pois.ewma.crit: Compute ARLs of Poisson EWMA control charts

In spc: Statistical Process Control -- Calculation of ARL and Other Control Chart Performance Measures

Compute ARLs of Poisson EWMA control charts

Description

Computation of the (zero-state) Average Run Length (ARL) at given mean mu.

Usage

pois.ewma.crit(lambda, L0, mu0, z0, AU=3, sided="two", design="sym", rando=FALSE,
mcdesign="transfer", N=101, jmax=4)

Arguments

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 "upper", "lower", and "two", respectively.
design	distinguishes between limits symmetric to the in-control mean mu0 and an ARL-unbiased design (ARL maximum at mu0); use the shortcuts "sym" and "unb", respectively, please.
rando	Switch between the standard limit treatment, FALSE, and an additional randomisation (to allow ‘perfect’ ARL calibration) by setting TRUE. If randomisation is used, then the corresponding probailities, gL and gU are determined, appropriately.
mcdesign	choose either "classic" which follows Borror, Champ and Rigdon (1998), or the more sophisticated "transfer" which improves the accuracy heavily.
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 A (sort of accuracy).

Details

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.

Value

Return one or two values being he control limit factors.

Author(s)

Sven Knoth

References

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.

See Also

later.

Examples

## 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)

spc documentation built on Oct. 24, 2022, 5:07 p.m.