| Title: | Quality Improvement Charts |
|---|---|
| Description: | Functions for making run charts [Anhoej, Olesen (2014) <doi:10.1371/journal.pone.0113825>] and basic Shewhart control charts [Mohammed, Worthington, Woodall (2008) <doi:10.1136/qshc.2004.012047>] for measure and count data. The main function, qic(), creates run and control charts and has a simple interface with a rich set of options to control data analysis and plotting, including options for automatic data aggregation by subgroups, easy analysis of before-and-after data, exclusion of one or more data points from analysis, and splitting charts into sequential time periods. Missing values and empty subgroups are handled gracefully. |
| Authors: | Jacob Anhoej [aut, cre], Timo Roeder [ctb] |
| Maintainer: | Jacob Anhoej <[email protected]> |
| License: | GPL-3 |
| Version: | 0.5.8 |
| Built: | 2025-01-15 04:55:33 UTC |
| Source: | https://github.com/anhoej/qicharts |
Creates a pareto chart from a categorical variable
paretochart( x, main, ylab = "Frequency", xlab = "", cumperc.by = 20, cex = 0.8, ... )paretochart( x, main, ylab = "Frequency", xlab = "", cumperc.by = 20, cex = 0.8, ... )
x |
Categorical vector to be plotted |
main |
Plot title |
ylab |
Label on y axis |
xlab |
Label on x axis |
cumperc.by |
Grid interval |
cex |
Number indicating the amount by which text and symbols should be magnified. |
... |
Further arguments to plot function |
A table of frequencies and percentages from the pareto analysis
Jacob Anhoej
x <- rep(LETTERS[1:9], c(256, 128, 64, 32, 16, 8, 4, 2, 1)) paretochart(x)x <- rep(LETTERS[1:9], c(256, 128, 64, 32, 16, 8, 4, 2, 1)) paretochart(x)
Plot qic object
## S3 method for class 'qic' plot(x, y = NULL, ...)## S3 method for class 'qic' plot(x, y = NULL, ...)
x |
List object returned from the qic() function. |
y |
Ignored. Included for compatibility with generic plot function. |
... |
Further arguments to plot function. |
Creates a qic plot.
y <- rnorm(24) p <- qic(y, plot.chart = FALSE) plot(p)y <- rnorm(24) p <- qic(y, plot.chart = FALSE) plot(p)
Run and control charts for quality improvement and control
qic( y, n, x, data, chart = c("run", "i", "mr", "xbar", "s", "t", "p", "c", "u", "g"), notes = NULL, cl = NULL, agg.fun = c("mean", "sum"), ylim = NULL, target = NULL, direction = NULL, freeze = NULL, breaks = NULL, exclude = NULL, negy = TRUE, dots.only = FALSE, multiply = 1, prime = FALSE, standardised = FALSE, x.format = "%Y-%m-%d", nint = 5, cex = 0.8, main, xlab = "Subgroup", ylab = "Indicator", sub = NULL, decimals = NULL, pre.text = "Before data", post.text = "After data", llabs = c("LCL", "CL", "UCL", "TRG"), runvals = FALSE, linevals = TRUE, plot.chart = TRUE, print.out = FALSE, ... )qic( y, n, x, data, chart = c("run", "i", "mr", "xbar", "s", "t", "p", "c", "u", "g"), notes = NULL, cl = NULL, agg.fun = c("mean", "sum"), ylim = NULL, target = NULL, direction = NULL, freeze = NULL, breaks = NULL, exclude = NULL, negy = TRUE, dots.only = FALSE, multiply = 1, prime = FALSE, standardised = FALSE, x.format = "%Y-%m-%d", nint = 5, cex = 0.8, main, xlab = "Subgroup", ylab = "Indicator", sub = NULL, decimals = NULL, pre.text = "Before data", post.text = "After data", llabs = c("LCL", "CL", "UCL", "TRG"), runvals = FALSE, linevals = TRUE, plot.chart = TRUE, print.out = FALSE, ... )
y |
Numeric vector of counts or measures to plot. Mandatory. |
n |
Numeric vector of sample sizes. Mandatory for P and U charts. |
x |
Subgrouping vector used for aggregating data and making x-labels. Mandatory for Xbar and S charts. |
data |
Data frame containing variables. |
chart |
Type of control chart. Possible types are:
|
notes |
Character vector of notes to be added to individual. data points. |
cl |
Value specifying the center line (if known). Must be of length one or same as number of subgroups (for variable center line). |
agg.fun |
String specifying the aggregate function if there is more than
one value per subgroup. Possible values are 'mean' and 'sum'. Only
relevant if you want to aggregate count data with run charts or I charts.
