R control chart with multiple lines

Question

I'm working with physicians on a project to monitor compliance to proper dosage of antibiotics. To track the proportion of events that are not compliant, physicians like to use P charts

I would like to generate a P-Chart with 3 limit lines (corresponding to 1, 2, and 3 SDs) above and below the central line. I have not found a way to do this. I would also like the plot to have several breaks that separate the data into several time periods, which I can do in the qicharts package but not in other packages.

There are several packages for R for generating P Charts. The one I like most is qicharts. The standard P-Chart from qicharts, and all of the other packages I've seen, generates a plot with a Central Line and an Upper Control Limit and a Lower Control Limit at +3 and -3 SD from the central line.

I would like to figure out how to generate additional +1, +2, and -1, -2 SD control lines on the same plot. Some option such as

LimitLines = c(1, 2, 3) where the default is LimitlLines = 3

Here is the code, modified from r-projects, to generate data, create the chart, and include two breaks:

# Setup parameters
m.beds       <- 300
m.stay       <- 4
m.days       <- m.beds * 7
m.discharges <- m.days / m.stay
p.pu         <- 0.08

# Simulate data
discharges  <- rpois(24, lambda = m.discharges)
patientdays <- round(rnorm(24, mean = m.days, sd = 100))
n.pu        <- rpois(24, lambda = m.discharges * p.pu * 1.5)
n.pat.pu    <- rbinom(24, size = discharges, prob = p.pu)
week        <- seq(as.Date('2014-1-1'),
               length.out = 24, 
               by         = 'week') 

# Combine data into a data frame
d <- data.frame(week, discharges, patientdays,n.pu, n.pat.pu)

# Create a P-chart to measure the number of patients with pressure ulcers (n.pat.pu) each week (week) as a proportion of all discharges (discharges) with breaks one third (8) and two thirds (16) of the way through the data

qic(n.pat.pu,
n        = discharges,
x        = week,
data     = d,
chart    = 'p',
multiply = 100,
breaks   = c(8,16),
main     = 'Hospital acquired pressure ulcers (P chart)',
ylab     = 'Percent patients',
xlab     = 'Week')

Answer 1

If you simply need to present the data, it is easy to create the chart yourself. Feel free to modify the function to your needs to make it easier.

Data:

Groups <- c(120, 110, 150, 110, 140, 160, 100, 150, 100, 130, 130, 100, 120, 110, 130, 110, 150, 110, 110)
Errors <- c(4, 3, 3, 3, 0, 6, 2, 2, 1, 5, 1, 5, 1, 1, 0, 1, 4, 0, 0)
Week <- length(Groups) #optional: input vector of week numbers
PchartData <- data.frame(Week,Groups,Errors)

Function:

Shewhart.P.Chart <- function(Groups, Errors, Week)
{
## Create from scratch
# p value
p <- Errors/Groups
# pbar
pbar <- mean(p)
# calculate control limits
UCL3 <- pbar+3*sqrt((pbar * ( 1 - pbar))/Groups)
UCL2 <- pbar+2*sqrt((pbar * ( 1 - pbar))/Groups)
UCL1 <- pbar+1*sqrt((pbar * ( 1 - pbar))/Groups)
LCL1 <- pbar-1*sqrt((pbar * ( 1 - pbar))/Groups)
LCL2 <- pbar-2*sqrt((pbar * ( 1 - pbar))/Groups)
LCL3 <- pbar-3*sqrt((pbar * ( 1 - pbar))/Groups)
## adjust the minimal value of the LCL to 0
LCL3[LCL3 < 0] <- 0
LCL2[LCL2 < 0] <- 0
LCL1[LCL1 < 0] <- 0
# plot pvalues
plot(c(1:length(Groups)),p, ylim = c(min(LCL3,p),max(UCL3,p)),
    main = "p Chart \n for Prescription Errors", xlab = "weeks", 
    ylab = 'Proportion nonconforming', col = "green", pch = 20,
    lty = 1, type = "b")
# add centerline reference
abline(h = pbar, col = "red")
# plot control limits at ±1s, 2s, and 3s
lines(c(1:length(Groups)),UCL1, col = "blue", lty = 2)
lines(c(1:length(Groups)),UCL2, col = "blue", lty = 2)
lines(c(1:length(Groups)),UCL3, col = "blue", lty = 2)
lines(c(1:length(Groups)),LCL3, col = "blue", lty = 2)
lines(c(1:length(Groups)),LCL2, col = "blue", lty = 2)
lines(c(1:length(Groups)),LCL1, col = "blue", lty = 2)
}

Breaks can easily be added into the forgoing, you would just need to segregate your data accordingly. It should be remembered though, if you do not have a change in the process used, the calculation for the limits should not be changed and your process may simply be out of statistical control and in need of standardization.