Title: Optimal Experimental Designs for Accelerated Life Testing
Version: 0.1.2
Description: Creates the optimal (D, U and I) designs for the accelerated life testing with right censoring or interval censoring. It uses generalized linear model (GLM) approach to derive the asymptotic variance-covariance matrix of regression coefficients. The failure time distribution is assumed to follow Weibull distribution with a known shape parameter and log-linear link functions are used to model the relationship between failure time parameters and stress variables. The acceleration model may have multiple stress factors, although most ALTs involve only two or less stress factors. ALTopt package also provides several plotting functions including contour plot, Fraction of Use Space (FUS) plot and Variance Dispersion graphs of Use Space (VDUS) plot. For more details, see Seo and Pan (2015) <doi:10.32614/RJ-2015-029>.
Depends: R (≥ 3.0.0)
License: GPL-3
LazyData: true
Imports: cubature (≥ 1.0), lattice (≥ 0.20), methods
RoxygenNote: 7.0.2
NeedsCompilation: no
Packaged: 2019-12-12 22:24:17 UTC; seoka
Author: Kangwon Seo [aut, cre], Rong Pan [aut]
Maintainer: Kangwon Seo <seoka@missouri.edu>
Repository: CRAN
Date/Publication: 2019-12-12 23:10:02 UTC

Optimal Experimental Designs for Accelerated Life Testing

Description

Creates the optimal (D, U and I) designs for the accelerated life testing with right censoring or interval censoring. It uses generalized linear model (GLM) approach to derive the asymptotic variance-covariance matrix of regression coefficients. The failure time distribution is assumed to follow Weibull distribution with a known shape parameter and log-linear link functions are used to model the relationship between failure time parameters and stress variables. The acceleration model may have multiple stress factors, although most ALTs involve only two or less stress factors. ALTopt package also provides several plotting functions including contour plot, Fraction of Use Space (FUS) plot and Variance Dispersion graphs of Use Space (VDUS) plot. For more details, see Seo and Pan (2015) <doi:10.32614/RJ-2015-029>.

Details

Package: ALTopt
Version: 0.1.2
Authors@R: as.person(c( "Kangwon Seo <seoka@missouri.edu> [aut, cre]", "Rong Pan <rong.pan@asu.edu> [aut]" ))
Depends: R (>= 3.0.0)
License: GPL-3
LazyData: true
Imports: cubature (>= 1.0), lattice (>= 0.20), methods
Built: R 3.6.1; ; 2019-12-12 12:30:00 UTC; windows

Index: 

alteval.ic              Design evaluation with interval censoring.
alteval.rc              Design evaluation with right censoring.
altopt.ic               Optimal design with interval censoring.
altopt.rc               Optimal design with right censoring.
compare.fus             Comparing designs using FUS
compare.vdus            Comparing designs using VDUS
convert.stress.level    Coding and decoding stress level
design.plot             Design plot.
pv.contour.ic           Contour plot of prediction variance for a
                        design with interval censoring.
pv.contour.rc           Contour plot of prediction variance for a
                        design with right censoring.
pv.fus.ic               FUS (Fraction of Use Space) plot for interval
                        censoring.
pv.fus.rc               FUS (Fraction of Use Space) plot for right
                        censoring.
pv.vdus.ic              VDUS (Variance Dispersion of Use Space) plot
                        for interval censoring.
pv.vdus.rc              VDUS (Variance Dispersion of Use Space) plot
                        for right censoring.

Author(s)

Kangwon Seo [aut, cre], Rong Pan [aut]

Maintainer: Kangwon Seo <seoka@missouri.edu>

References

Seo, K. and Pan, R. (2015) ALTopt: An R Package for Optimal Experimental Design of Accelerated Life Testing. The R Journal, 7(2), 177-188.

