # Define a vector of decision costs.
H <- rbewmacc(X, UC, C)                   # for subgroups of size 1
# fit optimal risk-based EWMA control chart
H_opt <- rbewmacc_opt(X, UC, C, n=1,lambada=0.20,nsigmas=3,K_init= 0,LKL=-5,UKL=5)
plot(H_opt)                              # plot RBEWMACC

# with vector of proportional decision costs
C <- c(1, 5, 60, 5)               # vector of decision costs
H <- rbewmacc(X, UC, C)           # traditional risk-based EWMA control chat

# fit optimal risk-based EWMA control chart
H_opt <- rbewmacc_opt(X, UC, C, n=1,lambada=0.20,nsigmas=3,K_init= 0,LKL=-5,UKL=5)
plot(H_opt)                           # plot RBEWMACC