In Auburngrads/SMRD: Statistical Methods For Reliability Data

SMRD:::vinny()
library(SMRD)

In this echapter...

Computer execution time vs. system load test

comptime.ld <- frame.to.ld(comptime,
                           response.column = 3, 
                           x.column = 2,
                           time.units = "Seconds", 
                           xlabel = "System.Load")

summary(comptime.ld)

censored.data.plot(comptime.ld,
                   xlab = "System Load")

Note that for each level of load only a single failure is observed. Therefore, the following functions return warnings stating that there are not enough failures to include in the plot.

comptime.mlest.out <- groupm.mleprobplot(comptime.ld, 
                                         distribution ="Lognormal", 
                                         group.var = 1, 
                                         relationship = "linear")

comptime.mlest.out2 <- groupm.mleprobplot(comptime.ld, 
                                          distribution ="Normal", 
                                          group.var = 1, 
                                          relationship = "linear")

SMRD:::resid.vs.order(comptime.mlest.out)

SMRD:::resid.vs.fit(comptime.mlest.out)

SMRD:::resid.vs.explan(comptime.mlest.out)

SMRD:::resid.probplot(comptime.mlest.out)

plot(comptime.mlest.out, 
     density.at = c(1, 3, 5))

plot(comptime.mlest.out, 
     density.at = c(1, 3, 5),
     response.on.yaxis = F)

#or more simply as

plot(comptime.mlest.out)

quantiles(comptime.mlest.out,new.data=5)

Example x Snubber data set

Snubber.ld <- frame.to.ld(snubber, 
                          response.column = "cycles", 
                          censor.column = "event",
                          time.units = "Cycles",
                          case.weight.column = "count",
                          x.columns = "design")

event.plot(Snubber.ld)
summary(Snubber.ld)

Snubber.groupi.nor.out <-  groupi.mleprobplot(Snubber.ld,"normal")

tmpxx <- groupi.contour(Snubber.ld,
                        "Weibull",
                        the.quantile = 0.1)

tmpxx <- groupi.contour(Snubber.ld,
                        "lognormal",
                        the.quantile = 0.1)

tmpxx <- groupi.contour(Snubber.ld,
                        "lognormal")

tmpxx <- groupi.contour(Snubber.ld,
                        "normal")

tmpxx <- groupi.contour(Snubber.ld,
                        "normal",
                        the.quantile = 0.1)

multiple.profile.plot(tmpxx, which = "x")
multiple.profile.plot(tmpxx, which = "y")

summary(Snubber.groupi.nor.out)

Snubber.groupm.nor.out <-  groupm.mleprobplot(Snubber.ld,
                                              distribution = "Normal",
                                              relationship ="class")

quantiles(Snubber.groupm.nor.out,
          new.data = "Old")

quantiles(Snubber.groupm.nor.out,
          new.data = "New")

plot(Snubber.groupm.nor.out)

PartA.ld <- frame.to.ld(parta,
                        response.column = "kilocycles",
                        x.columns = "operator")

groupi.contour(PartA.ld,
               rel.or.conf = "",
               "Weibull",
               the.quantile = 0.10)

groupi.contour(PartA.ld,
               "Weibull",
               the.quantile = 0.10)

groupi.contour(PartA.ld,
               rel.or.conf = "",
               "Weibull",
               the.quantile = 0.005)

groupi.contour(PartA.ld,
               "Weibull",
               the.quantile = 0.005)

Zelen capacator data

ZelenCap.ld <- frame.to.ld(zelencap,
                           response.column = 1,
                           censor.column = 2,
                           case.weight.column = 3,
                           x.columns = c(4, 5),
                           time.units = "Hours")

Fitting distributions at individual conditions

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

summary(ZelenCap.groupi.Weibull.out)

names(xmat(ZelenCap.ld))

Fit categorical

Constrain the Weibull shape parameters to be the same - like one-way ANOVA

ZelenCap.groupm.out1 <-
  groupm.mleprobplot(ZelenCap.ld,
                     distribution = "Weibull")

SMRD:::resid.vs.order(ZelenCap.groupm.out1)

SMRD:::resid.vs.fit(ZelenCap.groupm.out1)

SMRD:::resid.vs.explan(ZelenCap.groupm.out1,
                        x.to.plot = 1)

SMRD:::resid.vs.explan(ZelenCap.groupm.out1,
                        x.to.plot = 2)

SMRD:::resid.probplot(ZelenCap.groupm.out1)

Fitting to celsius only

ZelenCap.groupm.out2 <-
  groupm.mleprobplot(ZelenCap.ld,
                     distribution = "Lognormal",
                     formula= Location ~ g(celsius),
                     relationship = c("arrhenius", "log"))

Fitting to volts only

ZelenCap.groupm.out3 <-
  groupm.mleprobplot(ZelenCap.ld,
                     distribution = "Lognormal",
                     formula= Location ~ g(volts),
                     relationship = c("arrhenius", "log"))

Fitting to celsius and volts

ZelenCap.groupm.out4 <-
  groupm.mleprobplot(ZelenCap.ld,
                     distribution = "normal",
                     formula = Location ~ g(celsius) +  g(volts))

ZelenCap.groupm.out5 <-
  groupm.mleprobplot(ZelenCap.ld,
                     distribution = "normal",
                     formula= Location ~ g(volts) + g(celsius))

Fitting to volts and celsius with interaction

ZelenCap.groupm.out6 <-
  groupm.mleprobplot(ZelenCap.ld,
                     distribution = "normal",
                     formula = Location ~ celsius + volts + celsius:volts )

Omit the formula, use default of linear on all X's

ZelenCap.groupm.out7 <-
  groupm.mleprobplot(ZelenCap.ld,
                     distribution = "Lognormal",
                     relationship = c("arrhenius","log"))

ZelenCap.groupm.out3 <- 
  groupm.mleprobplot(ZelenCap.ld, 
                     distribution = "Lognormal", 
                     relationship = c("linear", "linear"), 
                     formula = Location ~ g(volts) + g(celsius) + g(volts):g(celsius))

#make a proper dataframe for new data (used below)
frame.new.data("165;188",ZelenCap.groupm.out3[[1]])

#temperature and voltage need be in the right order, semicolon separated
quantiles(ZelenCap.groupm.out3,
          new.data = "165;188")

failure.probabilities(ZelenCap.groupm.out3,
                      new.data = "165;188")

SMRD:::resid.vs.explan.multiple(ZelenCap.groupm.out3)
residual.plots(ZelenCap.groupm.out3)

Example 7 Nelson's Superalloy Fatigue vs Stress Data

superalloy.ld <- frame.to.ld(superalloy,
                             response.column = 1,
                             censor.column = 2,
                             x.columns = c(4,5,6),
                             data.title = "Nelson's Super Alloy Fatigue Data",
                             time.units = "Kilocycles")

summary(superalloy.ld)

censored.data.plot(superalloy.ld)

Fitting a model with NON-CONSTANT variance

The following code is used to fit a regression model with a non-constant variance where the 2nd and 3rd col of the model matrix are LogStress and LogStress2. Note that this is not working right now and may cause R to crash - not clear why.

gmlest(superalloy.ld,
       dist = "Weibull",
       explan.vars = list(mu.relat = c(2,3),
                          sigma.relat = c(2)))

We can use the following to prepare new.data from a string

frame.new.data("165;150", ZelenCap.groupm.out3[[1]])

Auburngrads/SMRD documentation built on Sept. 14, 2020, 2:21 a.m.