k_factor_normal {cmstatr}

Calculate k factor for basis values (kB, kA) with normal distribution

Description

The factors returned by this function are used when calculating basis values (one-sided confidence bounds) when the data are normally distributed. The basis value will be equal to \bar{x} - k s, where \bar{x} is the sample mean, s is the sample standard deviation and k is the result of this function. This function is internally used by basis_normal() when computing basis values.

Usage

k_factor_normal(n, p = 0.9, conf = 0.95)

Arguments

n

the number of observations (i.e. coupons)

p

the desired content of the tolerance bound. Should be 0.90 for B-Basis and 0.99 for A-Basis

conf

confidence level. Should be 0.95 for both A- and B-Basis

Details

This function calculates the k factors used when determining A- and B-Basis values for normally distributed data. To get kB, set the content of the tolerance bound to p = 0.90 and the confidence level to conf = 0.95. To get kA, set p = 0.99 and conf = 0.95. While other tolerance bound contents and confidence levels may be computed, they are infrequently needed in practice.

The k-factor is calculated using equation 2.2.3 of Krishnamoorthy and Mathew (2008).

This function has been validated against the kB tables in CMH-17-1G for each value of n from n = 2 to n = 95. It has been validated against the kA tables in CMH-17-1G for each value of n from n = 2 to n = 75. Larger values of n also match the tables in CMH-17-1G, but R emits warnings that "full precision may not have been achieved." When validating the results of this function against the tables in CMH-17-1G, the maximum allowable difference between the two is 0.002. The tables in CMH-17-1G give values to three decimal places.

For more information about tolerance bounds in general, see Meeker, et. al. (2017).

Value

the calculated factor

References

K. Krishnamoorthy and T. Mathew, Statistical Tolerance Regions: Theory, Applications, and Computation. Hoboken: John Wiley & Sons, 2008.

W. Meeker, G. Hahn, and L. Escobar, Statistical Intervals: A Guide for Practitioners and Researchers, Second Edition. Hoboken: John Wiley & Sons, 2017.

“Composite Materials Handbook, Volume 1. Polymer Matrix Composites Guideline for Characterization of Structural Materials,” SAE International, CMH-17-1G, Mar. 2012.

See Also

basis_normal()

Examples

kb <- k_factor_normal(n = 10, p = 0.9, conf = 0.95)
print(kb)

## [1] 2.35464

# This can be used to caclulate the B-Basis if
# the sample mean and sample standard deviation
# is known, and data is assumed to be normally
# distributed

sample_mean <- 90
sample_sd <- 5.2
print("B-Basis:")
print(sample_mean - sample_sd * kb)

## [1] B-Basis:
## [1] 77.75587