Type: Package
Title: Statistical Package for Reliability Data Analysis
Version: 1.2
Date: 2025-03-28
Author: Yili Hong [aut, cre], Yimeng Xie [aut], Zhibing Xu [aut]
Maintainer: Yili Hong <yilihong@vt.edu>
Depends: survival, nlme
Description: The Statistical Package for REliability Data Analysis (SPREDA) implements recently-developed statistical methods for the analysis of reliability data. Modern technological developments, such as sensors and smart chips, allow us to dynamically track product/system usage as well as other environmental variables, such as temperature and humidity. We refer to these variables as dynamic covariates. The package contains functions for the analysis of time-to-event data with dynamic covariates and degradation data with dynamic covariates. The package also contains functions that can be used for analyzing time-to-event data with right censoring, and with left truncation and right censoring. Financial support from NSF and DuPont are acknowledged.
License: GPL-2
NeedsCompilation: no
Packaged: 2025-03-29 13:56:01 UTC; yilih
Repository: CRAN
Date/Publication: 2025-03-29 14:20:02 UTC

Statistical Package for Reliability Data Analysis

Description

The Statistical Package for REliability Data Analysis (SPREDA) implements recently-developed statistical methods for the analysis of reliability data. Modern technological developments, such as sensors and smart chips, allow us to dynamically track product/system usage as well as other environmental variables, such as temperature and humidity. We refer to these variables as dynamic covariates. The package contains functions for the analysis of time-to-event data with dynamic covariates and degradation data with dynamic covariates. The package also contains functions that can be used for analyzing time-to-event data with right censoring, and with left truncation and right censoring. Financial support from NSF and DuPont are acknowledged.

Details

Package: SPREDA
Type: Package
Version: 1.2
Date: 2025-03-28
License: GPL-2

Contains functions that are useful for the analysis of reliability data.

Author(s)

Yili Hong, Yimeng Xie, and Zhibing Xu

Maintainer: Yili Hong <yilihong@vt.edu>

References

Hong, Y., W. Q. Meeker, and J. D. McCalley (2009). Prediction of Remaining Life of Power Transformers Based on Left Truncated and Right Censored Lifetime Data. The Annals of Applied Statistics, Vol. 3, pp. 857-879.

Hong, Y. and Meeker, W. Q. (2010), Field-Failure and Warranty Prediction Using Auxiliary Use-rate Data. Technometrics, Vol. 52, pp. 148-159.

Hong, Y. and Meeker, W. Q. (2013), Field-Failure Predictions Based on Failure-time Data with Dynamic Covariate Information, Technometrics, Vol. 55, pp. 135-149.

Hong, Y. (2013), On Computing the Distribution Function for the Poisson Binomial Distribution, Computational Statistics and Data Analysis, Vol. 59, pp. 41-51.

Hong. Y., Y. Duan, W. Q. Meeker, D. L. Stanley, and X. Gu (2014), Statistical Methods for Degradation Data with Dynamic Covariates Information and an Application to Outdoor Weathering Data, Technometrics, DOI: 10.1080/00401706.2014.915891.

Meeker, W. Q. and L. A. Escobar (1998). Statistical Methods for Reliability Data. John Wiley & Sons.

Meeker, W. Q. and L. A. Escobar (2014). RSplida. http://www.public.iastate.edu/~stat533/.

Xu, Z., Y. Hong, and R. Jin (2014), Nonlinear General Path Models for Degradation Data with Dynamic Covariates, submitted.

Dynamic covariates for the coating data.

Description

A data frame with 36 observations and 9 variables.

Usage

data(Coatingenv)

Format

SPEC_NUM

Observation id.

TIME

Observation time for each id.

UVB

a dynamic covariate.

UVA

a dynamic covariate.

VIS

a dynamic covariate.

TEMP

a dynamic covariate.

RH

a dynamic covariate.

UV

a dynamic covariate.

GROUP

Group for each id.

