Statistics Used In Computing And Drawing A Shewhart G Chart

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Statistics used in computing and drawing a Shewhart g chart stats.g.Rd

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, 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 [email protected]

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 = 0.005 #> Standard deviation = 0.07053368 #> #> Control limits at nsigmas = 3 #> LCL UCL #> 0 0.216601 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 = 5 #> Group sample size = 1 #> Center of group statistics = 171 #> Standard deviation = 170.4993 #> #> Control limits at nsigmas = 3 #> LCL UCL

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