# cusumPfaCed: Cusum Probability of False Alarm and Conditional Expected... In mistat: Data Sets, Functions and Examples from the Book: "Modern Industrial Statistics" by Kenett, Zacks and Amberti

 cusumPfaCed R Documentation

## Cusum Probability of False Alarm and Conditional Expected Delay

### Description

Compute the Probability of False Alarm, PFA, and the Conditional Expected Delay, CED, for the Normal, Binomial and Poisson distributions

### Usage

```cusumPfaCedBinom(size0 = 0, prob0 = 1, size1 = 0, prob1 = 1,
tau = 10, N = 100, limit = 10000, seed = NA,
kp = 1, km = -1, hp = 3, hm = -3, side = "both",
printSummary = TRUE)

cusumPfaCedNorm(mean0 = 0, sd0=1, mean1=0, sd1=1,
tau=10, N=100, limit=10000, seed=NA,
kp=1, km=-1, hp=3, hm=-3, side="both",
printSummary = TRUE)

cusumPfaCedPois(lambda0 = 0, lambda1=1,
tau=10, N=100, limit=10000, seed=NA,
kp=1, km=-1, hp=3, hm=-3, side="both",
printSummary = TRUE)
```

### Arguments

 `size0` number of trials (zero or more) `prob0` probability of success on each trial `size1` number of trials (zero or more) after a process level change `prob1` probability of success on each trial after a process level change `mean0` distribution mean `sd0` distribution standard deviation `mean1` distribution mean after a process level change `sd1` distribution standard deviation after a process level change `lambda0` (non-negative) mean `lambda1` (non-negative) mean after a process level change `tau` time on which the process level change occurs `N` the number of replicates `limit` safety parameter, stop rule for procedures with very long ARL `seed` a single value, interpreted as an integer. If specified make the simulation replicable. `kp` K^+ parameter of the control scheme `km` K^- parameter of the control scheme `hp` h^+ parameter of the control scheme `hm` h^- parameter of the control scheme `side` a character string specifying the side of the control scheme, must be one of "both" (default), "upper" or "lower" `printSummary` logical, if `TRUE` print a summary of the cusum PFA and CED

### Value

a list with elements:

 `rls ` a numeric vector representing the Run Length of the simulation `statistics ` a numeric vector with summary statistics `run` a list of length `N` elements each of which has single numeric elements `violationLower`, `violationUpper` and `rl`

Daniele Amberti

### References

Kenett, R., Zacks, S. with contributions by Amberti, D. Modern Industrial Statistics: with applications in R, MINITAB and JMP. Wiley.

### Examples

```cusumPfaCedNorm(mean1=1.5,
tau=100,
N=100,
limit=1000,
seed=123)
```

mistat documentation built on March 7, 2023, 6:43 p.m.