design {CautiousLearning}

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

lambda

EWMA smoothing constant.

k

CUSUM reference value.

m

number of in-control observations used to estimate the process mean and standard deviation at the beginning of the monitoring phase.

arl0, alpha, beta, H

desired in-control average run-length and constants defining the empirical guaranteed in-control performance condition. See equations (2) and (6) in Capizzi and Masarotto (2019).

A, B

constants controlling when the parameters estimate are updated. See equation (3) in Capizzi and Masarotto (2019). If A=NA and B=NA, the no-learning control limits are computed.

Ninit, Nfinal

number of iterations used in the stochastic approximation algorithm. See Capizzi and Masarotto (2019), Appendix A.

Value

A list with the following elements:

chart

string describing the control chart ("X", "EWMA" or "CUSUM").

lambda

EWMA smoothing constant (only when chart=="EWMA").

k

CUSUM reference value (only when chart=="CUSUM").

limit

numeric vector of length equal to five containing the constants defining the cautiuos learning control limits, i.e, L_\infty, \Delta, A, B and m (see equation (3) and (4) in Capizzi and Masarotto (2019)).

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)