If |
ylim |
Range of y axis limits. |
target |
Value specifying a target line to plot. |
direction |
Value indication direction of improvement, 0 (down) or 1 (up). |
freeze |
Number identifying the last data point to include in
calculations of center and limits (ignored if |
breaks |
Numeric vector of break points. Useful for splitting graph in two or more sections with separate center line and control limits. |
exclude |
Numeric vector of data points to exclude from calculations of center and control lines. |
negy |
Logical value, if TRUE, the y axis is allowed to be negative (only relevant for I and Xbar charts). |
dots.only |
Logical value. If TRUE, data points are not connected by lines and runs analysis is not performed. Useful for comparison and funnel plots. |
multiply |
Integer indicating a number to multiply y axis by, e.g. 100 for percents rather than proportions. |
prime |
Logical value, if TRUE, control limits incorporate between-subgroup variation as proposed by Laney (2002). This is recommended for data involving very large sample sizes. Only relevant for P and U charts. |
standardised |
Logical value, if TRUE, creates a standardised control chart, where points are plotted in standard deviation units along with a center line at zero and control limits at 3 and -3. Only relevant for P, U and Xbar charts. |
x.format |
Date format of x axis labels. See ?strftime for date formats. |
nint |
Number indicating (approximately) the desired number of tick marks on the x axis. |
cex |
Number indicating the amount by which text and symbols should be magnified. |
main |
Character string specifying the title of the plot. |
xlab |
Character string specifying the x axis label. |
ylab |
Character string specifying the y axis label. |
sub |
Character string specifying a subtitle to be printed in the lower left corner of the plot. |
decimals |
Integer indicating the number of decimals shown for center and limits on the plot. Default behaviour is smart rounding to at least two significant digits. |
pre.text |
Character string labelling pre-freeze period |
post.text |
Character string labelling post-freeze period |
llabs |
Character vector with four elements specifying labels for lower control limit, centre line, upper control limit and target line respectively |
runvals |
Logical value, if TRUE, prints statistics from runs analysis on plot. |
linevals |
Logical value, if TRUE, prints values for center and control lines on plot. |
plot.chart |
Logical value, if TRUE, prints plot. |
print.out |
Logical value, if TRUE, prints return value |
... |
Further arguments to plot function. |
If chart is not specified, qic() plots a run
chart. Non-random variation will be marked by a dashed, yellow center line
(the median) if either the longest run of data points above or below the
median is longer than predicted or if the graph crosses the median fewer
times than predicted (see references for details).
Only the y argument giving the count or measure of interest is
mandatory for a run chart. If a denominator argument, n, is given,
will be plotted. If a subgrouping argument, x, is given,
, within each subgroup will be plotted. This behaviour
can be modified using the agg.fun argument.
With controlcharts, data aggregation by subgroups is handled
according to chart type. For P, U, and I charts, data are aggregated as
described for the run chart. For the C chart, the sum of counts,
sum(y), within each subgroups will be plotted.
For Xbar and S charts, the subgrouping argument, x, is mandatory.
However, the sample size argument, n, is irrelevant and will be
ignored.
The subgrouping argument, x, is irrelevant for T and G charts, and,
if given, an error will occur if any subgroup has more than one element.
If more than one note is present within any subgroup, the first
note (alphabetically) is chosen.
If both prime and standardised are TRUE, points are
plotted in units corresponding to Laney's modified "standard deviation",
which incorporates the variation between subgroups.
A list of of class qic containing values and parameters of the qic plot.
Runs analysis:
Jacob Anhoej, Anne Vingaard Olesen (2014). Run Charts Revisited: A Simulation Study of Run Chart Rules for Detection of Non-Random Variation in Health Care Processes. PLoS ONE 9(11): e113825. doi: 10.1371/journal.pone.0113825 .
