hrbu {WeibullR}

Hirose and Ross beta unbias factors for Weibull MLE

Description

hrbu generates the reduction factor based on the mean bias of the weibull MLE beta parameter(roughly C4^6) for complete failure samples, modestly increased correction as number of suspensions increases.

Usage

 hrbu(Qx, Qs=NULL)

Arguments

Qx

The quantity of actual failures

Qs

An optional quantity of suspensions

Details

This, as many references, discuss the bias reduction in terms of mean.

Value

A factor to be multiplied to the MLE Beta account for known bias.

References

Hirose, H. (1999) "Bias Correction for the Maximum Likelihood Estimation in Two-parameter Weibull Distribution" IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 6, No.1 Ross, R. (1996) "Bias and Standard Deviation Due to Weibull Parameter Estimation for Small Data Sets" IEEE Transactions on Dielectrics and Electrical Insulation, Vol. 3, No.1

Examples

failures<-c(90,96,30,49,82)
suspensions<-c(100,45,10)
MLEfit<-mlefit(mleframe(failures,suspensions))
MLE_Unbiased<-c(MLEfit[1],MLEfit[2]*hrbu(length(failures),length(suspensions)))