rbcusumcc {rbcc}

Risk-based Cumulative Sum Control Charts

Description

Calculate Risk-based Cumulative Sum univariate Control Charts

Usage

rbcusumcc(X, UC, C, n, T=5, se.shift=1, K=0)

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

a correction component(default value is 0).

Value

cost0

Total cost of a monitoing 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

cusumy

Observed values of CUSUM statistic with measurement errors for a given data

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 with measurement errors for a given data

obsu

Below target observed values of CUSUM statistic 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,rbcusumcc_opt, 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.
n <- 1                     # Individual observation

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 <- 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)

# 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)

# Plot of traditional and optimal risk based cusum control charts
plot(H_opt)