Jacob Anhoej (2015). Diagnostic Value of Run Chart Analysis: Using Likelihood Ratios to Compare Run Chart Rules on Simulated Data Series. PLoS ONE 10(3): e0121349. doi: 10.1371/journal.pone.0121349
Mark F. Schilling (2012). The Surprising Predictability of Long Runs. Math. Mag. 85, 141-149.
Zhenmin Chen (2010). A note on the runs test. Model Assisted Statistics and Applications 5, 73-77.
Calculation of control limits:
Douglas C. Montgomery (2009). Introduction to Statistical Process Control, Sixth Edition, John Wiley & Sons.
James C. Benneyan (2001). Number-Between g-Type Statistical Quality Control Charts for Monitoring Adverse Events. Health Care Management Science 4, 305-318.
Lloyd P. Provost, Sandra K. Murray (2011). The Health Care Data Guide: Learning from Data for Improvement. San Francisco: John Wiley & Sons Inc.
David B. Laney (2002). Improved control charts for attributes. Quality Engineering, 14(4), 531-537.
set.seed(1) # Run chart of 24 samples of a random continuous variable # with an approximate mean = 12 and standard deviation = 3. y <- rnorm(24, 12, 3) qic(y) # Add subgroup vector (dates) and a target x <- seq.Date(as.Date('2013-08-04'), by = 'week', length = 24) qic(y, x = x, target = 16) # Individuals control chart qic(y, x = x, chart = 'i') # Xbar control chart, sample size = 5 y <- rnorm(5 * 24) x <- rep(x, 5) qic(y, x = x, chart = 'xbar') # Create data frame with counts and sample sizes by week d <- data.frame(week = seq.Date(as.Date('2013-08-04'), by = 'week', length = 36), y = c(rbinom(24, 20, 0.5), rbinom(12, 20, 0.8)), n = round(rnorm(36, 20, 2))) # Proportions control chart qic(y, n, x = week, data = d[1:24,], chart = 'p') # Introduce change in process performance qic(y, n, x = week, data = d, chart = 'p') # Freeze baseline to first 24 samples qic(y, n, x = week, data = d, chart = 'p', freeze = 24) # Break control chart before and after change qic(y, n, x = week, data = d, chart = 'p', breaks = 24) # Introduce extreme sample value and notes d$a <- '' d$a[30] <- 'Extreme value' d$y[30] <- 1 qic(y, n, x = week, data = d, chart = 'p', breaks = 24, notes = a) # Exclude value from calculations d$a[30] <- 'Value excluded from calculations' qic(y, n, x = week, data = d, chart = 'p', breaks = 24, notes = a, exclude = 30)set.seed(1) # Run chart of 24 samples of a random continuous variable # with an approximate mean = 12 and standard deviation = 3. y <- rnorm(24, 12, 3) qic(y) # Add subgroup vector (dates) and a target x <- seq.Date(as.Date('2013-08-04'), by = 'week', length = 24) qic(y, x = x, target = 16) # Individuals control chart qic(y, x = x, chart = 'i') # Xbar control chart, sample size = 5 y <- rnorm(5 * 24) x <- rep(x, 5) qic(y, x = x, chart = 'xbar') # Create data frame with counts and sample sizes by week d <- data.frame(week = seq.Date(as.Date('2013-08-04'), by = 'week', length = 36), y = c(rbinom(24, 20, 0.5), rbinom(12, 20, 0.8)), n = round(rnorm(36, 20, 2))) # Proportions control chart qic(y, n, x = week, data = d[1:24,], chart = 'p') # Introduce change in process performance qic(y, n, x = week, data = d, chart = 'p') # Freeze baseline to first 24 samples qic(y, n, x = week, data = d, chart = 'p', freeze = 24) # Break control chart before and after change qic(y, n, x = week, data = d, chart = 'p', breaks = 24) # Introduce extreme sample value and notes d$a <- '' d$a[30] <- 'Extreme value' d$y[30] <- 1 qic(y, n, x = week, data = d, chart = 'p', breaks = 24, notes = a) # Exclude value from calculations d$a[30] <- 'Value excluded from calculations' qic(y, n, x = week, data = d, chart = 'p', breaks = 24, notes = a, exclude = 30)
Summary function for tcc objects.
