In Auburngrads/SMRD: Statistical Methods For Reliability Data

SMRD:::vinny()
library(SMRD)

In this echapter...

DeviceA.ld <- frame.to.ld(devicea, 
                          data.title = "Device-A ALT Results",
                          response.column = 1,
                          time.units = "Hours",
                          censor.column = 2,
                          case.weight.column = 3,
                          x.columns = 4, 
                          xlab = "Degrees C")

print(DeviceA.ld)
summary(DeviceA.ld)

censored.data.plot(DeviceA.ld)

censored.data.plot(DeviceA.ld, 
                   y.axis ="log", 
                   x.axis = "Arrhenius")

groupi.mleprobplot(DeviceA.ld, 
                   distribution = "Weibull")

four.groupi.mleprobplot(DeviceA.ld)

DeviceA.weib.groupi <- 
  groupi.mleprobplot(DeviceA.ld,
                     distribution = "Weibull")

print(DeviceA.weib.groupi)
summary(DeviceA.weib.groupi)

DeviceA.lognor.groupi <- 
  groupi.mleprobplot(DeviceA.ld,
                     distribution = "Lognormal")

summary(DeviceA.lognor.groupi)

failure.probabilities(DeviceA.lognor.groupi)
quantiles(DeviceA.lognor.groupi)

four.groupm.mleprobplot(DeviceA.ld, 
                        relationship = "Arrhenius")

DeviceA.lognor.groupm <- 
  groupm.mleprobplot(DeviceA.ld, 
                     distribution = "Lognormal", 
                     relationship = "Arrhenius")

failure.probabilities(DeviceA.lognor.groupm, 
                      new.data = 10)

quantiles(DeviceA.lognor.groupm, 
          new.data = "10")

plot(DeviceA.lognor.groupm)

## or, more specifically to get quantiles at 60 degrees C,

quantiles(DeviceA.lognor.groupm, 
          new.data = 60)

## failure probabilities at 60 and 10 degrees C,

failure.probabilities(DeviceA.lognor.groupm, 
                      new.data = 60, 
                      time = c(1000,2000,5000,10000,20000,50000))

failure.probabilities(DeviceA.lognor.groupm, 
                      new.data = 10, 
                      time = c(1000,2000,5000,10000,20000,50000))

plot(DeviceA.lognor.groupm, 
     censor.time = 5000, 
     quant.lines = c(.01,.05,.1))

quantiles(DeviceA.lognor.groupm, 
          new.data = 60, 
          to = 0.2)

failure.probabilities(DeviceA.lognor.groupm, 
                      new.data = 60, 
                      time.vec = c(10000,100000))

failure.probabilities(DeviceA.lognor.groupm, 
                      new.data = 60, 
                      time.vec = c(500,600,700,800,900,1000))

## plot with a confidence interval for 10 degrees

DeviceA.groupm.mleprobplot <- 
  groupm.mleprobplot(DeviceA.ld,
                     distribution = "Lognormal",
                     relationship = "Arrhenius",
                     ci.list = 1)

print(DeviceA.groupm.mleprobplot,
      print.vcv = T,
      stress.state = 0)

## fix the activation energy to EA=.72

groupm.mleprobplot(DeviceA.ld, 
                   distribution = "Lognormal", 
                   relationship = "Arrhenius", 
                   ci.list = 1,
                   theta.start = c(-13, 0.72, 0.99), 
                   parameter.fixed = c(F, T, F))

mylarpoly example also using mylarsub

mylarpoly.ld <- frame.to.ld(mylarpoly,
                            response.column = 1,
                            x.column = 2, 
                            data.title = "Mylar-Polyurethane Insulating Structure", 
                            time.units = "Minutes", 
                            xlab = "kV/mm")

mylarsub.ld <- frame.to.ld(mylarsub,
                           response.column = 1,
                           x.column = 2,
                           data.title = "Mylar-Polyurethane Insulating Structure", 
                           time.units = "Minutes", 
                           xlab = "kV/mm")

print(mylarpoly.ld)
summary(mylarpoly.ld)

censored.data.plot(mylarpoly.ld, 
                   x.axis = "log", 
                   y.axis = "log")

mylarpoly.lognor.groupi <- 
  groupi.mleprobplot(mylarpoly.ld,
                     distribution = "Lognormal")

text(-1.06459, -1.74056,"361.4 kV/mm")
text(2.23807, -2.1,"219.0")
text(3.88939, -2.1,"157.1")
text(5.23223, -2.1,"122.4")
text(6.90171, -2.1,"100.3")

summary(mylarpoly.lognor.groupi,
        stress.state = 0)

mylarsub.lognor.groupm <- 
  groupm.mleprobplot(mylarsub.ld,
                     distribution = "Lognormal",
                     relationship = c("log"),
                     new.data = c(50))

text(2.50825, -2.27,"219.0")
text(3.83294, -2.27,"157.1")
text(4.84914, -2.27,"122.4")
text(5.95607, -2.27,"100.3")
text(9.56722, -2.26083,"50 kV/mm")

