design {CautiousLearning} R Documentation

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, Linf, 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)

```

[Package CautiousLearning version 1.0.1 Index]