bintol.int {tolerance}R Documentation

Binomial Tolerance Intervals

Description

Provides 1-sided or 2-sided tolerance intervals for binomial random variables. From a statistical quality control perspective, these limits use the proportion of defective (or acceptable) items in a sample to bound the number of defective (or acceptable) items in future productions of a specified quantity.

Usage

bintol.int(x, n, m, alpha = 0.05, P = 0.99, side = 1, 
           method = c("LS", "WS", "AC", "JF", "CP", "AS", 
           "LO"), a1 = 0.5, a2 = 0.5)

Arguments

x The number of defective (or acceptable) units in the sample.
n The size of the random sample of units selected for inspection.
m The quantity produced in future groups.
alpha The level chosen such that 1-alpha is the confidence level.
P The proportion of the defective (or acceptable) units in future samples of size m to be covered by this tolerance interval.
side Whether a 1-sided or 2-sided tolerance interval is required (determined by side = 1 or side = 2, respectively).
method The method for calculating the lower and upper confidence bounds, which are used in the calculation of the tolerance bounds. The default method is "LS", which is the large-sample method. "AC" gives the Agresti-Coull method, which is also appropriate when the sample size is large. "JF" is Jeffreys' method, which is a Bayesian approach to the estimation. "CP" is the Clopper-Pearson method, which provides a more conservative interval. "AS" is the arcsine method, which is appropriate when the sample proportion is not too close to 0 or 1. "LO" is the logit method, which also is appropriate when the sample proportion is not too close to 0 or 1, but yields a more conservative interval. More information on these methods can be found in the "References".
a1 This specifies the first shape hyperparameter when using Jeffreys' method.
a2 This specifies the second shape hyperparameter when using Jeffreys' method.

Value

bintol.int returns a data frame with items:

alpha The specified significance level.
P The proportion of defective (or acceptable) units in future samples of size m.
p.hat The proportion of defective (or acceptable) units in the sample, calculated by x/n.
1-sided.lower The 1-sided lower tolerance bound. This is given only if side = 1.
1-sided.upper The 1-sided upper tolerance bound. This is given only if side = 1.
2-sided.lower The 2-sided lower tolerance bound. This is given only if side = 2.
2-sided.upper The 2-sided upper tolerance bound. This is given only if side = 2.

References

Brown, L. D., Cai, T. T., and DasGupta, A. (2001), Interval Estimation for a Binomial Proportion, Statistical Science, 16, 101–133.

Hahn, G. J. and Chandra, R. (1981), Tolerance Intervals for Poisson and Binomial Variables, Journal of Quality Technology, 13, 100–110.

See Also

Binomial

Examples

 

## 85%/90% 1-sided binomial tolerance limits for a future 
## lot of 500 when a sample of 40 were drawn from a lot of 
## 1000.  The Agresti-Coull, Clopper-Pearson, and large-sample
## methods are presented for comparison.

bintol.int(x = 40, n = 1000, m = 500, alpha = 0.15, P = 0.90,
           side = 1, method = "AC")
bintol.int(x = 40, n = 1000, m = 500, alpha = 0.15, P = 0.90,
           side = 1, method = "CP")
bintol.int(x = 40, n = 1000, m = 500, alpha = 0.15, P = 0.90,
           side = 1, method = "LS")
 

[Package tolerance version 0.1.0 Index]