# stats.g: Statistics used in computing and drawing a Shewhart g chart In qcc: Quality Control Charts

## Description

These functions are used to compute statistics required by the g chart (geometric distribution) for use with the qcc package.

## Usage

 ```1 2 3``` ```stats.g(data, sizes) sd.g(data, sizes, ...) limits.g(center, std.dev, sizes, conf) ```

## Arguments

 `data` the observed data values `center` sample center statistic `sizes` sample sizes (not used) `std.dev` standard deviation of geometric distribution `conf` a numeric value used to compute control limits, specifying the number of standard deviations (if 'conf' > 1) or the confidence level (if 0 < 'conf' < 1). `...` further arguments are ignored.

## Details

The g chart plots the number of non-events between events. np charts do not work well when the probability of an event is rare (see example below). Instead of plotting the number of events, the g chart plots the number of non-events between events.

## Value

The function `stats.g()` returns a list with components `statistics` and `center`.

The function `sd.g()` returns `std.dev` the standard deviation sqrt(1-p)/p.

The function `limits.g()` returns a matrix with lower and upper control limits.

## Note

The geometric distribution is quite skewed so it is best to set conf at the required confidence interval (0 < conf < 1) rather than as a multiplier of sigma.

## Author(s)

Greg Snow greg.snow@ihc.com

## References

Kaminsky, FC et. al. (1992) Statistical Control Charts Based on a Geometric Distribution, Journal of Quality Technology, 24, pp 63–69.
Yang, Z et. al. (2002) On the Performance of Geometric Charts with Estimated Control Limits, Journal of Quality Technology, 34, pp 448–458.

`qcc`

## Examples

 ```1 2 3 4``` ```success <- rbinom(1000, 1, 0.01) num.noevent <- diff(which(c(1,success)==1))-1 qcc(success, type = "np", sizes = 1) qcc(num.noevent, type = "g") ```

### Example output  ```Package 'qcc' version 2.7
Type 'citation("qcc")' for citing this R package in publications.
List of 11
\$ call      : language qcc(data = success, type = "np", sizes = 1)
\$ type      : chr "np"
\$ data.name : chr "success"
\$ data      : int [1:1000, 1] 0 0 0 0 0 0 0 0 0 0 ...
..- attr(*, "dimnames")=List of 2
\$ statistics: Named int [1:1000] 0 0 0 0 0 0 0 0 0 0 ...
..- attr(*, "names")= chr [1:1000] "1" "2" "3" "4" ...
\$ sizes     : num [1:1000] 1 1 1 1 1 1 1 1 1 1 ...
\$ center    : num 0.009
\$ std.dev   : num 0.0944
\$ nsigmas   : num 3
\$ limits    : num [1, 1:2] 0 0.292
..- attr(*, "dimnames")=List of 2
\$ violations:List of 2
- attr(*, "class")= chr "qcc"
List of 11
\$ call      : language qcc(data = num.noevent, type = "g")
\$ type      : chr "g"
\$ data.name : chr "num.noevent"
\$ data      : num [1:9, 1] 106 166 17 76 72 17 187 27 268
..- attr(*, "dimnames")=List of 2
\$ statistics: Named num [1:9] 106 166 17 76 72 17 187 27 268
..- attr(*, "names")= chr [1:9] "1" "2" "3" "4" ...
\$ sizes     : int [1:9] 1 1 1 1 1 1 1 1 1
\$ center    : num 104
\$ std.dev   : num 103
\$ nsigmas   : num 3
\$ limits    : num [1, 1:2] 0 414
..- attr(*, "dimnames")=List of 2
\$ violations:List of 2
- attr(*, "class")= chr "qcc"
Warning message:
In limits.g(center = 104, std.dev = 103.498792263485, sizes = c(1L,  :
The Geometric distribution is quite skewed, it is better to set conf at the required confidence level (0 < conf < 1) instead of as a multiplier of sigma.
```

qcc documentation built on May 2, 2019, 9:15 a.m.