## S3 method for class 'tcc' summary(object, ...)## S3 method for class 'tcc' summary(object, ...)
object |
tcc object |
... |
Ignored. Included for compatibility with generic summary function. |
A data frame with summary statistics of the tcc object.
# Build data frame for example d <- data.frame(x = rep(1:24, 4), mo = (rep(seq(as.Date('2014-1-1'), length.out = 24, by = 'month'), 4)), n = rbinom(4 * 24, 100, 0.5), d = round(runif(4 * 24, 90, 110)), g1 = rep(c('a', 'b'), each = 48), g2 = rep(c('A', 'B'), each = 24)) # P chart p <- tcc(n, d, mo, g1 = g1, g2 = g2, breaks = 12, data = d, chart = 'p') plot(p) summary(p)# Build data frame for example d <- data.frame(x = rep(1:24, 4), mo = (rep(seq(as.Date('2014-1-1'), length.out = 24, by = 'month'), 4)), n = rbinom(4 * 24, 100, 0.5), d = round(runif(4 * 24, 90, 110)), g1 = rep(c('a', 'b'), each = 48), g2 = rep(c('A', 'B'), each = 24)) # P chart p <- tcc(n, d, mo, g1 = g1, g2 = g2, breaks = 12, data = d, chart = 'p') plot(p) summary(p)
Run and control charts for multivariate data i trellis (grid) layout.
tcc( n, d, x, g1, g2, breaks, notes, data, chart = c("run", "i", "mr", "xbar", "s", "t", "p", "c", "u", "g"), multiply = 1, freeze = NULL, exclude, target = NA, n.sum = FALSE, y.neg = TRUE, y.percent = FALSE, y.expand = NULL, x.pad = 1, x.date.format = NULL, cl.lab = TRUE, cl.decimals = NULL, main, xlab = "Subgroup", ylab = "Value", subtitle = NULL, caption = NULL, cex = 1, pex = 1, prime = TRUE, flip = FALSE, dots.only = FALSE, print.summary = FALSE, ... )tcc( n, d, x, g1, g2, breaks, notes, data, chart = c("run", "i", "mr", "xbar", "s", "t", "p", "c", "u", "g"), multiply = 1, freeze = NULL, exclude, target = NA, n.sum = FALSE, y.neg = TRUE, y.percent = FALSE, y.expand = NULL, x.pad = 1, x.date.format = NULL, cl.lab = TRUE, cl.decimals = NULL, main, xlab = "Subgroup", ylab = "Value", subtitle = NULL, caption = NULL, cex = 1, pex = 1, prime = TRUE, flip = FALSE, dots.only = FALSE, print.summary = FALSE, ... )
n |
Numerator, numeric vector of counts or measures to plot. Mandatory. |
d |
Denominator, numeric vector of subgroup sizes. Mandatory for P and U charts. |
x |
Subgrouping vector used for aggregating data by subgroup and making x-labels. Mandatory for Xbar and S charts. |
g1 |
Grouping vector 1 used for trellis layout (facets). |
g2 |
Grouping vector 2 used for trellis layout (facets). |
breaks |
Numeric vector of break points. Useful for splitting graph in two or more sections with separate center line and control limits. |
notes |
Character vector of notes to be added to individual. data points. |
data |
Data frame containing variables. |
chart |
Type of control chart. Possible types are:
|
multiply |
Integer indicating a number to multiply y axis by, e.g. 100
for percents rather than proportions. See also |
freeze |
Number identifying the last data point to include in
calculations of center and limits (ignored if |
exclude |
Numeric vector of data points to exclude from runs analysis and calculations of center and control lines (same for each facet). |
target |
Numeric value indicating a target value to be plotted as a horizontal line (same for each facet). |
n.sum |
Logical value indicating whether the mean (default) or sum of numerator (n argument) per subgroup should be plotted. Only relevant for run, C, and I charts with multiple counts per subgroup. |
y.neg |
Logical value. If TRUE (default), the y axis is allowed to be negative (only relevant for I and Xbar charts). |
y.percent |
Logical. If TRUE, formats y axis labels as percent. |
y.expand |
Numeric value to include in y axis. Useful e.g. for beginning y axis at zero. |
x.pad |
Number indicating expansion of x axis to make room for center line labels. |
x.date.format |
Date format of x axis labels. See |
cl.lab |
Logical value. If TRUE (default), plots center line labels. |
cl.decimals |
Number of decimals on center line labels. |
main |
