Guaranteed In-Control Control Chart Performance with Cautious Parameter Learning

Description

Functions in this package allow to design, study and apply control charts based on the cautious parameter learning approach described in Capizzi and Masarotto (2019).

On system where the openMP standard is supported, these functions can take advantage of the computing power offered by a multicore workstation. See omp for the default setting.

Details

The package includes the following functions:

• Computation of the control limits via stochastic approximation: x.cl, ewma.cl, cusum.cl;

• Estimation errors and conditional run-length simulation: ruv and rcrl;

• Application to real data: cautiousLearning;

• Controlling the number of used openMP cores and the random number generator seeds: hasOMP, setOMPThreads and setSITMOSeeds.

Author(s)

Giovanna Capizzi <giovanna.capizzi@unipd.it> and Guido Masarotto <guido.masarotto@unipd.it>

Maintainer: Giovanna Capizzi

References

Capizzi, G. and Masarotto, G. (2019) "Guaranteed In-Control Control Chart Performance with Cautious Parameter Learning", accepted for publication in Journal of Quality Technology, a copy of the paper can be obtained from the authors.

Applications of control charts based on the cautious learning approach

Description

This function applies and, optionally, plots a control chart based on the cautious learning approach described in Capizzi and Masarotto (2019).

Usage

cautiousLearning(chart, x, mu0, s0, plot = TRUE)

Arguments

Value

The function returns (invisibly when plot==TRUE) a numeric matrix containing

Author(s)

Giovanna Capizzi and Guido Masarotto

References

Capizzi, G. and Masarotto, G. (2019) "Guaranteed In-Control Control Chart Performance with Cautious Parameter Learning", accepted for publication in Journal of Quality Technology, a copy of the paper can be obtained from the authors.

Examples

## EWMA control chart (nominal ARL=500, 
## initial estimates based on 100 in-control observations)
chart <- list(chart = "EWMA",
              lambda = 0.2,
              limit = c(Linf=3.187, Delta=0.427, A=1.5, B=50, m=100))
## Phase I estimates
set.seed(12345)
xic <- rnorm(100, 12 , 3)
m0 <- mean(xic)
s0 <- sd(xic)
## Phase II observations (one sigma mean shift starting at i=501)
x <- c(rnorm(500, 12, 3), rnorm(50, 15, 3))
## Monitoring
y <- cautiousLearning(chart, x, m0, s0)
head(y)
tail(y)

Design of control charts based on the cautious learning approach

Description

These functions compute the control limits of X (x.cl), EWMA (ewma.cl) and CUSUM (cusum.cl) control charts based on the cautious learning approach. The stochastic approximation algorithm, described in the Appendix A of Capizzi and Masarotto (2019), is used.

When openMP is supported, computation can be distribuited on multiple cores. See omp.

Usage

x.cl(m, arl0, alpha = 0.1, beta = 0.05, H = 200, A = 1.5, B = 50, 
     Ninit = 1000, Nfinal = 30000)

ewma.cl(lambda, m, arl0, alpha = 0.1, beta = 0.05, H = 200, A = 1.5, B = 50, 
        Ninit = 1000, Nfinal = 30000)

cusum.cl(k, m, arl0, alpha = 0.1, beta = 0.05, H = 200, A = 1.5, B = 50, 
         Ninit = 1000, Nfinal = 30000)

Arguments

Value

A list with the following elements:

Author(s)

Giovanna Capizzi and Guido Masarotto

References

Capizzi, G. and Masarotto, G. (2019) "Guaranteed In-Control Control Chart Performance with Cautious Parameter Learning", accepted for publication in Journal of Quality Technology, a copy of the paper can be obtained from the authors.

Examples

## Only for testing: the number of iterations is reduced 
## to reduce the computing time
Ninit <- 50
Nfinal <- 100
H <- 50
x.cl(100, 500, Ninit=Ninit, Nfinal=Nfinal, H=H)
x.cl(100, 500, A=NA, B=NA, Ninit=Ninit, Nfinal=Nfinal, H=H)
ewma.cl(0.2, 100, 500, Ninit=Ninit, Nfinal=Nfinal, H=H)
cusum.cl(1, 100, 500, Ninit=Ninit, Nfinal=Nfinal, H=H)

## Using the default number of iterations
x.cl(100, 500)
x.cl(100, 500, A=NA, B=NA)
ewma.cl(0.2,100, 500)
cusum.cl(1, 100, 500)

Support for parallel computation

Description

The functions can be used

• to check if the current system supports the openMP standard;

• to control the number of used cores;

• to set the seeds of the random number generators.

Usage

hasOMP()

setOMPThreads(nthreads)

setSITMOSeeds(seed)

Arguments

Details

Each openMP thread (or the single thread used on systems where openMP is not supported) uses a separate sitmo random number generator. See sitmo-package.

Value

Function hasOMP returns TRUE/FALSE if the system supports/does not support openMP.

Functions setOMPThreads and setSITMOSeeds do not return any value.

Note

When the package is loaded, the following code is automatically executed

• if (hasOMP()) setOMPThreads(parallel::detectCores())

• setSITMOSeeds(runif(1))

Author(s)

Giovanna Capizzi and Guido Masarotto

Estimation errors and conditional run-length simulation

Description

Function ruv simulates the standardized estimation errors at the starting of the monitoring phase (see Section 2.3 of Capizzi and Masarotto (2019)).

Function rcrl simulates, under different in-control or out-control scenarios, the conditional run-length given the standardized estimation errors. When openMP is supported, computation can be distribuited on multiple cores. See omp.

Usage

ruv(n, m)

rcrl(n, chart, u, v, tau, delta, omega, maxrl = 1000000L)

Arguments

Value

Author(s)

Giovanna Capizzi and Guido Masarotto

References

Capizzi, G. and Masarotto, G. (2019) "Guaranteed In-Control Control Chart Performance with Cautious Parameter Learning", accepted for publication in Journal of Quality Technology, a copy of the paper can be obtained from the authors.

Examples

ruv(5, 100)
## EWMA control chart (nominal ARL=500, 
## initial estimates based on 100 in-control observations)
chart <- list(chart = "EWMA",
              lambda = 0.2,
              limit = c(Linf=3.187, Delta=0.427, A=1.5, B=50, m=100))
rcrl(10, chart, 2, 1, 50, 2, 1)