rQCC (version 2.22.12)

factors.for.chart: Factors for constructing control charts

Description

Factors for constructing control charts.

Usage

factors.cc(n, factor=c( "A","A1","A2","A3", "B1","B2","B3","B4","B5","B6", "c2","c4",
                        "d2","d3","D1","D2","D3","D4", "E1", "E2", "E3"), sigmaFactor=3)

Value

It returns a numeric value.

Arguments

n

sample size (\(n \ge 1\)).

factor

a character string specifying the foctor.
"c2", "c4", "d2", "d3" for control chart lines; "A", "A1", "A2", "A3" for averages for computing control limits; "B1", "B2", "B3", "B4", "B5", "B6" for standard devations; "D1", "D2", "D3", "D4" for ranges; and "E1", "E2", "E3" for individuals. For "d3", the calculation is not accurate when \(n>100\).

sigmaFactor

a factor for the standard deviation (\(\sigma\)).
For example, the American Standard uses "3*sigma" limits (0.27% false alarm rate), while the British Standard uses "3.09*sigma" limits (0.20% false alarm rate).

Author

Chanseok Park

Details

The values of the factors are used for constructing various control charts.

For example, the conventional \(\bar{X}\) chart with the sample standard deviation is given by $$\bar{\bar{X}} \pm A_3 \bar{S}.$$

For more details, refer to vignette("factors.cc", package="rQCC").

References

ASTM (2010). Manual on Presentation of Data and Control Chart Analysis (STP 15-D), 8th edition. American Society for Testing and Materials, West Conshohocken, PA.

ASTM (1951). Manual on Quality Control of Materials (STP 15-C), American Society for Testing and Materials, Philadelphia, PA.

See Also

c4.factor{rQCC} for \(c_4\) factor for the finite-sample unbiasing factor to estimate the standard deviation (\(\sigma\)) under the normal distribution using various estimators such as the sample standard deviation, the sample range, the median absolute deviation (MAD), and the Shamos estimator.

Examples

## A3 is used for constructing the conventional X-bar chart 
#  with the sample standard deviation.
factors.cc(n=10, factor="A3")


## Unbiasing factor for the standard deviation 
#           using the sample standard deviation.
factors.cc(n=10, factor="c4")
#  The above is the same as below:
c4.factor(n=10, estimator="sd")


## Unbiasing factor for the standard deviation 
#           using the sample range. 
factors.cc(n=10, factor="d2")
#  The above is the same as below:
c4.factor(n=10, estimator="range") 


## Table B2 in Supplement B of ASTM (1951).
char = c("A","A1","A2","c2", "B1","B2","B3","B4", "d2","d3","D1","D2","D3","D4")
nn = 2L:25L

res=NULL
for(n in nn){tmp=NULL;for(ch in char) tmp=c(tmp,factors.cc(n,ch));res=rbind(res,tmp)}
rownames(res) = paste0("n=",nn)
round(res,4)


## Table 49 in Chapter 3 of ASTM (2010).
char = c("A","A2","A3","c4", "B3","B4","B5","B6", "d2","d3","D1","D2","D3","D4")
nn = 2L:25L

res=NULL
for(n in nn){tmp=NULL;for(ch in char) tmp=c(tmp,factors.cc(n,ch));res=rbind(res,tmp)}
rownames(res) = paste0("n=",nn)
round(res,4)


## Table 50 in Chapter 3 of ASTM (2010).
char = c("E2", "E3")
nn = 2L:25L

res=NULL
for(n in nn){tmp=NULL;for(ch in char) tmp=c(tmp,factors.cc(n,ch));res=rbind(res,tmp)}
rownames(res) = paste0("n=",nn)
round(res,3)