View source: R/pois.ewma.crit.R
pois.ewma.crit | R Documentation |
Computation of the (zero-state) Average Run Length (ARL) at given mean mu
.
pois.ewma.crit(lambda, L0, mu0, z0, AU=3, sided="two", design="sym", rando=FALSE,
mcdesign="transfer", N=101, jmax=4)
lambda |
smoothing parameter of the EWMA p control chart. |
L0 |
value of the so-called in-control Average Run Length (ARL) for the Poisson EWMA control chart. |
mu0 |
in-control mean. |
z0 |
so-called headstart (give fast initial response). |
AU |
in case of the lower chart deployed as reflecting upper barrier – might be increased step by step until the resulting lower limit does not change anymore. |
sided |
distinguishes between one- and two-sided EWMA control chart by choosing |
design |
distinguishes between limits symmetric to the in-control mean |
rando |
Switch between the standard limit treatment, |
mcdesign |
choose either |
N |
number of states of the approximating Markov chain; is equal to the dimension of the resulting linear equation system. |
jmax |
number of digits for the to be calculated factors |
The monitored data follow a Poisson distribution with mu
.
Here we solve the inverse task to the usual ARL calculation. Hence, determine the control limit factors
so that the in-control ARL is (roughly) equal to L0
.
The ARL values underneath the routine are determined by Markov chain approximation.
The algorithm is just a grid search that takes care of the discrete ARL behavior.
Return one or two values being he control limit factors.
Sven Knoth
C. M. Borror, C. W. Champ and S. E. Rigdon (1998) Poisson EWMA control charts, Journal of Quality Technonlogy 30(4), 352-361.
M. C. Morais and S. Knoth (2020) Improving the ARL profile and the accuracy of its calculation for Poisson EWMA charts, Quality and Reliability Engineering International 36(3), 876-889.
later.
## Borror, Champ and Rigdon (1998), page 30, original value is A = 2.8275
mu0 <- 4
lambda <- 0.2
L0 <- 351
A <- pois.ewma.crit(lambda, L0, mu0, mu0, mcdesign="classic")
print(round(A, digits=4))
## Morais and Knoth (2020), Table 2, lambda = 0.27 column
lambda <- 0.27
L0 <- 1233.4
ccgg <- pois.ewma.crit(lambda,1233.4,mu0,mu0,design="unb",rando=TRUE,mcdesign="transfer")
print(ccgg, digits=3)
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