tolerance (version 0.4.0)

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", "WBE"), 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 the same for either method chosen. "HE" is the Howe method and is often viewed as being extremely accurate, even

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. 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")