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.

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

## Value

the calculated factor

## 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.

basis_normal()

## Examples

kb <- k_factor_normal(n = 10, p = 0.9, conf = 0.95)
print(kb)
#>  2.35464

##  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:")
#>  "B-Basis:"
print(sample_mean - sample_sd * kb)
#>  77.75587

##  B-Basis:
##  77.75587