nporder: Sample Size Determination for Tolerance Limits Based on Order...

In tolerance: Statistical Tolerance Intervals and Regions

Sample Size Determination for Tolerance Limits Based on Order Statistics

Description

For given values of m, alpha, and P, this function solves the necessary sample size such that the r-th (or (n-s+1)-th) order statistic is the [100(1-alpha)%, 100(P)%] lower (or upper) tolerance limit (see the Details section below for further explanation). This function can also report all combinations of order statistics for 2-sided intervals.

Usage

np.order(m, alpha = 0.05, P = 0.99, indices = FALSE)

Arguments

m	See the Details section below for how m is defined.
alpha	1 minus the confidence level attained when it is desired to cover a proportion P of the population with the order statistics.
P	The proportion of the population to be covered with confidence 1-alpha with the order statistics.
indices	An optional argument to report all combinations of order statistics indices for the upper and lower limits of the 2-sided intervals. Note that this can only be calculated when m>1.

Details

For the 1-sided tolerance limits, m=s+r such that the probability is at least 1-alpha that at least the proportion P of the population is below the (n-s+1)-th order statistic for the upper limit or above the r-th order statistic for the lower limit. This means for the 1-sided upper limit that r=1, while for the 1-sided lower limit it means that s=1. For the 2-sided tolerance intervals, m=s+r such that the probability is at least 1-alpha that at least the proportion P of the population is between the r-th and (n-s+1)-th order statistics. Thus, all combinations of r>0 and s>0 such that m=s+r are considered.

Value

If indices = FALSE, then a single number is returned for the necessary sample size such that the r-th (or (n-s+1)-th) order statistic is the [100(1-alpha)%, 100(P)%] lower (or upper) tolerance limit. If indices = TRUE, then a list is returned with a single number for the necessary sample size and a matrix with 2 columns where each row gives the pairs of indices for the order statistics for all permissible [100(1-alpha)%, 100(P)%] 2-sided tolerance intervals.

References

Hanson, D. L. and Owen, D. B. (1963), Distribution-Free Tolerance Limits Elimination of the Requirement That Cumulative Distribution Functions Be Continuous, Technometrics, 5, 518–522.

Scheffe, H. and Tukey, J. W. (1945), Non-Parametric Estimation I. Validation of Order Statistics, Annals of Mathematical Statistics, 16, 187–192.

See Also

nptol.int

Examples

 
## Only requesting the sample size.

np.order(m = 5, alpha = 0.05, P = 0.95)

## Requesting the order statistics indices as well.

np.order(m = 5, alpha = 0.05, P = 0.95, indices = TRUE)

tolerance documentation built on May 29, 2024, 7:38 a.m.