Package ‘weibulltoolkit’January 15, 2012 Type Package Title Basic Weibull analysis of reliability and life data, producing Weibull plots. Version 0.2.2 Date January 15, 2011 Author Jurgen Symynck <[email protected]>, Filip De Bal <[email protected]> Maintainer Jurgen Symynck <[email protected]> Depends survival, splines Description The 'Weibull Toolkit' for R provides basic functionality for Weibull-based fatigue and reliability analysis. It generates useful plots of the life data, and calculates betabinomial and Monte Carlo pivotal confidence bounds for B-lives (Currently, the latter bounds are only correct for complete data). This software project was initiated as part of the FATIMAT project, and is a perpetual work in progress. It was initially developed to study R itself and the Weibull analysis in general: the toolkit should not (yet) be treated als a viable alternative to better equipped and more reliable commercial software. License GPL-3 URL http://mechanics.kahosl.be/fatimat, http: //sourceforge.net/projects/weibulltoolkit BugReports email the authors at <[email protected]> or <[email protected]> LazyLoad yes R topics documented: options.wb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . plot.wb . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . wbparams.to.ft . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Index 2 4 6 8 1 signif An integer describing the significant digits of various numbers to be displayed. col. for which (at the time of writing) it takes a few seconds to complete the simulation. Usage options. ylim A vector determining the plotting range of the vertical axis of the Weibull plot. Boolean switch (TRUE or FALSE) controlling whether the plot is created in a new window. lwd.title A string with the title of the legend box. Reccomended values are 2000 <= R <= 5000. Possible legend locations are "bottomright". coordinate.wb() calculates horizontal limits automatically from the data argument. col The color of a Weibull plot. Higher R values result in better Monte Carlo confidence bounds but longer calculation times. see points in the package graphics lwd An integer describing the line width of both the Weibull fitted line and the confidence bounds. legend. ylab Strings containing labels for the X and Y axis. The subtitle of the Weibull plot. "top". main sub add . The default value is 1000. High values are needed for good confidence bounds at the lower scale of the Weibull model. R An integer describing the number of Monte Carlo simulations on which the Monte Carlo pivotal confidence bounds are based.size A number determining the relative legend text size.grid The color of the grid. xlim A vector determining the plotting range of the horizontal axis of the Weibull plot. legend. See colors from package grDevices for available colors. plot. "left". "bottom". "topright".2 options. "bottomleft".size A number determining the relative coordinate text label size. See colors from package grDevices for available colors..wb Weibull Plotting Options Description The options. Can either be an integer or a string.text.) Arguments The main title of the Weibull plot. legend. Allowed values come from the interval ]0. For more info. used for plotting the datapoints.points An integer describing the size of the datapoints. Can either be an integer or a string..wb(.1[ xlab. "right" and "center". pch An integer describing the plotting symbol.wb() function handles the numerous options for creating Weibull plots.wb options. "topleft".position A string keyword describing the location of the legend in the plot window.text. is.fittedline Boolean switch controlling the plotting of the fitted line.plot.datapoints Boolean switch controlling the plotting of the datapoints.wb(defaults).bbb Boolean switch controlling the plotting of beta binomial confidence bounds.options. method. before changing any options. it creates a list named options. Also.plot.wb() returns a list containing the current options of the Weibull toolkit. and borrows some code from it.wb() function tries to mimic the behavior of the par function from the graphics package. . To Do • Prevent the options. is.