Source

Hong. Y., Y. Duan, W. Q. Meeker, D. L. Stanley, and X. Gu (2014), Statistical Methods for Degradation Data with Dynamic Covariates Information and an Application to Outdoor Weathering Data, Technometrics, DOI: 10.1080/00401706.2014.915891.

Dynamic covariates for coating data

Description

A data frame with 36 observations and 4 variables.

Usage

data(Coatingout)

Format

SPEC_NUM

Observation id.

TIME

Observation time for each id.

DAMAGE_Y

Response for each id.

GROUP

Group for each id.

Source

Hong. Y., Y. Duan, W. Q. Meeker, D. L. Stanley, and X. Gu (2014), Statistical Methods for Degradation Data with Dynamic Covariates Information and an Application to Outdoor Weathering Data, Technometrics, DOI: 10.1080/00401706.2014.915891.

Parametric Fitting for Lifetime Data

Description

Fit parametric models (based on log-location-scale family of distributions) to right censored and/or left truncated data, with (dynamic) covariates.

Usage

Lifedata.MLE(formula, data, xt.dat = NULL, dist, method = "BFGS", 
subset, truncation, na.action, weights, ref_time = NULL, starts = NULL, ...)

Arguments

formula

A formula object, which has a Surv object on the left of ~ and covariates on the right.

data

A data frame used to evaluate variables in the formula, subset and weights arguments.

xt.dat

A data frame contains dynamic covariates. The first and second columns must be sample id and time. If specified, cumulative exposure model will be used to fit the data.

dist

Distribution used in the model. Can be "weibull", "lognormal", "loglogistic", "frechet".

method

Default is "BFGS". This function calls optim to do optimization. Other options can be found in optim.

subset

This is an optional argument that specifies the subset of observations to be used in the fitting procedure.

truncation

An optional data frame contains truncation time and indicators.

na.action

Indicates what to be done when data contain missing values.

weights

An optional vector of weights for each observation.

ref_time

An optional vector of reference time (start time) of dynamic covariates. If it is NULL, ref_time is a vector of 0's.

starts

Initial values for parameters.

...

Further arguments can be passed to optim.

Details

The default method for choosing start values can sometimes failed, the user may need to try several start values to make the function work.

Value

This function returns an object of class "Lifedata.MLE". An "Lifedata.MLE" object is a list of

call

Called function.

formula

Formula argument in the input.

coef

Vector of coefficients.

vov

Variance-covariance matrix of coef.

min

-loglikelihood evaluated at coef.

surv

Survival probabilities.

dat

Dataset used to fit the model.

Author(s)

Yili Hong

References

Yili Hong and William Q. Meeker. Field-Failure Predictions Based on Failure-Time Data With Dynamic Covariate Information. Technometrics, 55(2), 135–149, 2013.

See Also

Surv, optim, summary.Lifedata.MLE. See methods(class="Lifedata.MLE") for all the functions related to "Lifedata.MLE" object.

Examples

#################################################################
### right censored data
data(shock)
res1=Lifedata.MLE(Surv(Distance, Censor)~1, data=shock, dist="weibull")
res1
summary(res1)

res2=Lifedata.MLE(Surv(Distance, Censor)~1, data=shock, dist="lognormal")
res2
summary(res2)

#################################################################
### left truncated right censoring data
data(testdata)
test=Lifedata.MLE(Surv(truncation.age, age, failure)~1, data=testdata,dist="weibull", 
method="Nelder-Mead", subset=(group=="MC_Old"))
summary(test)  


#################################################################
### dynamix covariates
data(Prod2.xt.dat)
data(Prod2.fai.dat)


test=Lifedata.MLE(Surv(failure.time, delta)~1, data=Prod2.fai.dat,xt.dat=Prod2.xt.dat,
starts=c(12, 3.5, log(2)), dist="weibull")
summary(test)

Splines basis functions

Description

Creation splines basis for M_splines, I_splines and C_splines

Usage

MIC.splines.basis(x, df = NULL, knots = NULL, boundary.knots = NULL, 
type = "Ms", degree = 3, delta = 0.01, eq.alloc = F)

