# Ktable: Tables of K-factors for Tolerance Intervals Based on... In tolerance: Statistical Tolerance Intervals and Regions

## 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

 ```1 2 3``` ```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")) ```

## 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.

## Value

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

## 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.

`K.factor`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16``` ``` ## 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") ```