Monroe, E. M., Pan, R., Anderson-Cook, C. M., Montgomery, D. C. and Borror C. M. (2011) A Generalized Linear Model Approach to Designing Accelerated Life Test Experiments, Quality and Reliability Engineering International 27(4), 595–607

Yang, T., Pan, R. (2013) A Novel Approach to Optimal Accelerated Life Test Planning With Interval Censoring, Reliability, IEEE Transactions on 62(2), 527–536

See Also

altopt.rc, altopt.ic, alteval.rc, alteval.ic, pv.contour.rc, pv.contour.ic, pv.fus.rc, pv.fus.ic, pv.vdus.rc, pv.vdus.ic, compare.fus, compare.vdus, design.plot, convert.stress.level

Examples


# D optimal design of two stress factors with right censoring.
Design.D <- altopt.rc("D", 100, 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01))

design.plot(Design.D$opt.design.rounded, x1, x2)

pv.contour.rc(Design.D$opt.design.rounded, x1, x2, 100, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01),
useCond = c(1.758, 3.159))

FUS.D <- pv.fus.rc(Design.D$opt.design.rounded, 100, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01),
useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

# U optimal design of two stress factors with right censoring.
Design.U <- altopt.rc("U", 100, 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useCond = c(1.758, 3.159))

design.plot(Design.U$opt.design.rounded, x1, x2)

pv.contour.rc(Design.U$opt.design.rounded, x1, x2, 100, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01),
useCond = c(1.758, 3.159))

FUS.U <- pv.fus.rc(Design.U$opt.design.rounded, 100, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01),
useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

# Comparing D and U optimal design.
compare.fus(FUS.D, FUS.U)

Objective function of D optimal design with interval censoring

Description

The internal function to calculate the objective function value of D optimal design with interval censoring plan.

Usage

Dobj.ic(x, formula, coef, nf, t, k, alpha)

Objective function of D optimal design with right censoring

Description

The internal function to calculate the objective function value of D optimal design with right censoring plan.

Usage

Dobj.rc(x, formula, coef, nf, tc, alpha)

Transform the array to the model matrix

Description

The internal function to make the model matrix corresponded to linear predictor model from the array (vector) containg coordinates of stress factors.

Usage

ExtendedForm(array, formula, nf)

Objective function of U optimal design with interval censoring

Description

The internal function to calculate the objective function value of U optimal design with interval censoring plan.

Usage

Iobj.ic(x, formula, coef, nf, t, k, alpha, useLower, useUpper)

Objective function of I optimal design with right censoring

Description

The internal function to calculate the objective function value of I optimal design with right censoring plan.

Usage

Iobj.rc(x, formula, coef, nf, tc, alpha, useLower, useUpper)

Calculates the prediction variance at the particular use condition

Description

The internal function to calculate the prediction variance

Usage

PreVar(location, formula, nf, infMtxInv)

Objective function of U optimal design with interval censoring

Description

The internal function to calculate the objective function value of U optimal design with interval censoring plan.

Usage

Uobj.ic(x, formula, coef, nf, t, k, alpha, useCond)

Objective function of U optimal design with right censoring

Description

The internal function to calculate the objective function value of U optimal design with right censoring plan.

Usage

Uobj.rc(x, formula, coef, nf, tc, alpha, useCond)

Design evaluation with interval censoring.

Description

alteval.ic calculates the objective function value (D, U or I) for a given design with interval censoring plan.

Usage

alteval.ic(
  designTable,
  optType,
  t,
  k,
  nf,
  alpha,
  formula,
  coef,
  useCond,
  useLower,
  useUpper
)

Arguments

designTable

a data frame containing the coordinates and the number of allocation of each design point. The design created by either altopt.rc or altopt.ic or any design matrix with the same form as those can be provided for this argument.

optType

the choice of "D", "U" and "I" optimality.

t

the total testing time.

k

the number of time intervals.

nf

the number of stress factors.

alpha

the value of the shape parameter of Weibull distribution.

formula

the object of class formula which is the linear predictor model.

coef

the numeric vector containing the coefficients of each term in formula.

useCond

the numeric vector of use condition. It should be provided when optType is "U". The length of the vector should be same as the number of stress factors.

useLower

the numeric vector of lower bound of use region. It should be provided when optType is "I". The length of the vector should be same as the number of stress factors.

useUpper

the numeric vector of upper bound of use region. It should be provided when optType is "I". The length of the vector should be same as the number of stress factors.