Arguments

x

values of covariate

df

number of splines needed which is equal to knots+degree

knots

number of knots needed which does not include the number of knots at the beginning

boundary.knots

the values of boundary knots, which are usually the minimum and maximum of covariate

type

types of splines basis needed, which can be Ms Is or Cs

degree

degree of the splines function

delta

the length of the spans to split the range of covariate

eq.alloc

indicators of whether the knots are equally allocated

Value

list(mat=mat,x=x, df=df, knots=knots,boundary.knots=boundary.knots, type=type,degree=degree,delta=delta)

mat

it is a matrix of splines basis

x

the input of covariate

df

the input of number of splines needed

knots

the input of number of knots needed not including the boundary

boundary.knots

the values of boundary knots

type

type of splines function which can be MS IS or Cs

degree

degree of the splines functions

delta

the length of the spans to split the range of covariate

Author(s)

Yili Hong

References

Hong. Y., Y. Duan, W. Q. Meeker, D. L. Stanley, and X. Gu (2014), Statistical Methods for Degradation Data with Dynamic Covariates Information and an Application to Outdoor Weathering Data, Technometrics, DOI: 10.1080/00401706.2014.915891.

See Also

i.spline.x, m.spline.x

Examples

MIC.splines.basis(x=runif(20), df = NULL, knots = 3, boundary.knots = NULL, 
    type = "Ms", degree = 4, delta = 0.01, eq.alloc = FALSE)

Dataset of failure information of Product 2.

Description

A data frame with 1800 observations and 3 variables.

Usage

data(Prod2.fai.dat)

Format

failure.time

a numeric vector

delta

a numeric vector

ce

a numeric vector

Source

Hong, Y. and W. Q. Meeker (2013). Field-Failure Predictions Based on Failure-Time Data With Dynamic Covariate Information. Technometrics, 55(2), 135–149.

Dataset of covariate information of Produce 2.

Description

A data frame with 80552 observations and 3 variables.

Usage

data(Prod2.xt.dat)

Format

id

a numeric vector of sample ids.

time

a numeric vector of time.

x1

a numeric vector of dynamic covariate x1.

Source

Yili Hong and William Q. Meeker. Field-Failure Predictions Based on Failure-Time Data With Dynamic Covariate Information. Technometrics, 55(2), 135–149, 2013.

Create an object for cumulative exposure

Description

Create a dataset with format that is suitable for analysis in the cumulative exposure model.

Usage

ce.dat.prep(xt.dat, failure.dat, ref_time = NULL)

Arguments

xt.dat

"data.frame" format object. The first and second columns are sample id and time, respectively. Other columns are dynamic covariates.

failure.dat

A "Surv" object. See Surv.

ref_time

Reference time for each sample. If not specified, ref_time is a vector of 0's.

Value

A list of failure.dat, xt.obj and aux.inf.

Mixed primal-dual bases algorithm for estimation of parameters with restriction.

Description

It is used to estimate the parameters which have restrictions on the domain based on mixed primal-dual bases algorithm.

Usage

cls(y, X)

Arguments

y

A vector for responses.

X

Matrix of covariates.

Value

y

A vector for responses;

x

Matrix of covariates;

betahat

Estimates of parameters;

yhat

Estimates of responses.

Author(s)

Yili Hong

References

Fraser, D. A. S. and H. Massam (1989), A mixed primal-dual bases algorithm for regression under inequality constraints. Application to concave regression. Scandinavian Journal of Statistics, Vol. 16, pp. 65-74.

See Also

clme and deglmx

Examples

y<-sort(rnorm(100, 10, 2))
x<-cbind(runif(100, 1, 3), sort(rnorm(100, 3, 1)))
res<-cls(y, x)

Functions for estimating parameters in the linear/nonlinear mixed models with dynamic covariates.

Description

Functions for estimating parameters in the linear/nonlinear mixed models with dynamic covariates. Those dynamic covariates will have restricted-shape effects such as monotonic increasing, decreasing or quadratic shape.