print(mylarsub.lognor.groupm,
      stress.state = 0)

summary(mylarsub.lognor.groupm,
        stress.state = 0)

plot(mylarsub.lognor.groupm)

plot(mylarsub.lognor.groupm, 
     data.ld = mylarpoly.ld, 
     add.density.at = 50,
     xlim = c(31,400))

quantiles(mylarsub.lognor.groupm, 
          new.data = 60, 
          to = 0.2)

failure.probabilities(mylarsub.lognor.groupm,
                      new.data = 60)

failure.probabilities(mylarsub.lognor.groupm, 
                      new.data = 60, 
                      time.vec = c(10,1000))


failure.probabilities(mylarsub.lognor.groupm, 
                      new.data = 50)

quantiles(mylarsub.lognor.groupm, 
          new.data = 50,
          to = 0.2)

mylarpoly.lognor.groupm <- 
  groupm.mleprobplot(mylarpoly.ld,
                     distribution = "Lognormal",
                     relationship = "class")

## example of bad model

mylarpoly.lognor.groupm <- 
  groupm.mleprobplot(mylarpoly.ld,
                     distribution = "Lognormal",
                     relationship = "log")

plot(mylarpoly.lognor.groupm)

mylarsub.lognor.groupm <- 
  groupm.mleprobplot(mylarsub.ld,
                     distribution = "Lognormal",
                     relationship = "log")

summary(mylarsub.lognor.groupm,
        stress.state = 0)

quantiles(mylarsub.lognor.groupm, 
          new.data = 50,
          to = 0.2)

mylarpoly.lognor.groupm <- 
  groupm.mleprobplot(mylarpoly.ld, 
                     distribution = "Lognormal",
                     relationship = "log")

summary(mylarpoly.lognor.groupm,
        stress.state = 0)

quantiles(mylarpoly.lognor.groupm, 
          new.data = 50,
          to = 0.2)

failure.probabilities(mylarpoly.lognor.groupm, 
                      new.data = 50)

plot(mylarpoly.lognor.groupm, 
     add.density.at = 50,
     xlim = c(31,400), 
     ylim=c(.1,10^8))

plot(mylarsub.lognor.groupm,
     data.ld = mylarpoly.ld, 
     add.density.at = 50, 
     xlim = c(31,400), 
     ylim = c(.1,10^8))


## make a model plot with detailed control of the x axis

plot(mylarsub.lognor.groupm,
     data.ld = mylarpoly.ld,
     density.at = c(100.3,122.4,157.1,219,50),
     title.option = 'blank',
     xlab = 'kV/mm', 
     hw.xaxis = list(ticlab = c(" 40", "100", "200","300", "400"),
                     ticloc = c(" 40", " 50", " 60", " 70", " 80", " 90", "100", "120", "140", "160","180", "200", "250","300","350", "400")))

ICDevice02 example

ICDevice2.ld <- frame.to.ld(icdevice2, 
                            response.column = c(1,2),
                            censor.column = 3,
                            case.weight.column = 4,
                            x.column = 5,  
                            data.title = "New Technology Device ALT", 
                            xlabel = "Degrees C", 
                            time.units = "Hours")

groupi.mleprobplot(ICDevice2.ld, 
                   distribution = "Lognormal")

ICDevice02.groupm.lognor <- 
  groupm.mleprobplot(ICDevice2.ld,
                     distribution = "Lognormal",
                     relationship = "Arrhenius",
                     ci.list = 6)

plot(ICDevice02.groupm.lognor,
     censor.time = 2304, 
     quant.lines = c(.01,0.1, .5))

quantiles(ICDevice02.groupm.lognor, 
          new.data = 100,
          to = 0.2)

failure.probabilities(ICDevice02.groupm.lognor, 
                      new.data = 100, 
                      time.vec = c(500,1000))

ICDevice2.groupm.lognor.ea <- 
  groupm.mleprobplot(ICDevice2.ld,
                     distribution = "Lognormal",
                     relationship = "Arrhenius",
                     ci.list = 6,
                     new.data = 100,
                     theta.start = c(-10.2, 0.8, 0.5),
                     parameter.fixed = c(F, T, F))

quantiles(ICDevice2.groupm.lognor.ea,
          new.data = 100,
          to = 0.2)

failure.probabilities(ICDevice2.groupm.lognor.ea, 
                      new.data = 100,
                      time.vec = c(500,1000))

plot(ICDevice2.groupm.lognor.ea, 
     censor.time = 2304,
     quant.lines = c(.01,0.1, .5))

