Statistics used in computing and drawing a Shewhart g chart

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

stats.g(data, sizes)
sd.g(data, sizes, ...)
limits.g(center, std.dev, sizes, nsigmas = NULL, conf = NULL)

Arguments

data

the observed data values

center

sample center statistic

sizes

sample sizes (not used)

std.dev

standard deviation of geometric distribution

nsigmas

a numeric value specifying the number of sigmas to use for computing control limits. It is ignored when the conf argument is provided.

conf

a numeric value in \((0,1)\) specifying the confidence level to use for computing control limits.

...

catches further ignored arguments.

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.

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.

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.

Author

Greg Snow greg.snow@ihc.com

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.

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)
#> ── Quality Control Chart ───────────────────────── 
#> 
#> Chart type                 = np 
#> Data (phase I)             = success 
#> Number of groups           = 1000 
#> Group sample size          = 1 
#> Center of group statistics = 0.008 
#> Standard deviation         = 0.08908423 
#> 
#> Control limits at nsigmas  = 3 
#>  LCL       UCL
#>    0 0.2752527
qcc(num.noevent, type = "g")
#> Warning: 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.
#> ── Quality Control Chart ───────────────────────── 
#> 
#> Chart type                 = g 
#> Data (phase I)             = num.noevent 
#> Number of groups           = 8 
#> Group sample size          = 1 
#> Center of group statistics = 107.375 
#> Standard deviation         = 106.8738 
#> 
#> Control limits at nsigmas  = 3 
#>      LCL UCL