Value

The objective function value corresponded by optType for a given design with interval censoring plan.

See Also

altopt.ic

Examples

# Evaluation of factorial design for interval censoring.
x1 <- c(0, 1, 0, 1)
x2 <- c(0, 0, 1, 1)
allocation <- c(25, 25, 25, 25)
facDes <- data.frame(x1, x2, allocation)

alteval.ic(facDes, "D", 30, 5, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01))

alteval.ic(facDes, "U", 30, 5, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useCond = c(1.758, 3.159))

alteval.ic(facDes, "I", 30, 5, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

Design evaluation with right censoring.

Description

alteval.rc calculates the objective function value (D, U or I) for a given design with right censoring plan.

Usage

alteval.rc(
  designTable,
  optType,
  tc,
  nf,
  alpha,
  formula,
  coef,
  useCond,
  useLower,
  useUpper
)

Arguments

designTable

a data frame containing the coordinates and the number of allocation of each design point. The design created by either altopt.rc or altopt.ic or any design matrix with the same form as those can be provided for this argument.

optType

the choice of "D", "U" and "I" optimality.

tc

the censoring time.

nf

the number of stress factors.

alpha

the value of the shape parameter of Weibull distribution.

formula

the object of class formula which is the linear predictor model.

coef

the numeric vector containing the coefficients of each term in formula.

useCond

the numeric vector of use condition. It should be provided when optType is "U". The length of the vector should be same as the number of stress factors.

useLower

the numeric vector of lower bound of use region. It should be provided when optType is "I". The length of the vector should be same as the number of stress factors.

useUpper

the numeric vector of upper bound of use region. It should be provided when optType is "I". The length of the vector should be same as the number of stress factors.

Value

The objective function value corresponded by optType for a given design with right censoring plan.

See Also

altopt.rc

Examples

# Evaluation of factorial design for right censoring.
x1 <- c(0, 1, 0, 1)
x2 <- c(0, 0, 1, 1)
allocation <- c(25, 25, 25, 25)
facDes <- data.frame(x1, x2, allocation)

alteval.rc(facDes, "D", 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01))

alteval.rc(facDes, "U", 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useCond = c(1.758, 3.159))

alteval.rc(facDes, "I", 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

Optimal design with interval censoring.

Description

altopt.ic creates D, U or I optimal design of the accelerated life testing with interval censoring plan.

Usage

altopt.ic(
  optType,
  N,
  t,
  k,
  nf,
  alpha,
  formula,
  coef,
  useCond,
  useLower,
  useUpper,
  nOpt = 1,
  nKM = 30,
  nCls = NULL
)

Arguments

optType

the choice of "D", "U" and "I" optimality.

N

the number of test units.

t

the total testing time.

k

the number of time intervals.

nf

the number of stress factors.

alpha

the value of the shape parameter of Weibull distribution.

formula

the object of class formula which is the linear predictor model.

coef

the numeric vector containing the coefficients of each term in formula.

useCond

the numeric vector of use condition. It should be provided when optType is "U". The length of the vector should be same as the number of stress factors.

useLower

the numeric vector of lower bound of use region. It should be provided when optType is "I". The length of the vector should be same as the number of stress factors.

useUpper

the numeric vector of upper bound of use region. It should be provided when optType is "I". The length of the vector should be same as the number of stress factors.

nOpt

the number of repetition of optimization process. Default is 1.

nKM

the number of repetition of k-means clustering. Default is 20.

nCls

the number of clusters used for k-means clustering. If not specified, it is set as the number of parameters in the linear predictor model.

