cautiousLearning {CautiousLearning} R Documentation

## 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

 `chart` list with the same elements as those returned by `x.cl`, `ewma.cl` and `cusum.cl`. `x` numeric vector containing the Phase II data. `mu0, s0` estimates of the in-control mean and standard deviation obtained by the Phase I reference sample. `plot` if `TRUE` the control statistics and the cautiuos control limits are plotted.

### Value

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

 `column 1 for X and EWMA, columns 1-2 for CUSUM` control statistic[s] `columns 2-4 for X and EWMA, columns 3-5 for CUSUM` central line, lower and upper control limits `columns 5-7 for X and EWMA, columns 6-8 for CUSUM` "cautious" estimates of the mean, standard deviation and critical value, i.e., using the notation in Capizzi and Masarotto (2019), mu.hat[i-d[i]], sigma.hat[i-d[i]] and L[i-d[i]].

### 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)