sewma.arl {spc} | R Documentation |
Computation of the (zero-state) Average Run Length (ARL) for different types of EWMA control charts (based on the sample variance S^2) monitoring normal variance.
sewma.arl(l,cl,cu,sigma,df,s2.on=TRUE,hs=1,sided="upper",r=40,qm=30)
l |
smoothing parameter lambda of the EWMA control chart. |
cl |
lower control limit of the EWMA control chart. |
cu |
upper control limit of the EWMA control chart. |
sigma |
true standard deviation. |
df |
actual degrees of freedom, corresponds to batch size. |
s2.on |
distinguish between S^2 and S chart. |
hs |
so-called headstart (give fast initial response). |
sided |
distinguish between one- and two-sided
two-sided EWMA-S^2 control charts
by choosing "upper" (upper chart
without reflection at cl – the actual value of
cl is not used),
"Rupper" (upper chart with reflection at cl ),
"Rlower" (lower chart with reflection at cu ),
and "two" (two-sided chart),
respectively. |
r |
dimension of the resulting linear equation system. |
qm |
number of quadrature nodes. |
sewma.arl
determines the Average Run Length (ARL) by numerically
solving the related ARL integral equation by means of
collocation (Chebyshev polynomials).
Returns a single value which resembles the ARL.
Sven Knoth
S. Knoth (2005), Accurate ARL computation for EWMA-S^2 control charts, Statistics and Computing 15, 341-352.
xewma.arl
for zero-state ARL computation of EWMA control charts
for monitoring normal mean.
## Knoth (2005) ## compare with Table 1 (p. 347): 249.9997 ## Monte Carlo with 10^9 replicates: 249.9892 +/- 0.008 l <- .025 df <- 1 cu <- 1 + 1.661865*sqrt(l/(2-l))*sqrt(2/df) sewma.arl(l,0,cu,1,df)