Value

A list with components

References

Monroe, E. M., Pan, R., Anderson-Cook, C. M., Montgomery, D. C. and Borror C. M. (2011) A Generalized Linear Model Approach to Designing Accelerated Life Test Experiments, Quality and Reliability Engineering International 27(4), 595–607

Yang, T., Pan, R. (2013) A Novel Approach to Optimal Accelerated Life Test Planning With Interval Censoring, Reliability, IEEE Transactions on 62(2), 527–536

See Also

kmeans, alteval.ic

Examples

## Not run: 
# Generating D optimal design for interval censoring.
altopt.ic("D", 100, 30, 5, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01))

# Generating U optimal design for interval censoring.
altopt.ic("D", 100, 30, 5, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useCond = c(1.758, 3.159))

# Generating I optimal design for interval censoring.
altopt.ic("D", 100, 30, 5, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useLower = c(1.458, 2.859),
useUpper = c(2.058, 3.459))

## End(Not run)

Optimal design with right censoring.

Description

altopt.rc creates D, U or I optimal design of the accelerated life testing with right censoring plan.

Usage

altopt.rc(
  optType,
  N,
  tc,
  nf,
  alpha,
  formula,
  coef,
  useCond,
  useLower,
  useUpper,
  nOpt = 1,
  nKM = 30,
  nCls = NULL
)

Arguments

optType

the choice of "D", "U" and "I" optimality.

N

the number of test units.

tc

the censoring time.

nf

the number of stress factors.

alpha

the value of the shape parameter of Weibull distribution.

formula

the object of class formula which is the linear predictor model.

coef

the numeric vector containing the coefficients of each term in formula.

useCond

the numeric vector of use condition. It should be provided when optType is "U". The length of the vector should be same as the number of stress factors.

useLower

the numeric vector of lower bound of use region. It should be provided when optType is "I". The length of the vector should be same as the number of stress factors.

useUpper

the numeric vector of upper bound of use region. It should be provided when optType is "I". The length of the vector should be same as the number of stress factors.

nOpt

the number of repetition of optimization process. Default is 1.

nKM

the number of repetition of k-means clustering. Default is 20.

nCls

the number of clusters used for k-means clustering. If not specified, it is set as the number of parameters in the linear predictor model.

Value

A list with components

References

Monroe, E. M., Pan, R., Anderson-Cook, C. M., Montgomery, D. C. and Borror C. M. (2011) A Generalized Linear Model Approach to Designing Accelerated Life Test Experiments, Quality and Reliability Engineering International 27(4), 595–607

Yang, T., Pan, R. (2013) A Novel Approach to Optimal Accelerated Life Test Planning With Interval Censoring, Reliability, IEEE Transactions on 62(2), 527–536

See Also

kmeans, alteval.rc

Examples

## Not run: 
# Generating D optimal design for right censoring.
altopt.rc("D", 100, 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01))

# Generating U optimal design for right censoring.
altopt.rc("D", 100, 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useCond = c(1.758, 3.159))

# Generating I optimal design for right censoring.
altopt.rc("D", 100, 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useLower = c(1.458, 2.859),
useUpper = c(2.058, 3.459))

## End(Not run)

Comparing designs using FUS

Description

compare.fus draws the FUS plots of multiple designs on a single frame.

Usage

compare.fus(...)

Arguments

...

Objects created by pv.fus.rc or pv.fus.ic.

Value

FUS plots of multiple designs.

See Also

pv.fus.rc, pv.fus.ic

Examples

## Not run: 
# Generating D optimal design and FUS plot.
Dopt <- altopt.rc("D", 100, 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01))

FUS.D <- pv.fus.rc(Dopt$opt.design.rounded, 100, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01),
useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

# Generating U optimal design and FUS plot.
Uopt <- altopt.rc("U", 100, 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useCond = c(1.758, 3.159))

FUS.U <- pv.fus.rc(Uopt$opt.design.rounded, 100, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01),
useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

# Comparing D and U optimal designs.
compare.fus(FUS.D, FUS.U)

## End(Not run)

Comparing designs using VDUS

Description

compare.vdus draws the VDUS plots of multiple designs on a single frame.

