K.factor.sim {tolerance}

Estimating K-factors for Simultaneous Tolerance Intervals Based on Normality

Description

Estimates k-factors for simultaneous tolerance intervals based on normality.

Usage

K.factor.sim(n, l = NULL, alpha = 0.05, P = 0.99, side = 1, 
         method = c("EXACT", "BONF"), m = 50)

Arguments

n

If method = "EXACT", this is the sample size of each of the l groups. If method = "BONF", then n can be a vector of different sample sizes for the l groups.

l

The number of normal populations for which the k-factors will be constructed simultaneously. If NULL, then it is taken to be the length of n.

alpha

The level chosen such that 1-alpha is the confidence level.

P

The proportion of the population to be covered by the tolerance interval.

side

Whether a k-factor for 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. "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".

Value

K.factor returns the k-factor for simultaneous tolerance intervals based on normality with the arguments specified above.

Note

For larger combinations of n and l when side = 2 and method = "EXACT", the calculation can be slow. For larger sample sizes when method = "BONF", there may be some accuracy issues with the 1-sided calculation since it depends on the noncentral t-distribution. The code is primarily intended to be used for moderate values of the noncentrality parameter. It will not be highly accurate, especially in the tails, for large values. See TDist for further details.

Thanks to Andrew Landgraf for providing the basic code for the method = "EXACT" procedure.

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

integrate, K.factor

Examples

 
## Reproducing part of Table B5 from Krishnamoorthy and 
## Mathew (2009).

n_sizes <- c(2:20, seq(30, 100, 10))
l_sizes <- 2:10
KM_table <- sapply(1:length(l_sizes), function(i)
                   sapply(1:length(n_sizes), function(j)
                   round(K.factor.sim(n = n_sizes[j], 
                   l = l_sizes[i], side=1, alpha = 0.1, 
                   P = 0.9),3)))
dimnames(KM_table) <- list(n = n_sizes, l = l_sizes)
KM_table