Character string specifying the title of the plot. |
xlab |
Character string specifying the x axis label. |
ylab |
Character string specifying the y axis label. |
subtitle |
Character string specifying the subtitle. |
caption |
Character string specifying the caption. |
cex |
Number indicating the amount by which text should be magnified. |
pex |
Number indicating the amount by which plotting symbols should be magnified. |
prime |
Logical value, If TRUE (default unless |
flip |
Logical. If TRUE rotates the plot 90 degrees. |
dots.only |
Logical value. If TRUE, data points are not connected by lines, prime is forced to be FALSE, and runs analysis is not performed. Useful for comparison and funnel plots. |
print.summary |
Logical. If TRUE, prints summary of tcc object. |
... |
Further arguments to ggplot function. |
tcc() is a wrapper function for ggplot2() that makes
multivariate run and control charts. It takes up to two grouping variables
for multidimensional trellis plots.
Note that, in contrast to the qic() function, the prime argument defaults to TRUE, which means that control limits of P and U charts by default incorporate between-subgroup variation as proposed by Laney (2002).
An object of class ggplot.
Runs analysis:
Jacob Anhoej, Anne Vingaard Olesen (2014). Run Charts Revisited: A Simulation Study of Run Chart Rules for Detection of Non-Random Variation in Health Care Processes. PLoS ONE 9(11): e113825. doi: 10.1371/journal.pone.0113825 .
Jacob Anhoej (2015). Diagnostic Value of Run Chart Analysis: Using Likelihood Ratios to Compare Run Chart Rules on Simulated Data Series. PLoS ONE 10(3): e0121349. doi: 10.1371/journal.pone.0121349
Mark F. Schilling (2012). The Surprising Predictability of Long Runs. Math. Mag. 85, 141-149.
Zhenmin Chen (2010). A note on the runs test. Model Assisted Statistics and Applications 5, 73-77.
Calculation of control limits:
Douglas C. Montgomery (2009). Introduction to Statistical Process Control, Sixth Edition, John Wiley & Sons.
James C. Benneyan (2001). Number-Between g-Type Statistical Quality Control Charts for Monitoring Adverse Events. Health Care Management Science 4, 305-318.
Lloyd P. Provost, Sandra K. Murray (2011). The Health Care Data Guide: Learning from Data for Improvement. San Francisco: John Wiley & Sons Inc.
David B. Laney (2002). Improved control charts for attributes. Quality Engineering, 14(4), 531-537.
# Run chart of 24 random normal variables tcc(rnorm(24)) # Build data frame for examples d <- data.frame(x = rep(1:24, 4), mo = (rep(seq(as.Date('2014-1-1'), length.out = 24, by = 'month'), 4)), n = rbinom(4 * 24, 100, 0.5), d = round(runif(4 * 24, 90, 110)), g1 = rep(c('a', 'b'), each = 48), g2 = rep(c('A', 'B'), each = 24)) # Run chart with two grouping variables tcc(n, d, mo, g1 = g1, g2 = g2, data = d) # P chart tcc(n, d, mo, g1 = g1, g2 = g2, data = d, chart = 'p') # P chart with baseline fixed to the first 12 data points tcc(n, d, mo, g1 = g1, g2 = g2, data = d, chart = 'p', freeze = 12) # P chart with two breaks and summary output tcc(n, d, mo, g1 = g1, g2 = g2, data = d, chart = 'p', breaks = c(12, 18), print.summary = TRUE)# Run chart of 24 random normal variables tcc(rnorm(24)) # Build data frame for examples d <- data.frame(x = rep(1:24, 4), mo = (rep(seq(as.Date('2014-1-1'), length.out = 24, by = 'month'), 4)), n = rbinom(4 * 24, 100, 0.5), d = round(runif(4 * 24, 90, 110)), g1 = rep(c('a', 'b'), each = 48), g2 = rep(c('A', 'B'), each = 24)) # Run chart with two grouping variables tcc(n, d, mo, g1 = g1, g2 = g2, data = d) # P chart tcc(n, d, mo, g1 = g1, g2 = g2, data = d, chart = 'p') # P chart with baseline fixed to the first 12 data points tcc(n, d, mo, g1 = g1, g2 = g2, data = d, chart = 'p', freeze = 12) # P chart with two breaks and summary output tcc(n, d, mo, g1 = g1, g2 = g2, data = d, chart = 'p', breaks = c(12, 18), print.summary = TRUE)
Run charts for multivariate data in trellis (grid) layout.
