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
computing basis values.
k_factor_normal(n, p = 0.9, conf = 0.95)
the number of observations (i.e. coupons)
the desired content of the tolerance bound. Should be 0.90 for B-Basis and 0.99 for A-Basis
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.
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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
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