exp2tol.int: 2-Parameter Exponential Tolerance Intervals

Description

Provides 1-sided or 2-sided tolerance intervals for data distributed according to a 2-parameter exponential distribution. Data with Type II censoring is permitted.

Usage

exp2tol.int(x, alpha = 0.05, P = 0.99, side = 1,
            method = c("GPU", "DUN"), type.2 = FALSE)

Arguments

A vector of data which is distributed according to the 2-parameter exponential distribution.

alpha

The level chosen such that 1-alpha is the confidence level.

The proportion of the population to be covered by this tolerance interval.

side

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

method

The method for how the upper tolerance bound is approximated. "GPU" is the Guenther-Patil-Upppuluri method. "DUN" is the Dunsmore method, which was empirically shown to be an improvement for samples greater than or equal t

type.2

Select TRUE if Type II censoring is present (i.e., the data set is censored at the maximum value present). The default is FALSE.

Value

exp2tol.int returns a data frame with items:
alphaThe specified significance level.
PThe proportion of the population covered by this tolerance interval.
1-sided.lowerThe 1-sided lower tolerance bound. This is given only if side = 1.
1-sided.upperThe 1-sided upper tolerance bound. This is given only if side = 1.
2-sided.lowerThe 2-sided lower tolerance bound. This is given only if side = 2.
2-sided.upperThe 2-sided upper tolerance bound. This is given only if side = 2.

References

Dunsmore, I. R. (1978), Some Approximations for Tolerance Factors for the Two Parameter Exponential Distribution, Technometrics, 20, 317--318. Engelhardt, M. and Bain, L. J. (1978), Tolerance Limits and Confidence Limits on Reliability for the Two-Parameter Exponential Distribution, Technometrics, 20, 37--39. Guenther, W. C., Patil, S. A., and Uppuluri, V. R. R. (1976), One-Sided $\beta$-Content Tolerance Factors for the Two Parameter Exponential Distribution, Technometrics, 18, 333--340.

Examples

Run this code

## 95\%/90\% 1-sided 2-parameter exponential tolerance intervals
## for a sample of size 50. 

set.seed(100)
x <- r2exp(50, 6, shift = 55)
out <- exp2tol.int(x = x, alpha = 0.05, P = 0.90, side = 1,
                   method = "DUN", type.2 = FALSE)
out

plottol(out, x, plot.type = "both", side = "upper", 
        x.lab = "2-Parameter Exponential Data")