simnormtol.int: 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)

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.

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.

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.

Examples

Run this code

## 95%/95% simultaneous 2-sided normal tolerance 
## intervals for three samples of unequal size. 

set.seed(100)
x <- list(rnorm(20),rnorm(10,1),rnorm(12,1,2))
out <- simnormtol.int(x = x, alpha = 0.05, P = 0.95, 
                      side = 2, method = "BONF")
out

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