Calculates a sequence of Cusum statistics
Description
Calculates a sequence of onesided upper Cusum statistics given the reference value and the control limit.
Usage
1 2 3 4 5 6 7 8 9 10 
Arguments
X 
A numeric vector. 
k 
The reference value. 
h 
The upper control limit. 
initial 
The starting value of the Cusum (C[0]). 
reset 
Logical indicating whether the Cusum is reset to 0 after crossing the control limit. 
x 
Object of class 
indexes 
A vector of indexes that select the elements of the cusum statistics that will be plotted. 
emphOOC 
A logical indicating whether out of control points should be emphasized in red. 
object 
Object of class 
... 
Additional arguments to 
Details
Cusum is assumed to be of the form: C[i] = max(0, C[i1] + X[i]  k),
where the signal occurs when C[i] > h. Note that X
can be the Cusum scores, or weights,
given by the loglikelihood ratio, in which case k = 0
would make sense.
Value
A object of class cusum
, which is a vector of the Cusum statistics, along with the following attributes:
X
, k
, h
, initial
, and reset
(which correspond to the original arguments provided to
the function) and resetCounter
, a vector of integers corresponding to cusum
that indicates when the
Cusum resets.
Methods (by generic)

print
: Prints thecusum
object by only showing the Cusum statistics and suppressing the attributes. 
plot
: Plots thecusum
object. 
signal
: Prints the indexes in acusum
object that exceed the control limit
References
Hawkins DM and Olwell DH. (1998) Cumulative Sum Charts and Charting for Quality Improvement. Springer.
Examples
1 2 3 4 5 6 7 8 9 10 11  y < cusum(rnorm(50), 0.2, 2)
y
# Plot the cusum
plot(y)
# Show the indexes where the chart signaled
signal(y)
# A look at the attributes
attributes(y)
