# normtolint: Normal (or Log-Normal) Tolerance Intervals In tolerance: Statistical Tolerance Intervals and Regions

## Description

Provides 1-sided or 2-sided tolerance intervals for data distributed according to either a normal distribution or log-normal distribution.

## Usage

 ```1 2 3``` ```normtol.int(x, alpha = 0.05, P = 0.99, side = 1, method = c("HE", "HE2", "WBE", "ELL", "KM", "EXACT", "OCT"), m = 50, log.norm = FALSE) ```

## Arguments

 `x` A vector of data which is distributed according to either a normal distribution or a log-normal distribution. `alpha` The level chosen such that `1-alpha` is the confidence level. `P` The proportion of the population 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 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"`. `log.norm` If `TRUE`, then the data is considered to be from a log-normal distribution, in which case the output gives tolerance intervals for the log-normal distribution. The default is `FALSE`.

## Details

Recall that if the random variable X is distributed according to a log-normal distribution, then the random variable Y = ln(X) is distributed according to a normal distribution.

## Value

`normtol.int` returns a data frame with items:

 `alpha` The specified significance level. `P` The proportion of the population covered by this tolerance interval. `x.bar` The sample mean. `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

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

Wald, A. and Wolfowitz, J. (1946), Tolerance Limits for a Normal Distribution, Annals of 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

`Normal`, `K.factor`

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11 12``` ``` ## 95%/95% 2-sided normal tolerance intervals for a sample ## of size 100. set.seed(100) x <- rnorm(100, 0, 0.2) out <- normtol.int(x = x, alpha = 0.05, P = 0.95, side = 2, method = "HE", log.norm = FALSE) out plottol(out, x, plot.type = "both", side = "two", x.lab = "Normal Data") ```

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