Usage

deglmx(fixed, data, dyn.data, id, time, random = NULL, linear = TRUE, ytrend, 
splinetrend = NULL, splinetype = NULL, degree = NULL, knots = NULL, 
weights = NULL, subset = NULL, start, maxiter = 10, method = "BFGS", ...)

Arguments

fixed

Formula with fixed effect.

data

Data with id, time, response, and fixed covariates.

dyn.data

Dynamic data with id, time, dynamic covariates.

id

The name of the id which is characters or string.

time

The name of time in the data or dyn.data which is characters or string.

random

The formula for random parts which should condition on the id.

linear

The index of linear or nonlinear.

ytrend

If ytrend=1 indicates the increasing trend of the response, if ytrend=-1 indicates the decreasing trend of the response.

splinetrend

They are a vector of trends of dynamic covariate effects. Define 1 as increasing trend and -1 as decreasing trend.

splinetype

They are a vector of the spline basis type which can be chosen among "Ms", "Is", and "Cs".

degree

The degree of the spline functions.

knots

The number of knots in the spline functions.

weights

Weights of the observation.

subset

Subset of the data.

start

The initial values for covariance and variance matrix.

maxiter

The maximum number of iteration in the optimization.

method

The method of optim function with "BFGS" as default. More details in optim.

...

Other items.

Value

The returned outputs belong to class of "deglmx". list(type = type, fit = fit, dat = dat.obj, dyn.mat = cov.mat.tmp, ytrend = ytrend, dyncovnames = dyncovnames, dyn.data = dyn.data, beta.index = beta.index, call = mfun)

type

Type of the model either linear mixed or nonlinear mixed models.

fit

The fitting results in the model including estimates, residuals, loglikelihood, and so on.

dat

The modified data.

dyn.mat

The spline basis functions.

ytrend

The indication of response trend either increasing (1) or decreasing (-1).

dyncovnames

Names of dynamic covariates in the model.

dyn.data

The modified dynamic data.

beta.index

Indications of parameters in the dyanmic covariates.

call

The call function in the model.

Note

For the nonlinear model, we currently only implement one specific nonlinear relationship.

Author(s)

Yili Hong

References

Hong. Y., Y. Duan, W. Q. Meeker, D. L. Stanley, and X. Gu (2014), Statistical Methods for Degradation Data with Dynamic Covariates Information and an Application to Outdoor Weathering Data, Technometrics, DOI: 10.1080/00401706.2014.915891.

Examples

 data(Coatingenv)
 data(Coatingout)
 
 
 fit=deglmx(DAMAGE_Y~UV+RH+TEMP, data=Coatingout, dyn.data=Coatingenv, 
           id="SPEC_NUM", time="TIME", random=~TIME|SPEC_NUM, linear=TRUE, ytrend=-1,  
           splinetrend=c(-1, -1, -1), splinetype=c("Is", "Cs", "Is"), degree=c( 3, 3, 3), 
           knots=c(4, 4, 4), weights=NULL, subset=NULL,start=c(0.017,0.0013,-0.404,0.0176), 
           maxiter=10, method='BFGS')
           
 fit=deglmx(DAMAGE_Y~G/(1+exp(-log(UV+RH+TEMP)/H)), data=Coatingout, dyn.data=Coatingenv, 
           id="SPEC_NUM", time="TIME", random=~G+H|SPEC_NUM, linear=FALSE, ytrend=-1,  
           splinetrend=c(1, 1, 1), splinetype=c("Is", "Cs", "Is"), degree=c( 3, 3, 3), 
           knots=c(4, 4, 4), weights=NULL, subset=NULL, start=c(0.1, 0.1, -0.5, 0.01), 
           maxiter=4)

i_spline basis

Description

Create the i_th splines basis for I_splines basis or C_splines basis

Usage

i.spline.x(xx, tt, i, k, delta = 1e-04, Cs = F)

Arguments

xx

values of of covariate

tt

values of knot sequence of the covariate

i

I_th splines basis

k

degree of the spline

delta

the length of the spans to split the range of covariate

Cs

indicator of whether the creation of C_splines basis is needed

Details

Creation of the i_th splines basis for I_splines basis or C_splines basis

Value

i.spline.x returns a vector of i_th splines basis for covariate values xx in knots i and degree k

Author(s)

Yili Hong

References

Hong. Y., Y. Duan, W. Q. Meeker, D. L. Stanley, and X. Gu (2014), Statistical Methods for Degradation Data with Dynamic Covariates Information and an Application to Outdoor Weathering Data, Technometrics, DOI: 10.1080/00401706.2014.915891.

