norm.OC: Operating Characteristic (OC) Curves for K-Factors for Tolerance Intervals Based on Normality

Description

Provides OC-type curves to illustrate how values of the k-factors for normal tolerance intervals, confidence levels, and content levels change as a function of the sample size.

Usage

norm.OC(k = NULL, alpha = NULL, P = NULL, n, side = 1, method = c("HE", "HE2", "WBE", "ELL", "KM", "EXACT",  "OCT"), m = 50)

Arguments

If wanting OC curves where the confidence level or content level is on the y-axis, then a single positive value of k must be specified. This would be the target k-factor for the desired tolerance interval. If k = NULL, then OC curves will be constructed where the k-factor value is found for given levels of alpha, P, and n.

alpha

The set of levels chosen such that 1-alpha are confidence levels. If wanting OC curves where the content level is being calculated, then each curve will correspond to a level in the set of alpha. If a set of P values is specified, then OC curves will be constructed where the k-factor is found and each curve will correspond to each combination of alpha and P. If alpha = NULL, then OC curves will be constructed to find the confidence level for given levels of k, P, and n.

The set of content levels to be considered. If wanting OC curves where the confidence level is being calculated, then each curve will correspond to a level in the set of P. If a set of alpha values is specified, then OC curves will be constructed where the k-factor is found and each curve will correspond to each combination of alpha and P. If P = NULL, then OC curves will be constructed to find the content level for given levels of k, alpha, and n.

A sequence of sample sizes to consider. This must be a vector of at least length 2 since all OC curves are constructed as functions of n.

side

Whether a 1-sided or 2-sided tolerance interval is required (determined by side = 1 or side = 2, respectively).

method

The method for calculating the k-factors. The k-factor for the 1-sided tolerance intervals is performed exactly and thus is the same for the chosen method. "HE" is the Howe method and is often viewed as being extremely accurate, even for small sample sizes. "HE2" is a second method due to Howe, which performs similarly to the Weissberg-Beatty method, but is computationally simpler. "WBE" is the Weissberg-Beatty method (also called the Wald-Wolfowitz method), which performs similarly to the first Howe method for larger sample sizes. "ELL" is the Ellison correction to the Weissberg-Beatty method when f is appreciably larger than n^2. A warning message is displayed if f is not larger than n^2. "KM" is the Krishnamoorthy-Mathew approximation to the exact solution, which works well for larger sample sizes. "EXACT" computes the k-factor exactly by finding the integral solution to the problem via the integrate function. Note the computation time of this method is largely determined by m. "OCT" is the Owen approach to compute the k-factor when controlling the tails so that there is not more than (1-P)/2 of the data in each tail of the distribution.

The maximum number of subintervals to be used in the integrate function, which is used for the underlying exact method for calculating the normal tolerance intervals.

Value

norm.OC returns a figure with the OC curves constructed using the specifications in the arguments.

References

Young, D. S. (2016), Normal Tolerance Interval Procedures in the tolerance Package, submitted.

Examples

Run this code

## The three types of OC-curves that can be constructed
## with the norm.OC function.
 
norm.OC(k = 4, alpha = NULL, P = c(0.90, 0.95, 0.99), 
        n = 10:20, side = 1)

norm.OC(k = 4, alpha = c(0.01, 0.05, 0.10), P = NULL, 
        n = 10:20, side = 1)

norm.OC(k = NULL, P = c(0.90, 0.95, 0.99), 
        alpha=c(0.01,0.05,0.10), n = 10:20, side = 1)