simnormtol.int {tolerance}

Simultaneous Normal (or Log-Normal) Tolerance Intervals

Description

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

Usage

simnormtol.int(x, alpha = 0.05, P = 0.99, side = 1,
               method = c("EXACT", "BONF"), m = 50, log.norm = FALSE)

Arguments

x

Either a matrix or list of vectors of the data. If a matrix, then the columns are the samples from the different normal (or log-normal) populations. If method = "EXACT", then x must be a matrix.

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 simultaneous 1-sided or 2-sided tolerance intervals are required (determined by side = 1 or side = 2, respectively).

method

The method for calculating the k-factors. "EXACT" is an exact method that can be used when all l groups have the same sample size. "BONF" is an approximate method using the Bonferroni inequality, which can be used when the l groups have different sample sizes.

m

The maximum number of subintervals to be used in the integrate function. This is necessary only for method = "EXACT". 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 means.

1-sided.lower

The simultaneous 1-sided lower tolerance bounds. This is given only if side = 1.

1-sided.upper

The simultaneous 1-sided upper tolerance bounds. This is given only if side = 1.

2-sided.lower

The simultaneous 2-sided lower tolerance bounds. This is given only if side = 2.

2-sided.upper

The simultaneous 2-sided upper tolerance bounds. This is given only if side = 2.

Note

The code for this functions is built upon code provided by Andrew Landgraf.

References

Krishnamoorthy, K. and Mathew, T. (2009), Statistical Tolerance Regions: Theory, Applications, and Computation, Wiley.

Mee, R. W. (1990), Simultaneous Tolerance Intervals for Normal Populations with Common Variance, Technometrics, 32, 83-92.

See Also

Normal, K.factor.sim

Examples

 
## 95%/95% simultaneous 1-sided normal tolerance 
## intervals for two samples of unequal size. 

set.seed(100)
x <- list(rnorm(5,1),rnorm(7,1,2))
out <- simnormtol.int(x = x, alpha = 0.05, P = 0.95, 
                      side = 1, method = "BONF")
out