k_factor_normal | R Documentation |

`kB`

, `kA`

) with normal
distributionThe 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.

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

`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 |

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).

the calculated factor

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()`

```
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
```

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