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

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 [e-mail]

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.

See Also

qcc

Examples

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.