abrem.fit: Fit Distributions to 'Abrem' Objects

In abrem: Abernethy Reliability Methods

Description

This function fits probability distributions to Abrem objects.

Usage

abrem.fit(x,...)

Arguments

x	Object of class "abrem".
...	Options for fitting the (life-)time observations, and for plotting the results.

Details

This function calculates fits for the (life-)time observations in the abrem object and adds them to the object alongside any pre-existing fits.

Fitting options are passed with the dist and method.fit arguments:

dist

A character string with the target distribution for fitting. Possible values are "weibull" or "weibull2p", "weibull3p" (three parameter Weibull), "lognormal" or "lognormal2p".

Defaults to "weibull".

in.legend

Logical value controlling the inclusion of various elements in the legend.

If in.legend=FALSE is passed, the resulting fit calculations will be omitted from the legend, leaving only observation summary data.

Defaults to TRUE.

method.fit

A vector of class "character" with fitting options.

Defaults to c("rr","xony").

• "rr": Rank Regression (RR). Depending on the method for calculating probability plot positions chosen during the creation of the Abrem object (see option pp and function Abrem), this can either be "exact median rank regression" or "Benard's approximate median rank regression". If this method is used then it is mandatory to additionally specify either X-on-Y or Y-on-X regression.

• "xony","yonx": Differentiate between X-on-Y and Y-on-X regression, respectively. For rank regression in lifetime analysis, it is best practice to use the X values ((life-)time observations) as the response variables whose horizontal distance to the fit line must be minimized, and the Y values (unreliabilities) as the explanatory variable.

• "mle": Maximum Likelihood Estimation (MLE), using many functions of the debias package.

• "mle-rba": Maximum Likelihood Estimation with Reduced Bias based on the median bias of the distributions MLE. This options uses functions RBAbeta and RBAsigmaof the debias package.

Additionally, one can pass any options available from options.abrem, such as col or is.plot.legend. The graphical options will be used when plotting the (life-)time observations using plot.abrem. Subsequent calls to abrem.conf will inherit these options.

The "prr" goodness-of-fit indicator is also calculated here. See the "Examples" section on how to retrieve it, see the "References" section for additional information on the prr and pve value.

Passing the threshold parameter here will result in plotting the fit (and its associated plot positions) with a threshold value subtracted.

If three parameter models like weibull3p are used and threshold = TRUE, the calculated third parameter (t0) of the last three-parameter fit in the abrem object will be used for plotting the graphical entities. If a numeric value is passed, then only the value from the last call to abrem.fit is used.

Currently, there is no graceful error recovery after attempting to fit lifetime data including negative time observations, for example abrem.fit(Abrem(-5:10)).

Value

The function returns its argument x, extended with the calculated fit and the optional graphical and calculation arguments as provided to the function.

To Do

• Research the effect of NA values in the (life-)time observations of the abrem argument when not using rank regression.

Author(s)

Jurgen Symynck [e-mail]

References

• Improved Goodness of Fit: P-value of the Correlation Coefficient, Wes Fulton

  http://www.barringer1.com/jun05prb.htm

See Also

options.abrem, Abrem

Examples

da1 <- Abrem(runif(5,100,2000))
da1 <- abrem.fit(da1,dist="weibull",method.fit=c("rr","xony"),pch=3)


prr <- da1$fit[[1]]$gof$prr
message("prr goodness-of-fit of first fit:")
message(paste0(prr,ifelse(prr >= 10," -> Good fit."," -> BAD fit!")))

da1 <- abrem.fit(da1,dist="weibull",method.fit="mle",col="red1")
da1 <- abrem.fit(da1,dist="weibull",method.fit="mle-rba",col="orange3",lty=2)
da1 <- abrem.fit(da1,dist="lognormal",method.fit=c("rr","xony"),col="steelblue3",pch=8)
#da1 <- abrem.conf(da1)
me <- "Comparison between RR, MLE, MLE-RBA and lognormal2p"
plot(da1,main=me);message(me)
message(paste0(
    "  RR : beta=",signif(da1$fit[[1]]$beta),
    ", eta=",signif(da1$fit[[1]]$eta)))
message(paste0(
    "  MLE: beta=",signif(da1$fit[[2]]$beta),
    ", eta=",signif(da1$fit[[2]]$eta)))
message(paste0(
    "  MLE: beta=",signif(da1$fit[[3]]$beta),
    ", eta=",signif(da1$fit[[3]]$eta)))
    
### threshold parameter usage demo ###
data(abrem_mix1)
earlyda <-abrem_mix1[1:10]
midda   <-abrem_mix1[11:131]
endda   <-abrem_mix1[132:200]
da       <-Abrem(abrem_mix1,col="gray",pch=1,
            label="Complete, unaltered dataset")
da21     <-Abrem(fail=endda,susp=c(earlyda,midda),col="black",pch=19)
da22     <-Abrem(fail=endda,susp=c(earlyda,midda),col="blue",pch=3)
da23     <-Abrem(fail=endda,susp=c(earlyda,midda),col="green3",pch=4)
da21 <- abrem.fit(da21,
    label="threshold=FALSE",dist="weibull3p",threshold=FALSE)
da22 <- abrem.fit(da22,
    label="threshold=TRUE",dist="weibull3p",threshold=TRUE)
da23 <- abrem.fit(da23,
    label="threshold=5000",dist="weibull3p",threshold=1800)
plot.abrem(list(da,da21,da22,da23),xlim=c(10,1e5),
    main="Threshold parameter usage")

abrem documentation built on May 2, 2019, 4:49 p.m.