Usage

compare.vdus(...)

Arguments

...

Objects created by pv.vdus.rc or pv.vdus.ic.

Value

VDUS plots of multiple designs.

See Also

pv.vdus.rc, pv.vdus.ic

Examples

## Not run: 
# Generating D optimal design and VDUS plot.
Dopt <- altopt.rc("D", 100, 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01))

VDUS.D <- pv.vdus.rc(Dopt$opt.design.rounded, 100, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01),
useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

# Generating U optimal design and VDUS plot.
Uopt <- altopt.rc("U", 100, 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useCond = c(1.758, 3.159))

VDUS.U <- pv.vdus.rc(Uopt$opt.design.rounded, 100, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01),
useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

# Comparing D and U optimal designs.
compare.vdus(VDUS.D, VDUS.U)

## End(Not run)

Coding and decoding stress level

Description

Convert the stress levels from the actual levels to standardized levels, and vice versa.

Usage

convert.stress.level(lowStLv, highStLv, actual = NULL, stand = NULL)

Arguments

lowStLv

a numeric vector containing the actual lowest stress level of each stress variable in design region.

highStLv

a numeric vector containing the actual highest stress level of each stress variable in design region.

actual

a data frame or numeric vector containing the design points in actual units.

stand

a data frame or numeric vector containing the design points in standardized units.

Value

When actual is provided, the function converts it to the standardized units and when stand is provided, the function converts it to the actual units.

Examples

## Not run: 
  # Generating D optimal design in coded unit.
  Design <- altopt.rc(optType = "D", N = 100, tc = 100, nf = 2, alpha = 1,
  formula = ~x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01))

  # Transform the coded unit to actual stress variable's level.
  convert.stress.level(lowStLv = c(34.834, 4.094), highStLv = c(30.288, 4.5),
  stand = Design$opt.design.rounded)

  # Transform the actual stress level to coded units.
  use <- c(38.281, 3.219)
  convert.stress.level(lowStLv = c(34.834, 4.094), highStLv = c(30.288, 4.5),
  actual = use)
  
## End(Not run)

Design plot.

Description

design.plot draws design plot as a form of a bubble plot of any two stress factors which are specified by xAxis and yAxis. The size of each bubble indicates the relative magnitude of allocation on each design point.

Usage

design.plot(design, xAxis, yAxis)

Arguments

design

the data frame containing the coordinates and the number of allocation of each design point. The design created by either altopt.rc or altopt.ic or any design matrix with the same form as those can be provided for this argument.

xAxis

the name of the factor to be displayed in x axis.

yAxis

the name of the factor to be displayed in y axis.

Value

The bubble plot of a design with two stress factors.

Examples

## Not run: 
# Design plot of D optimal design with right censoring.
Design1 <- altopt.rc("D", 100, 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01))

design.plot(Design1$opt.design.rounded, x1, x2)

## End(Not run)

Perform the k-means clustering and make design table

Description

The internal function to perform the k-means clustering and make design table.

Usage

kmeansCls(Mtx, nCls)

Contour plot of prediction variance for a design with interval censoring.

Description

pv.contour.ic draws the contour plot of prediction variance for a given design with interval censoring plan. Either useCond or use region (useLower and useUpper) should be provided.