[1 determining the width of the calculated confidence intervals.plot. One might.wb(col="pink") options.grid Boolean switch controlling the plotting of the grid. is. there is no way to reset the options to the default values using this function.plot. Can either be "MRR" (Median Rank Regression) or "Surv" (Maximum Likelihood Estimation.datacoordinates Boolean switch controlling the plotting of the text labels (the coordinates on the plot) next to the datapoints. is.wb(list(col="pink".plot. In the latter case.points An integer controlling the amount of data-coordinates through which the Monte Carlo pivotal confidence bounds are drawn. store the option list in a temporary variable like default <. CL Details The options. is.cb Boolean switch controlling the plotting of Monte Carlo confidence bounds. do not access the list directly. options. cb. Value options.XonY. It can be used in different ways: options. Currently.wb() for restoring it later by running options. is.options.wb 3 A number from the interval [0. is.weibulltoolkit list from being accessible outside of the options. Y-on-X is buggy and should be avoided. holding the options.reg The method for calculating beta and eta. there is no ranking applied to the data so no plotting positions are calculated or displayed.plot.regression Boolean switch controlling whether the MRR regression is either X-on-Y (default) or Y-on-X.plot.legend Boolean switch controlling the plotting of the legend.weibulltoolkit.wb() Returns the currently used options and there values.R=300)) Sets the specified options. Currently. is. One should always use the options.wb() function to access the option list. options. MLE).wb() function.wb()$ylim options. • Add the possibibilty to reset to the default values.wb("ylim") Returns the current value of an option. wb() demonstration\n") options.wb() options.wb(wbparams.wb(wbparams. for marking special points.wb() behaves as follows: • Displays the two-parameter Weibull cumulative distribution function as a straight line on Weibull probability paper.wb() function.3. • Monte Carlo pivotal confidence bounds are calculated and displayed.legend=FALSE) plot.to.1000)..3.col="red") plot.wb(wbparams.ft(15.2.) Arguments d d is a survival object of class "Surv" from the survival package.4 plot.col="green") options.to. .ft(8. where some observations are not failures.wb(d = NULL.ft([email protected]="blue") plot. • The Weibull parameters can also be calculated by using Maximum Likelihood Estimation.to..is.wb(add=TRUE) plot.. • (right-) Censored data (suspensions) are supported. additional options as specified in the description of the options.2000).wb(defaults) plot. plot. ...be> See Also plot.wb(wbparams. available via the survreg() function of the survival package.1000).wb(R=300.wb Author(s) Jurgen Symynck <jurgen. Beta-binomial confidence bounds can be displayed. where the times-to-failure are the dependent variable..wb Weibull Plotting Description The plot.main="options. Currently. Currently..wb() function creates a Weibull plot from lifetime and reliability data. reccomended for small to medium sample sizes (2-100).to.wb Examples defaults <. Usage plot. • Observations are by default ranked using the ’Median Rank Regression’ (MRR) method.3000). only complete and right censored data are supported by the toolkit.ft(5.plot. . • The mark() function draws a point on the plot with dotted lines extending towards the axes.2.options. • The Weibull line is fitted using X-on-Y regression by default. To Do • The critical correlation coefficient (ccc^2) is only displayed for failures up to ten.53. and to calculate the Monte Carlo pivotal confidence bounds as used in the SuperSMITH(TM) Weibull software for reliability testing.1)) This toolkit is being developed as a means for studying both R itself and the Weibull analysis in general. they are too optimistic. Hoboken N. Some issues of the software that need to be addressed are: • The Monte Carlo pivotal confidence bounds are currently only correct forcomplete. the Monte Carlo pivotal confidence bounds are only correct for complete. • Find out if the MLE parameter estimation survreg() can be altered to MLE-RBA (Reduced Bias) • Find out if survreg() can be used for median rank regression of failure data. 2003) . ccc^2 for more failures are to be generated using time-consuming Monte Carlo simulation. for both complete and censored data. but there appears to be a slight difference between the values generated by them and those from commercial software packages. eta and the pivotal confidence bounds on a selection of B-lives. With censored data. The New Weibull Handbook. messing up the perpendicular axis.0005. Lawless. Type vignette("MCpivotalbounds_status".wb 5 Details An example of a survival object with three dead and two live observations: d <. The code for this can be found in the source.0. For censored data. The current goal of the toolkit is to generate Weibull plots. censored data.. Statistical Models and Methods for Lifetime Data. displaying the key information about B-lives and goodness of fit. When these are displayed.be> References Robert B.J.package="weibulltoolkit") at the R prompt to check the current status of the Monte Carlo pivotal confidence bounds. 