# Kfactor: Estimating K-factors for Tolerance Intervals Based on... In tolerance: Statistical Tolerance Intervals and Regions

## Description

Estimates k-factors for tolerance intervals based on normality.

## Usage

 ```1 2 3``` ```K.factor(n, f = NULL, alpha = 0.05, P = 0.99, side = 1, method = c("HE", "HE2", "WBE", "ELL", "KM", "EXACT", "OCT"), 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 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"`.

## Value

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

## Note

For larger sample sizes, there may be some accuracy issues with the 1-sided calculation since it depends on the noncentral t-distribution. The code is primarily intended to be used for moderate values of the noncentrality parameter. It will not be highly accurate, especially in the tails, for large values. See `TDist` for further details.

## 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.

Owen, D. B. (1964), Controls of Percentages in Both Tails of the Normal Distribution, Technometrics, 6, 377-387.

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

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ``` ## 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 = 50) 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 = 50) ```

tolerance documentation built on Feb. 6, 2020, 5:08 p.m.