Usage

pv.contour.ic(
  design,
  xAxis,
  yAxis,
  t,
  k,
  nf,
  alpha,
  formula,
  coef,
  useCond = NULL,
  useLower = NULL,
  useUpper = NULL
)

Arguments

design

the data frame containing the coordinates and the number of allocation of each design point. The design created by either altopt.rc or altopt.ic or any design matrix with the same form as those can be provided for this argument.

xAxis

the name of the factor to be displayed in x axis.

yAxis

the name of the factor to be displayed in y axis.

t

the total testing time.

k

the number of time intervals.

nf

the number of stress factors.

alpha

the value of the shape parameter of Weibull distribution.

formula

the object of class formula which is the linear predictor model.

coef

the numeric vector containing the coefficients of each term in formula.

useCond

the vector of specified use condition. If it is provided, the contour line will be generated up to this point.

useLower, useUpper

the vector of the use region. If these are provided, the contour line will be generated up to this region. Note that either useCond or both of useLower, useUpper should be provided.

Value

The contour plot of prediction variance for interval censoring.

See Also

altopt.ic

Examples

## Not run: 
# Contour plot of prediction variance of U optimal design with interval censoring.
Design <- altopt.ic("D", 100, 30, 5, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useCond = c(1.758, 3.159))

pv.contour.ic(Design$opt.design.rounded, x1, x2, 30, 5, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01), useCond = c(1.758, 3.159))

## End(Not run)

Contour plot of prediction variance for a design with right censoring.

Description

pv.contour.rc draws the contour plot of prediction variance for a given design with right censoring plan. Either useCond or use region (useLower and useUpper) should be provided.

Usage

pv.contour.rc(
  design,
  xAxis,
  yAxis,
  tc,
  nf,
  alpha,
  formula,
  coef,
  useCond = NULL,
  useLower = NULL,
  useUpper = NULL
)

Arguments

design

the data frame containing the coordinates and the number of allocation of each design point. The design created by either altopt.rc or altopt.ic or any design matrix with the same form as those can be provided for this argument.

xAxis

the name of the factor to be displayed in x axis.

yAxis

the name of the factor to be displayed in y axis.

tc

the censoring time.

nf

the number of stress factors.

alpha

the value of the shape parameter of Weibull distribution.

formula

the object of class formula which is the linear predictor model.

coef

the numeric vector containing the coefficients of each term in formula.

useCond

the vector of specified use condition. If it is provided, the contour line will be generated up to this point.

useLower, useUpper

the vector of the use region. If these are provided, the contour line will be generated up to this region. Note that either useCond or both of useLower, useUpper should be provided.

Value

The contour plot of prediction variance for right censoring.

See Also

altopt.rc

Examples

## Not run: 
# Contour plot of prediction variance of U optimal design with right censoring.
Design <- altopt.rc("D", 100, 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useCond = c(1.758, 3.159))

pv.contour.rc(Design$opt.design.rounded, x1, x2, 100, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01), useCond = c(1.758, 3.159))

## End(Not run)

FUS (Fraction of Use Space) plot for interval censoring.

Description

pv.fus.ic draws the FUS plot of prediction variance for a given design with interval censoring plan. The use region (useLower and useUpper) should be provided.

Usage

pv.fus.ic(
  design,
  t,
  k,
  nf,
  alpha,
  formula,
  coef,
  useLower = NULL,
  useUpper = NULL
)

Arguments

design

the data frame containing the coordinates and the number of allocation of each design point. The design created by either altopt.rc or altopt.ic or any design matrix with the same form as those can be provided for this argument.

t

the total testing time.

k

the number of time intervals.

nf

the number of stress factors.

alpha

the value of the shape parameter of Weibull distribution.

formula

the object of class formula which is the linear predictor model.

coef

the numeric vector containing the coefficients of each term in formula.

useLower, useUpper

the vectors containing the lower bound and upper bound for the use region. They should be provided for FUS plot.

Value

The "trellis" object which includes the FUS plot for interval censoring.

See Also

altopt.ic

Examples

## Not run: 
# FUS plot of I optimal design with interval censoring.
Design <- altopt.ic("I", 100, 30, 5, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

pv.fus.ic(Design$opt.design.rounded, 30, 5, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01),
useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

## End(Not run)

FUS (Fraction of Use Space) plot for right censoring.