2004) Jerald F.event=c(1. Fifth Edition (Robert B.1. Author(s) Jurgen Symynck <jurgen. beta.78). Currently.Surv(time=c(27.wb() • Fix bug while displaying axis labels containing characters. the axis ticks and labels are drawn outside the plotting window. the bounds are still too optimistic for heavily censored datasets with few failures.100. Abernethy. Warning This package and its functions are a perpetual work in progress.0. Abernethy. uncensored data.100.symynck@kahosl. • Fix bug that displays numeric(0) in the legend when supplying the Blives = F0(0) option to plot.wb() returns a list containing the median ranked dataset (if appropriate). like 5e-4 instead of 0. 2nd edition (Wiley-Interscience. Value plot.plot. r2$eta). 1998) Chi-Chao Lui.be/fatimat/index. fail=NULL. Stefan cel Mare University of Suceava.ro/conf_1/ tehnomusjournal/pagini/journal2011/files/7.plot. An Introduction to the Bootstrap (Chapman & Hall. 2011). R. uncensored failures: d2 <.wb(d2.Surv(rweibull(6.01).php/downloads-and-information/ 40/171 Jurgen Symynck.title="Uniformly distributed". available on http://www.0. r2$beta.Weibullnews. Monte Carlo pivotal confidence bounds for Weibull analysis.usv. main="Weibull & Uniformly Distributed Failures\n".1000)) r1 <.1.be/fatimat http://sourceforge.be/fatimat/index.c(0.1.title="Weibull distributed".to. Filip De Bal. 1997) Efron.kahosl. Filip De Bal.01)) mark(get.position="topright".500)) r2 <.ft(n. Meeker and Luis A. r1$beta.legend.3. perfectly matching a two-parameter Weibull distribution with the supplied shape and scale parameters. eta. with implementations in R (New Technologies and Products in Machine Manufacturing Technology.6 wbparams.0.ft William Q. and Tibshirani. New York. Weibull analysis using R.to. Stefan cel Mare University of Suceava.kahosl. kahosl. Surv.add=TRUE) ## mark a point mark(get.php/downloads-and-information/40/198 SuperSMITH(TM) Weibull homepage (http://www.com/contents.htm) http://mechanics. A Comparison Between The Weibull And Lognormal Models Used To Analyse Reliability Data (dissertation from University of Nottingham.plot..legend. Statistical Methods for Reliability Data (Wiley-Interscience. available on http://mechanics.fim.legend.blife(c(0.ft Create (un-)Censored Testdata From Weibull Parameters Description Create a set of observations.net/projects/Weibulltoolkit See Also options.blife(c(0.to. survreg Examples ## plot Weibull distributed.10. Usage wbparams. Escobar.1.01).01)) wbparams.0. uncensored failures: d1 <. col="blue") ## plot uniformy distributed . method.c(0. B. beta.1.r1$eta).pdf and http://mechanics.Surv(runif(10.rank = "qbeta") .wb(d1.wb. col="red". 1993) Jurgen Symynck.0. in a nutshell (New Technologies and Products in Machine Manufacturing Technology. 2010). resp. fail if specified.wbparams() for more details. Currently.wbparams. The dataset will have beta and eta as its Weibull parameters.legend.3. the number of actual failures in the dataset (0 < fail <= n). Value An object of class "Surv" with n observations of which there are fail failures.R=300)) # invisible() prevents plot.wb(d1.to. beta. In that case the dataset is treated as Type 2 censored. See get.R=300. col="red".to..ft 7 Arguments n An integer determining the desired number of observations.wbparams.wbparams.1000) invisible(plot.add=TRUE. ### ### d1 <.pch=4.to.ft(8. only "MRR" is supported.3.wb(d2.be> Examples ### plot two synthetic datasets with ### shape = 3 and scale 1000.wb to return data. eta slope and shape parameters of the Weibull distribution for this dataset.position="topleft")) .3. Author(s) Jurgen Symynck <jurgen.1000) invisible(plot. d2 <.ft(10.symynck@kahosl. Either "MRR" or "Surv". method="MRR" method used for the rank regression. 3 plot. 2. 2 Surv.wb.to.wb. 4 points.Index colors. 6 8 . 4. 6 wbparams. 6 par. 2 options.ft. 6 survreg.