See Also

m.spline.x

Examples

i.spline.x(xx=runif(20), tt=c(0, 0, 0, 0.3, 0.6, 0.8, 1, 1, 1 ), i=3, k=3, 
delta = 1e-04, Cs = FALSE)
i.spline.x(xx=runif(20), tt=c(0, 0, 0, 0.3, 0.6, 0.8, 1, 1, 1 ), i=3, k=3, 
delta = 1e-04, Cs = TRUE)

Kaplan-Meier Location

Description

Calculate the location of Kaplan-Meier estimator.

Usage

kaplan.meier.location(fit)

Arguments

fit

survfit object.

Value

xloc, yloc

x, y locations.

Author(s)

Yili Hong

Examples

require(survival)
fit <- survfit(Surv(time, status) ~ x, data = aml)
kaplan.meier.location(fit)

Calculate MLE for Lifetime Distribution

Description

Calculate MLE for samples from lifetime distribution, e.g., Weibull distribution. The observations can be complete or censored.

Usage

lifetime.mle(dat, minusloglik, starts, method = "BFGS", hessian = TRUE,...)

Arguments

dat

First column contains event times, second column contains event indicators.

minusloglik

-loglikelihood.

starts

Initial values for parameters.

method

Default is "BFGS". This function call optim to do optimation. Other options can be found in optim.

hessian

A logical value. If TRUE, hessian matrix will be returned. Default is TRUE.

...

Further arguments can be passed to optim.

Value

A list of

call

Called function.

coef

The best minimizer found.

vov

Variance-covariance matrix of coef.

min

-loglikelihood evaluated at coef.

dat

Dataset used.

minusloglik

-loglikelihood function.

Author(s)

Yili Hong

See Also

optim

Examples

#censored samples from Weibull distribution
dat=cbind(c(1.1,2,3.6,4,5.3,7,7,7), c(1,1,1,1,1,0,0,0))
res=lifetime.mle(dat, minusloglik=miniusloglik.sev, starts=c(0,1))
res$coef  #return \eqn{u, log(\sigma)}

M_splines basis

Description

Creation of M_splines basis

Usage

 m.spline.x(x, tt, i, k)

Arguments

x

a value of the covariate

tt

values of knot sequence of the covariate

i

the i_th M_spline function

k

degree of the spline

Value

m.spline.x returns a value of M_spline basis value for x in i_th spline degree of k

Author(s)

Yili Hong

References

Hong. Y., Y. Duan, W. Q. Meeker, D. L. Stanley, and X. Gu (2014), Statistical Methods for Degradation Data with Dynamic Covariates Information and an Application to Outdoor Weathering Data, Technometrics, DOI: 10.1080/00401706.2014.915891.

See Also

i.spline.x

Examples

m.spline.x(x=0.3, tt=c(0, 0, 0, 0.3, 0.6, 0.8, 1, 1, 1 ), i=2, k=3)

The Standard Largest Extreme Value Distribution

Description

The cdf, pdf, quantile function, and random number generation for the standard largest extreme value distribution.

Usage

plev(z)
dlev(z)
qlev(p)
rlev(n)

Arguments

z

Vector of values where the cdf or pdf to be evaluated.

p

Vector of probabilities where the quantile function to be evaluated.

n

Number of random samples. If input is a vector, then the number generated is the length of it.

Value

plev returns cdf, dlev returns pdf, qlev returns quantiles, and rlev returns random samples.

