tolerance (version 1.1.1)

normtol.int: Normal (or Log-Normal) Tolerance Intervals

Description

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

Usage

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

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

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.

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.

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.

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

## 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")