Description Usage Arguments Details Value Note References See Also Examples
Provides 1sided tolerance limits for the difference between two independent normal random variables. If the ratio of the variances is known, then an exact calculation is performed. Otherwise, approximation methods are implemented.
1 2  diffnormtol.int(x1, x2, var.ratio = NULL, alpha = 0.05,
P = 0.99, method = c("HALL", "GK", "RG"))

x1 
A vector of sample data which is distributed according to a normal distribution (sample 1). 
x2 
Another vector of sample data which is distributed according to a normal distribution (sample 2). It can be of a different sample size than
the sample specified by 
var.ratio 
A specified, known value of the variance ratio (i.e., the ratio of the variance for population 1 to the variance of population 2).
If 
alpha 
The level chosen such that 
P 
The proportion of the population to be covered by the tolerance limits. 
method 
The method for estimating the variance ratio. This only needs to be specified in the case when

Satterthwaite's approximation for the degrees of freedom is used when the variance ratio is unknown.
diffnormtol.int
returns a data frame with items:
alpha 
The specified significance level. 
P 
The proportion of the population covered by this tolerance interval. 
diff.bar 
The difference between the sample means. 
1sided.lower 
The 1sided lower tolerance bound. 
1sided.upper 
The 1sided upper tolerance bound. 
Unlike other tolerance interval functions, the output from diffnormtol.int
cannot be passed to plottol
.
Guo, H. and Krishnamoorthy, K. (2004), New Approximate Inferential Methods for the Reliability Parameter in a StressStrength Model: The Normal Case, Communications in Statistics  Theory and Methods, 33, 1715–1731.
Hall, I. J. (1984), Approximate OneSided Tolerance Limits for the Difference or Sum of Two Independent Normal Variates, Journal of Quality Technology, 16, 15–19.
Krishnamoorthy, K. and Mathew, T. (2009), Statistical Tolerance Regions: Theory, Applications, and Computation, Wiley.
Reiser, B. J. and Guttman, I. (1986), Statistical Inference for Pr(Y < X): The Normal Case, Technometrics, 28, 253–257.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 
## 90%/99% tolerance limits for the difference between two
## simulated normal data sets. This data is taken from
## Krishnamoorthy and Mathew (2009). Note that there is a
## calculational error in their example, which yields different
## results with the output below.
x1 < c(10.166, 5.889, 8.258, 7.303, 8.757)
x2 < c(0.204, 2.578, 1.182, 1.892, 0.786, 0.517, 1.156,
0.980, 0.323, 0.437, 0.397, 0.050, 0.812, 0.720)
diffnormtol.int(x1, x2, alpha = 0.10, P = 0.99, method = "HALL")
diffnormtol.int(x1, x2, alpha = 0.10, P = 0.99, method = "GK")
diffnormtol.int(x1, x2, alpha = 0.10, P = 0.99, method = "RG")
diffnormtol.int(x1, x2, var.ratio = 3.8, alpha = 0.10, P = 0.99)

Add the following code to your website.
For more information on customizing the embed code, read Embedding Snippets.