# k_factor_normal: Calculate k factor for basis values (kB, kA) with normal... In cmstatr: Statistical Methods for Composite Material Data

 k_factor_normal R Documentation

## 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.

### 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.

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



cmstatr documentation built on Sept. 9, 2023, 9:06 a.m.