tolerance (version 0.4.0)

K.factor: Estimating K-factors for Tolerance Intervals Based on Normality

Description

Estimates k-factors for tolerance intervals based on normality.

Usage

K.factor(n, f = NULL, alpha = 0.05, P = 0.99, side = 1, 
         method = c("HE", "WBE", "ELL", "EXACT"), m = 50)

Arguments

n

The (effective) sample size.

f

The number of degrees of freedom associated with calculating the estimate of the population standard deviation. If NULL, then f is taken to be n-1.

alpha

The level chosen such that 1-alpha is the confidence level.

P

The proportion of the population to be covered by the 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 k-factors. The k-factor for the 1-sided tolerance intervals is performed exactly and thus is the same for the chosen method. "HE" is the Howe method and is often viewed as being extremely accurate, even

m

The maximum number of subintervals to be used in the integrate function. This is necessary only for method = "EXACT". The larger the number, the more accurate the solution. Too low of a value can result in an error.

Value

• K.factor returns the k-factor for tolerance intervals based on normality with the arguments specified above.

References

Ellison, B. E. (1964), On Two-Sided Tolerance Intervals for a Normal Distribution, Annals of Mathematical Statistics, 35, 762--772. Howe, W. G. (1969), Two-Sided Tolerance Limits for Normal Populations - Some Improvements, Journal of the American Statistical Association, 64, 610--620. Krishnamoorthy, K. and Mathew, T. (2009), Statistical Tolerance Regions: Theory, Applications, and Computation, Wiley. Odeh, R. E. and Owen, D. B. (1980), Tables for Normal Tolerance Limits, Sampling Plans, and Screening, Marcel-Dekker. Wald, A. and Wolfowitz, J. (1946), Tolerance Limits for a Normal Distribution, Annals of the Mathematical Statistics, 17, 208--215. Weissberg, A. and Beatty, G. (1969), Tables of Tolerance Limit Factors for Normal Distributions, Technometrics, 2, 483--500.

See Also

integrate, K.table, normtol.int, TDist

Examples

## Showing the effect of the Howe, Weissberg-Beatty, 
## and exact estimation methods as the sample size increases.

K.factor(10, P = 0.95, side = 2, method = "HE")
K.factor(10, P = 0.95, side = 2, method = "WBE")
K.factor(10, P = 0.95, side = 2, method = "EXACT", m = 5)

K.factor(100, P = 0.95, side = 2, method = "HE")
K.factor(100, P = 0.95, side = 2, method = "WBE")
K.factor(100, P = 0.95, side = 2, method = "EXACT", m = 5)

K.factor(1000, P = 0.95, side = 2, method = "HE")
K.factor(1000, P = 0.95, side = 2, method = "WBE")
K.factor(1000, P = 0.95, side = 2, method = "EXACT", m = 5)