In Auburngrads/SMRD: Statistical Methods For Reliability Data

SMRD:::vinny()
library(SMRD)

In This echapter...

An overview of the SMRD package features

An overview of working with life.data objects

Creating life.data objects with frame.to.ld()
Viewing and subsetting elements
Plotting life.data objects

`SMRD` Package Features

SMRD is designed to easily return estimation/prediction results for many types of failure data

Multiple failure events
Censored data (right, left, and interval censoring)
Truncated data (right, left, and interval truncation)
Failure data with explanatory variables (failure-time regression)
Repeated measures degradation data (linear & non-linear mixed effects)
Repairable system failure data (recurring events)
Physical/performance degradation data
Failure data with prior information (Bayesian reliability)
Reliability growth test data
Reliability test simulations

SMRD facilitates minimal data pre-processing through flexible event definitions

Organizations often use different terms to describe the same event
- 'Failure' = 'Failed' = 'Fail' = 'dead' = 'died'
- 'right' = 'rcensored' = 'suspended' = 'alive'
- 'left' = 'doa' = 'lcensored'
- 'interval' = 'int' = 'icensored' = 'grouped'
Many applications use ambiguous numerical codes to represent these events
- Often, the numerical event codes used by one software package don't coincide with those used by other packages
- SMRD allows for flexible event definitions to utilize the data as-is
- Event definitions can even be mixed
- SMRD event definitions easily mapped to survival numeric definitions

The table below shows the default SMRD default event definitions

fail <- strsplit(SMRDOptionsDefaults()$SMRD.F,  split = ',')[[1]]
left <- strsplit(SMRDOptionsDefaults()$SMRD.Lc, split = ',')[[1]]
righ <- strsplit(SMRDOptionsDefaults()$SMRD.Rc, split = ',')[[1]]
intv <- strsplit(SMRDOptionsDefaults()$SMRD.Ic, split = ',')[[1]]
lengths <- lapply(X = list(fail,left,righ,intv), 
                  FUN = function(x) length(x))

Length <- max(unlist(lengths))

fails <- c(fail, rep('', Length-length(fail)))
lefts <- c(left, rep('', Length-length(left)))
righs <- c(righ, rep('', Length-length(righ)))
intvs <- c(intv, rep('', Length-length(intv)))
dats <- data.frame(fails,lefts,righs,intvs)
colnames(dats) <- c('Failed', 
                    'Left-censored',
                    'Right-censored',
                    'Interval-censored') 
DT::datatable(dats, options = list(pageLength = 20))

SMRD includes over 100 datasets

Many of these data sets still need to be documented
A list of these data sets is returned using data(package = "SMRD")
Likewise, the names and descriptions of the data sets is shown in the table below

DT::datatable(as.data.frame(data(package = 'SMRD')$results[,c(-2)]))

Analyzing the Leiblien-Zelen Data Set `lzbearing`

Overview of the data set

Complete data set 23 observations
Most basic of the data sets included in the package

DT::datatable(lzbearing, options = list(pageLength = 8))

Many functions in the SMRD package require a life.data object. life.data objects are created using the function frame.to.ld.

lzbearing.ld <- frame.to.ld(lzbearing, 
                            response.column = 1,
                            time.units = "Megacycles")

Once the life.data has been created, several plots and values can be produced

event.plot(lzbearing.ld)

summary(lzbearing.ld)

print(lzbearing.ld)

plot(lzbearing.ld, distribution = "lognormal")

Many other plots and numerical results can also be easily returned as shown in the next example

Plots
- Nonparametric CDF plots
- Parametric CDF plots
- ML CDF and hazard plots
- Explanatory variable plots
- Multi-failure mode plots
- Relative likelihood surfaces
- Relative likelihood curves
Numerical results
- $F(t)$ at specified values of $t$
- $h(t)$ at specified values of $t$
- $t^{-1}(p)$ at specified values of $p$
- ML parameter estimates and standard errors
- Logit and log transformed confidence intervals (pointwise and simultaneous)

Example: Analyzing the `shockabsorber` dataset

Dataset: `shockabsorber`

This example demonstrates some of the SMRD functions to analyze the shockabsorber dataset used throughout the text

shockabsorber

Creating the life.data object

shock.ld <- frame.to.ld(frame = shockabsorber,
                        response.column = 1,
                        failure.mode.column = 2,
                        censor.column = 3,
                        time.units = 'Kilometers')

Nonparametric & Parametric CDF plots

par(mfrow = c(1,2), bg = NA)
plot(shock.ld)
plot(shock.ld, distribution = 'lognormal')

Maximum likelihood plots $F(t)$ \& $h(t)$

par(mfrow = c(1,2), bg = NA)
mlehazplot(shock.ld,  distribution = 'lognormal', param.loc = 'topleft')
mleprobplot(shock.ld, distribution = 'weibull', param.loc = 'topleft')

Relative likelihood surface plots

simple.contour(shock.ld, 
               distribution = 'sev', 
               threeD = T, 
               original.par = F,
               static = T)

simple.contour(shock.ld, 
               distribution = 'sev',
               show.confidence = F, 
               zoom = 1.75,
               static = T)

Maximum likelihood estimate results

(print(mlest(shock.ld, distribution = 'weibull')))

Example: Nelson's Super-Alloy Data Set `superalloy`

superalloy.ld <- frame.to.ld(superalloy,
                             response.column = 1, 
                             censor.column = 2,
                             x.columns = c(5,6,4),
                             time.units = "Kilocycles")

summary(superalloy.ld)

censored.data.plot(superalloy.ld, 
                   explan.var = 1)

censored.data.plot(superalloy.ld, 
                   explan.var = 3,
                   response.on.yaxis = F)

censored.data.plot(superalloy.ld, 
                   explan.var = 3, 
                   x.axis = "log", 
                   y.axis = "log")

censored.data.plot(superalloy.ld, 
                   explan.var = 3,
                   response.on.yaxis = F, 
                   x.axis = "log", 
                   y.axis = "log")