trc( x, chart = c("run", "i"), xscale = "same", yscale = "same", dec = NULL, xpad = 0.1, pch = 20, cex = 0.7, gap = 0.5, target = NA, ... )trc( x, chart = c("run", "i"), xscale = "same", yscale = "same", dec = NULL, xpad = 0.1, pch = 20, cex = 0.7, gap = 0.5, target = NA, ... )
x |
Formula object to plot. The formula is of the form y ~ x | g1 + g2 + ..., indicating that plots of y (on the y-axis) versus x (on the x-axis) should be produced conditional on the variables g1, g2. |
chart |
Type of chart: 'run' or 'i'. |
xscale |
Scaling of x-axes: 'same' or 'free'. |
yscale |
Scaling of y-axes: 'same' or 'free'. |
dec |
Number of decimals of median value. The default behaviour (smart rounding to at least two significant digits) should be satisfactory in most cases. |
xpad |
Number specifying the fraction by which to extend the x-axis in order to make space for the median label. |
pch |
Plotting character. |
cex |
Number indicating the magnification of plotting character. |
gap |
Number indicating spacing between panels. |
target |
Value specifying a target line to plot. |
... |
Further arguments to xyplot. |
This function is a wrapper for xyplot from the
lattice package. Some usefull arguments from
xyplot are main, ylab, xlab, and
layout.
Returns an object of class "trellis".
# Trellis run chart on 1 conditioning variable d1 <- data.frame(y = rnorm(96, 12, 3), expand.grid(x = 1:24, g = LETTERS[1:4])) trc(y ~ x | g, data = d1, main = 'Trellis run chart') # Add target line trc(y ~ x | g, data = d1, main = 'Trellis run chart', target = 20) # Trellis run chart on 2 conditioning variables d2 <- data.frame(y = rnorm(144, 12, 3), expand.grid(x = seq.Date(as.Date('2014-1-1'), by = 'week', length.out = 24), g1 = LETTERS[1:3], g2 = letters[1:2])) trc(y ~ x | g1 + g2, data = d2, main = 'Trellis run chart') # Introduce a shift in process performance d2$y[132:144] <- d2$y[132:144] * 3 trc(y ~ x | g1 + g2, data = d2, main = 'Trellis run chart') # Make I chart trc(y ~ x | g1 + g2, data = d2, main = 'Trellis run chart', chart = 'i')# Trellis run chart on 1 conditioning variable d1 <- data.frame(y = rnorm(96, 12, 3), expand.grid(x = 1:24, g = LETTERS[1:4])) trc(y ~ x | g, data = d1, main = 'Trellis run chart') # Add target line trc(y ~ x | g, data = d1, main = 'Trellis run chart', target = 20) # Trellis run chart on 2 conditioning variables d2 <- data.frame(y = rnorm(144, 12, 3), expand.grid(x = seq.Date(as.Date('2014-1-1'), by = 'week', length.out = 24), g1 = LETTERS[1:3], g2 = letters[1:2])) trc(y ~ x | g1 + g2, data = d2, main = 'Trellis run chart') # Introduce a shift in process performance d2$y[132:144] <- d2$y[132:144] * 3 trc(y ~ x | g1 + g2, data = d2, main = 'Trellis run chart') # Make I chart trc(y ~ x | g1 + g2, data = d2, main = 'Trellis run chart', chart = 'i')