xewma.crit {spc} | R Documentation |
Computation of the critical values (similar to alarm limits) for different types of EWMA control charts monitoring normal mean.
xewma.crit(l,L0,mu0=0,zr=0,hs=0,sided="one",limits="fix",r=40)
l |
smoothing parameter lambda of the EWMA control chart. |
L0 |
in-control ARL. |
mu0 |
in-control mean. |
zr |
reflection border for the one-sided chart. |
hs |
so-called headstart (give fast initial response). |
sided |
distinguish between one- and two-sided
two-sided EWMA control chart by choosing "one" and "two" ,
respectively. |
limits |
distinguish between different control limits behavior. |
r |
number of quadrature nodes, dimension of the resulting linear
equation system is equal to r+1 (one-sided) or r
(two-sided). |
xewma.crit
determines the critical values (similar to alarm limits)
for given in-control ARL L0
by applying secant rule and using xewma.arl()
.
Returns a single value which resembles the critical value
c
.
Sven Knoth
S. V. Crowder (1989), Design of exponentially weighted moving average schemes, Journal of Quality Technology 21, 155-162.
xewma.arl
for zero-state ARL computation.
l <- .1 incontrolARL <- c(500,5000,50000) sapply(incontrolARL,l=l,sided="two",xewma.crit,r=30) # accuracy with 30 nodes sapply(incontrolARL,l=l,sided="two",xewma.crit) # accuracy with 40 nodes sapply(incontrolARL,l=l,sided="two",xewma.crit,r=50) # accuracy with 50 nodes ## Crowder (1989) ## two-sided EWMA control charts with fixed limits l <- c(.05,.1,.15,.2,.25) L0 <- 250 round(sapply(l,L0=L0,sided="two",xewma.crit),digits=2) ## original values are 2.32, 2.55, 2.65, 2.72, and 2.76.