Description

pv.fus.rc draws the FUS plot of prediction variance for a given design with right censoring plan. The use region (useLower and useUpper) should be provided.

Usage

pv.fus.rc(
  design,
  tc,
  nf,
  alpha,
  formula,
  coef,
  useLower = NULL,
  useUpper = NULL
)

Arguments

design

the data frame containing the coordinates and the number of allocation of each design point. The design created by either altopt.rc or altopt.ic or any design matrix with the same form as those can be provided for this argument.

tc

the censoring time.

nf

the number of stress factors.

alpha

the value of the shape parameter of Weibull distribution.

formula

the object of class formula which is the linear predictor model.

coef

the numeric vector containing the coefficients of each term in formula.

useLower, useUpper

the vectors containing the lower bound and upper bound for the use region. They should be provided for FUS plot.

Value

The "trellis" object which includes the FUS plot for right censoring.

See Also

altopt.rc

Examples

## Not run: 
# FUS plot of I optimal design with right censoring.
Design <- altopt.rc("I", 100, 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

pv.fus.rc(Design$opt.design.rounded, 100, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01),
useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

## End(Not run)

VDUS (Variance Dispersion of Use Space) plot for interval censoring.

Description

pv.vdus.ic draws the VDUS plot of prediction variance for a given design with interval censoring plan. The use region (useLower and useUpper) should be provided.

Usage

pv.vdus.ic(
  design,
  t,
  k,
  nf,
  alpha,
  formula,
  coef,
  useLower = NULL,
  useUpper = NULL
)

Arguments

design

the data frame containing the coordinates and the number of allocation of each design point. The design created by either altopt.rc or altopt.ic or any design matrix with the same form as those can be provided for this argument.

t

the total testing time.

k

the number of time intervals.

nf

the number of stress factors.

alpha

the value of the shape parameter of Weibull distribution.

formula

the object of class formula which is the linear predictor model.

coef

the numeric vector containing the coefficients of each term in formula.

useLower, useUpper

the vectors containing the lower bound and upper bound for the use region. They should be provided for VDUS plot.

Value

The "trellis" object which includes the VDUS plot for interval censoring.

See Also

altopt.ic

Examples

## Not run: 
# VDUS plot of I optimal design with interval censoring.
Design <- altopt.ic("I", 100, 30, 5, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

pv.vdus.ic(Design$opt.design.rounded, 30, 5, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01),
useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

## End(Not run)

VDUS (Variance Dispersion of Use Space) plot for right censoring.

Description

pv.vdus.rc draws the VDUS plot of prediction variance for a given design with right censoring plan. The use region (useLower and useUpper) should be provided.

Usage

pv.vdus.rc(
  design,
  tc,
  nf,
  alpha,
  formula,
  coef,
  useLower = NULL,
  useUpper = NULL
)

Arguments

design

the data frame containing the coordinates and the number of allocation of each design point. The design created by either altopt.rc or altopt.ic or any design matrix with the same form as those can be provided for this argument.

tc

the censoring time.

nf

the number of stress factors.

alpha

the value of the shape parameter of Weibull distribution.

formula

the object of class formula which is the linear predictor model.

coef

the numeric vector containing the coefficients of each term in formula.

useLower, useUpper

the vectors containing the lower bound and upper bound for the use region. They should be provided for VDUS plot.

Value

The "trellis" object which includes the VDUS plot for right censoring.

See Also

altopt.rc

Examples

## Not run: 
# VDUS plot of I optimal design with right censoring.
Design <- altopt.rc("I", 100, 100, 2, 1, formula = ~ x1 + x2 + x1:x2,
coef = c(0, -4.086, -1.476, 0.01), useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

pv.vdus.rc(Design$opt.design.rounded, 100, 2, 1,
formula = ~ x1 + x2 + x1:x2, coef = c(0, -4.086, -1.476, 0.01),
useLower = c(1.458, 2.859), useUpper = c(2.058, 3.459))

## End(Not run)