Statistics used in computing and drawing a Shewhart g chart

Description

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

Usage

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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.

See Also

qcc

Examples

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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")

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