tolerance (version 3.0.0)

K.table: Tables of K-factors for Tolerance Intervals Based on Normality

Description

Tabulated summary of k-factors for tolerance intervals based on normality. The user can specify multiple values for each of the three inputs.

Usage

K.table(n, alpha, P, side = 1, f = NULL, method = c("HE", 
        "HE2", "WBE", "ELL", "KM", "EXACT", "OCT"), m = 50,
        by.arg = c("n", "alpha", "P"))

Value

K.table returns a list with a structure determined by the argument by.arg described above.

Arguments

n

A vector of (effective) sample sizes.

alpha

The level chosen such that 1-alpha is the confidence level. Can be a vector.

P

The proportion of the population to be covered by this tolerance interval. Can be a vector.

side

Whether a 1-sided or 2-sided tolerance interval is required (determined by side = 1 or side = 2, respectively).

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. Only a single value can be specified for f.

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 for small sample sizes. "HE2" is a second method due to Howe, which performs similarly to the Weissberg-Beatty method, but is computationally simpler. "WBE" is the Weissberg-Beatty method (also called the Wald-Wolfowitz method), which performs similarly to the first Howe method for larger sample sizes. "ELL" is the Ellison correction to the Weissberg-Beatty method when f is appreciably larger than n^2. A warning message is displayed if f is not larger than n^2. "KM" is the Krishnamoorthy-Mathew approximation to the exact solution, which works well for larger sample sizes. "EXACT" computes the k-factor exactly by finding the integral solution to the problem via the integrate function. Note the computation time of this method is largely determined by m. "OCT" is the Owen approach to compute the k-factor when controlling the tails so that there is not more than (1-P)/2 of the data in each tail of the distribution.

m

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

by.arg

How you would like the output organized. If by.arg = "n", then the output provides a list of matrices sorted by the values specified in n. The matrices have rows corresponding to the values specified by 1-alpha and columns corresponding to the values specified by P. If by.arg = "alpha", then the output provides a list of matrices sorted by the values specified in 1-alpha. The matrices have rows corresponding to the values specified by n and columns corresponding to the values specified by P. If by.arg = "P", then the output provides a list of matrices sorted by the values specified in P. The matrices have rows corresponding to the values specified by 1-alpha and columns corresponding to the values specified by n.

Details

The method used for estimating the k-factors is that due to Howe as it is generally viewed as more accurate than the Weissberg-Beatty method.

References

Howe, W. G. (1969), Two-Sided Tolerance Limits for Normal Populations - Some Improvements, Journal of the American Statistical Association, 64, 610--620.

Weissberg, A. and Beatty, G. (1969), Tables of Tolerance Limit Factors for Normal Distributions, Technometrics, 2, 483--500.

See Also

K.factor

Examples

## Tables generated for each value of the sample size.

K.table(n = seq(50, 100, 10), alpha = c(0.01, 0.05, 0.10), 
        P = c(0.90, 0.95, 0.99), by.arg = "n")

## Tables generated for each value of the confidence level.

K.table(n = seq(50, 100, 10), alpha = c(0.01, 0.05, 0.10), 
        P = c(0.90, 0.95, 0.99), by.arg = "alpha")

## Tables generated for each value of the coverage proportion.

K.table(n = seq(50, 100, 10), alpha = c(0.01, 0.05, 0.10), 
        P = c(0.90, 0.95, 0.99), by.arg = "P")