LRbounds: Likelihood Ratio bounds

In WeibullR: Weibull Analysis for Reliability Engineering

Likelihood Ratio bounds

Description

Generates bounds across a double-sided confidence interval based on a likelihood ratio contour.

Usage

LRbounds(x,  dist="weibull", CL=0.9, unrel=NULL,  contour=NULL, dof=1,
                control=NULL, debias="none", show=c(FALSE,FALSE))

Arguments

x	A dataframe such as generated by mleframe with column names 'left', 'right' and optionally 'qty'. Exact failure data (occurrences) have same time entered in both 'left' and 'right' columns. Suspension data has last known life[time] entered in 'left' column and -1 entered in 'right' column. The left(early) interval bound for left-censored data must be entered as zero. (NA is not accepted).
dist	A string defining a distribution to be fit. Implemented distributions are "weibull" (default) and "lognormal". (Only 2-parameter models are accepted.)
CL	A scalar for the double-sided confidence interval of interest. Default = 0.9, for 90
unrel	An optional vector of unreliability values to be used as the descriptive quantiles at which the bounds will be calculated.
contour	An optional dataframe object previously generated by MLEcontour on x, consistent with CL and dist.
dof	An integer value indicating degrees of freedom to apply to the Chi square test, which defaults to dof=1 for confidence interval bound use. Should be set to 2 for comparison of two models each with 2 parameters.
control	A list having specifically named options for control of the bounds preparation. List item 'ptDensity' an integer value for the number of points to be plotted around the circumference of the (each) 2p contour. List item 'tzpoints' controls the number of t0 trials in a 3p iteration (see Details). List item RadLimit a convergence limit for the contour radials based on specific units such as Eta/Eta_hat and Beta/Beta_hat.
debias	A place holder for an optional string argument indicating the adjustment to be applied to the shape or standard deviation parameter of the fitted data.
show	A vector of logicals determining whether and how a graphic of the bounds shall be displayed. For 2-parameter bounds only the first element is considered and a crude graphic is provided for the bounds. For 3-parameter bounds the first element determines whether a wblr graphic is displayed for the bounds, while the second element determines whether the series of contours generated to develop the bounds is displayed.

Details

The approach used for 3p bounds has been to vary the threshold value through a selection of increments from the optimized MLE toward zero. Then 2-parameter contours based on a likelihood ratio determined from the optimized MLE are plotted as if looking down on a 3 dimensional plot with threshold values in the z-direction. The bounds are then derived from the farthest extent of all the contours. tzpoints is a control argument that can be used to alter the number of threshold values (tz's) to be sampled. The tzpoints control argument is a vector having 3 elements. The first element controls the number of positive tz values to be sampled. The second and third elements of the tzpoints vector control the sequence of negative tz values according to the relationship tzpoints_neg<-seq(tzpoints[3],tzpoints[2], by=tzpoints[3]).

A bias adjustment, if specified, is applied to the shape parameter of generated contours. In this way such adjustment is passed into the bounds preparation.Abernethy's "Justified Likelihood Function" has not been demonstrated to be academically accepted. For this reason no attempt has been made to implement similar modification related to bias adjustment. Contribution of evidence or a method contrary to this position will gladly be reviewed by the package maintainer.

Value

Returns a dataframe holding values of percentiles, lower, datum, and upper values of the bound.

References

William Q. Meeker and Luis A. Escobar, (1998) "Statistical Methods for Reliability Data", Wiley-Interscience, New York

Robert B. Abernethy, (2008) "The New Weibull Handbook, Fifth Edition"

John I. McCool, (2012) "Using the Weibull Distribution: Reliability, Modeling and Inference"

Examples

set.seed(4321)
data<-rlnorm(30,2,1.2)
bounds<-LRbounds(mleframe(data[7:30],data[1:6]), dist="lognormal")

WeibullR documentation built on June 26, 2022, 3 a.m.