Reliability data sets

Description

A set of data for simple reliablility analyses, taken from the book by Meeker and Escobar.

Usage

braking
capacitor
 cracks
genfan
ifluid
imotor
turbine
valveSeat

Details

• braking: Locomotive age at the time of replacement of braking grids, 1-4 replacements for each locomotive. The grids are part of two manufacturing batches.

• capacitor: Data from a factorial experiment on the life of glass capacitors as a function of voltage and operating temperature. There were 8 capacitors at each combination of temperature and voltage. Testing at each combination was terminated after the fourth failure.

  • temperature: temperature in degrees celcius

  • voltage: applied voltage

  • time: time to failure

  • status: 1=failed, 0=censored

• cracks: Data on the time until the development of cracks in a set of 167 identical turbine parts. The parts were inspected at 8 selected times.

  • day: time of inspection

  • fail: number of fans found to have cracks, at this inspection

• Data set genfan: Time to failure of 70 diesel engine fans.

  • hours: hours of service

  • status: 1=failure, 0=censored

  Data set ifluid: A data frame with two variables describing the time to electrical breakdown of an insulating fluid.

  • time: hours to breakdown

  • voltage: test voltage in kV

• Data set imotor: Breakdown of motor insulation as a function of temperature.

  • temp: temperature of the test

  • time: time to failure or censoring

  • status: 0=censored, 1=failed

• Data set turbine: Each of 432 turbine wheels was inspected once to determine whether a crack had developed in the wheel or not.

  • hours: time of inspection (100s of hours)

  • inspected: number that were inspected

  • failed: number that failed

• Data set valveSeat: Time to replacement of valve seats for 41 diesel engines. More than one seat may be replaced at a particular service, leading to duplicate times in the data set. The final inspection time for each engine will have status=0.

  • id: engine identifier

  • time: time of the inspection, in days

  • status: 1=replacement occured, 0= not

Note

The usage above assumes that the survival package is attached via library(survival) or via another package that depends on survival, e.g., mstate. If not, then either survival::turbine or data(reliability, package="survival") can be used.

References

Meeker and Escobar, Statistical Methods for Reliability Data, 1998.

Examples

survreg(Surv(time, status) ~ temperature + voltage, capacitor)

# Figure 16.7 of Meeker, cumulative replacement of locomotive braking
#  grids
gfit <- survfit(Surv(day1, day2, status) ~ batch, braking, id= locomotive)
plot(gfit, cumhaz=TRUE, col=1:2, xscale=30.5, conf.time= c(6,12,18)*30.5, 
     xlab="Locomotive Age in Months", 
     ylab="Mean cumulative number of replacements")

# Replacement of valve seats.  In this case the cumulative hazard is the 
#  natural target, an estimate of the number of replacements by a given time
#  (known as the cumulative mean function = CMF in relability).
# When two valve seats failed at the same inspection, we need to jitter one
#  of the times, to avoid a (time1, time2) interval of length 0
ties <- which(with(valveSeat, diff(id)==0 & diff(time)==0))  #first of a tie
temp <- valveSeat$time
temp[ties] <- temp[ties] - .1 # jittered time
vdata <- valveSeat
vdata$time1 <- ifelse(!duplicated(vdata$id), 0, c(0, temp[-length(temp)]))
vdata$time2 <- temp
fit2 <- survfit(Surv(time1, time2, status) ~1, vdata, id=id)
## Not run: 
plot(fit2, cumhaz= TRUE, xscale= 365.25, 
      xlab="Years in service", ylab = "Expected number of repairs")

## End(Not run)