cautiousLearning {CautiousLearning}

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), \hat{\mu}_{i-d_i}, \hat{\sigma}_{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)
head(y)
tail(y)