Tantalum capacitor example

Tantalum.ld <- frame.to.ld(tantalum, 
                           response.column = 1,
                           censor.column = 2, 
                           case.weight.column = 3, 
                           x.column = c(4, 5), 
                           data.title = "Tantalum Capacitor Data", 
                           time.units = "Hours", 
                           xlabel = c("Volts","DegreesC"))

summary(Tantalum.ld)

design.plot(Tantalum.ld)
text(35.5864, 93.0106,"4/1000",cex = 1.2)
text(40.6815, 93.0106,"4/200",cex = 1.2)
text(46.5611, 93.0106,"2/50",cex = 1.2)
text(51.5986, 93.0106,"4/53 ",cex = 1.2)
text(46.3883, 53.8499,"6/502",cex = 1.2)
text(56.9744, 53.8499,"1/50",cex = 1.2)
text(46.4459, 10.737,"1/175",cex = 1.2)
text(62.4743,  10.737,"18/174",cex = 1.2)
title(main = "Tantalum Accelerated Life Test  Setup")

groupi.Tantalum <- 
  groupi.mleprobplot(Tantalum.ld,
                     distribution = "Weibull",
                     group = c(1, 2))

summary(groupi.Tantalum)

Tantalum.groupm.weib <- 
  groupm.mleprobplot(Tantalum.ld, 
                     group.var = c(1,2),
                     distribution = "Weibull",
                     relationship  = c("log","Arrhenius"))

summary(Tantalum.groupm.weib,
        stress.state = 0)

## doing a conditional model plot
plot(Tantalum.groupm.weib, 
     fixed.other.values = "30",
     focus.variable = "celsius")

plot(Tantalum.groupm.weib, 
     focus.variable = "volts", 
     fixed.other.values = 40)

failure.probabilities(Tantalum.groupm.weib, 
                      new.data = "35;85" )

quantiles(Tantalum.groupm.weib, 
          new.data = "35;85" )

Tantalum.groupm.weib <- 
  groupm.mleprobplot(Tantalum.ld,
                     group.var = c(1,2), 
                     distribution = "Weibull", 
                     relationship = c("log","Arrhenius"), 
                     formula = Location ~ + g(volts) +  g(celsius) + g(volts):g(celsius))

classh insulation example

Don't have this data set

classh.turn.ld <- frame.to.ld(classh,
                              response.column = "Turn.hours",
                              censor.column = "Turn.censor", 
                              x.columns = "Temp", 
                              data.title = "Class H Turn Failures")

summary(classh.turn.ld)

## analyze the classh.turn failure-times

censored.data.plot(classh.turn.ld, 
                   y.axis = "log", 
                   x.axis = "Arrhenius")

classh.turn.groupi <- 
  groupi.mleprobplot(classh.turn.ld,
                     distribution = "Lognormal")

summary(classh.turn.groupi)

classh.turn.groupm <- 
  groupm.mleprobplot(classh.turn.ld,
                     distribution = "Lognormal",
                     relationship = "Arrhenius")

summary(classh.turn.groupm)

plot(classh.turn.groupm)
plot(classh.turn.groupm, 
     density.at = c(180,190,200,220,240,260), 
     censor.time = 12000, 
     quant.lines = c(.01,.1,.5))

quantiles(classh.turn.groupm,
          new.data = 180)

failure.probabilities(classh.turn.groupm, 
                      new.data = 180)

## get and analyze the ground failures

classh.ground.ld <- frame.to.ld(classh, 
                                response.column = "Ground.hours",
                                censor.column = "Ground.censor",
                                x.columns = "Temp",
                                data.title = "Class H Ground Failures")

summary(classh.ground.ld)

## analyze the classh.ground failure-times

censored.data.plot(classh.ground.ld, 
                   y.axis = "log",
                   relationships = "Arrhenius")

classh.ground.groupi <- 
  groupi.mleprobplot(classh.ground.ld,
                     distribution = "Lognormal")

summary(classh.ground.groupi)

classh.ground.groupm <- 
  groupm.mleprobplot(classh.ground.ld,
                     distribution = "Lognormal",
                     relationship = "Arrhenius")

summary(classh.ground.groupm)

plot(classh.ground.groupm)

## get and analyze the phase failures

classh.phase.ld <- frame.to.ld(classh,
                               response.column = "Phase.hours",
                               censor.column = "Phase.censor", 
                               x.columns = "Temp",
                               data.title = "Class H Phase Failures")

print(classh.phase.ld)

summary(classh.phase.ld)

censored.data.plot(classh.phase.ld,
                   y.axis = "log",
                   relationships = "Arrhenius")

classh.phase.groupi <- 
  groupi.mleprobplot(classh.phase.ld,
                     distribution = "Lognormal")

summary(classh.phase.groupi)

classh.phase.groupm <- 
  groupm.mleprobplot(classh.phase.ld,
                     distribution = "Lognormal",
                     relationship = "Arrhenius")

summary(classh.phase.groupm)

plot(classh.phase.groupm)

quantiles(classh.phase.groupm, 
          new.data = 180)

failure.probabilities(classh.phase.groupm, 
                      new.data = 180)

AlloyZ.groupm <- 
  groupm.mleprobplot(AlloyZ.ld,
                     distribution = "Weibull",
                     relationship = "Log")

plot(AlloyZ.groupm, 
     density.at = c(20,50,100,200))