Author(s)

Yili Hong

See Also

psev, dsev, qsev, rsev.

Examples

plev(c(2,3))
dlev(c(2,3))
qlev(0.1)
rlev(10)

Plot function for the class of "deglmx".

Description

Plots of dynamic covariates and fitting of the model in the class of "deglmx".

Usage

plotdeglmx(x, type)

Arguments

x

The fitting results of class "deglmx".

type

If type=1, plot the spline effect plot. If type=2, plot the fitting plots. If type is missing, plot all of them.

Author(s)

Yili Hong

See Also

deglmx

Examples

 data(Coatingenv)
 data(Coatingout)
 
 
 fit=deglmx(DAMAGE_Y~UV+RH+TEMP, data=Coatingout, dyn.data=Coatingenv, 
           id="SPEC_NUM", time="TIME", random=~TIME|SPEC_NUM, linear=TRUE, ytrend=-1,  
           splinetrend=c(-1, -1, -1), splinetype=c("Is", "Cs", "Is"), degree=c( 3, 3, 3), 
           knots=c(4, 4, 4),weights=NULL, subset=NULL,start=c(0.017,0.0013,-0.404,0.0176), 
           maxiter=10, method='BFGS')
 plotdeglmx(x=fit)
 plotdeglmx(x=fit, type=1)
 plotdeglmx(x=fit, type=1)

The Standard Smallest Extreme Value Distribution

Description

The cdf, pdf, quantile function, and random number generation for the standard smallest extreme value distribution.

Usage

psev(z)
dsev(z)
qsev(p)
rsev(n)

Arguments

z

Vector of values where the cdf or pdf to be evaluated.

p

Vector of probabilities where the quantile function to be evaluated.

n

Number of random samples. If input is a vector, then the number generated is the length of it.

Value

psev returns cdf, dsev returns pdf, qsev returns quantiles, and rsev returns random samples.

Author(s)

Yili Hong

See Also

plev, dlev, qlev, rlev.

Examples

psev(c(2,3))
dsev(c(2,3))
qsev(0.1)
rsev(10)

Shock Absorber Failure Data

Description

A data frame with 38 observations and 3 variables.

Usage

data(shock)

Format

Distance

a numeric vector

Mode

a factor with levels Censored Mode1 Mode2

Censor

a numeric vector

Source

Meeker, W. Q. and L. A. Escobar. Statistical Methods for Reliability Data. John Wiley & Sons, 1998.

Summaries of "Lifedata.MLE" Object

Description

These functions summaries a "Lifedata.MLE" object.

Usage

## S3 method for class 'Lifedata.MLE'
summary(object, ...)

Arguments

object

A "Lifedata.MLE" object.

...

Additional arguments.

Value

summary.Lifedata.MLE returns an object of class "summary.Lifedata.MLE", which is a list of

call

Component from obj.

coef

Vector of coefficients.

vcov

Variance-covariance matrix of coef

coefmat

Matrix contains mean, sd, 95\% lower CI and 95\% upper CI of coefficients.

min

Component from obj.

surv

Component from obj.

dat

Component from obj.

ori.coef

coef component in obj.

ori.vcov

vcov component in obj.

See Also

Lifedata.MLE

Testdata

Description

This dataset involves left truncation and right censoring.

Usage

data(testdata)

Format

A data frame with 710 observations on the following 9 variables.

age

a numeric vector

failure

a numeric vector

manufacture.year

a numeric vector

manufacturer

a factor with levels MA MB MC MD ME Other

cooling

a factor with levels FIFE NIFE NINE Unknown

insulation

a factor with levels d55 d65

truncation

a numeric vector

truncation.age

a numeric vector

group

a factor with levels MA_New MB_Old MC.ME.Other_New MC_Old MD_Old ME_Old Other_Old

Source

Hong, Y., W. Q. Meeker, and J. D. McCalley. Prediction of Remaining Life of Power Transformers Based on Left Truncated and Right Censored Lifetime Data . The Annals of Applied Statistics, 3(2), 857–879, 2009.