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

## 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 x_bar - k s, where x_bar 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

 `1` ```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()`
 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17``` ```kb <- k_factor_normal(n = 10, p = 0.9, conf = 0.95) print(kb) ##  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) ##  B-Basis: ##  77.75587 ```