| rbcusumcc_opt {rbcc} | R Documentation |
Optimized Risk-based CUSUM Control Charts
Description
Calculate Optimized Risk-based Univariate cumulative sum (CUSUM) Control Chart
Usage
rbcusumcc_opt(X, UC, C, n, T=5, se.shift=1, 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). |
T |
A numeric value specifying the number of standard errors of the summary statistics at which the cumulative sum is out of control (The defualt value is 5). |
se.shift |
The amount of shift to detect in the process, measured in standard errors of the CUSUM statistics (default value is 1). |
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 |
LCLx |
Lower decision bound of CUSUM chart for a given data |
UCLx |
Upper decision bound of CUSUM control chart for a given data |
LCLy |
Lower decision bound of CUSUM chart for a given data with measurement uncertainity |
UCLy |
Upper decision bound of CUSUM chart for a given data with measurement uncertainity |
cusumx |
Real values of CUSUM statistic for a given data |
cusumy |
Observed values of CUSUM statistic for a given data with measurement errors |
reall |
Below target real values of CUSUM statistic for a given data |
realu |
Above target real values of CUSUM statistic for a given data |
obsl |
Below target observed values of CUSUM statistic for a given data with measurement errors |
obsu |
Below target observed values of CUSUM statistic of a given data with measurement errors |
Kopt |
Optimal 'K' paramater of a risk-based CUSUM control chart |
Author(s)
Aamir Saghir, Attila I. Katona, Zsolt T. Kosztyan*
e-mail: kzst@gtk.uni-pannon.hu
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,rbcusumcc, rbewmacc,rbewmacc_opt, 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.
n <- 1 # For individual obervations use n=1
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 <- rbcusumcc(X, UC, C, n, T=5, se.shift=1, K=0) # for subgroups of size 1
plot(H) # plot RBCC
# optimal risk-based CUSUM control chart
H_opt <- rbcusumcc_opt(X, UC, C, n, T=5, se.shift=1, K_init= 0, LKL=-5, UKL=5)
# with vector of proportional decision costs
C <- c(1, 5, 60, 5) # vector of decision costs
H <- rbcusumcc(X, UC, C, n, T=5, se.shift=1, K=0)
H_opt <- rbcusumcc_opt(X, UC, C, n, T=5, se.shift=1, K_init= 0, LKL=-5, UKL=5)
# optimal risk-based CUSUM control chart
summary(H_opt) # summarize the reults
# Plot of traditional and optimal risk based cusum control charts
plot(H_opt)