Dialectric Breakdown Strength

Keywords: two-way analysis of variance, nonlinear regression, gamma regression, dispersion modelling

Description

These data are the result of a study involving the analysis of performance degradation data from accelerated tests. The response variable is dialectric breakdown strength in kilo-volts, and the predictor variables are time in weeks and temperature in degrees Celcius. The study can be viewed as an 8 by 4 factorial experiment.


	Variable		Description

	Strength		Dialectric breakdown strength in kilovolts
	Time		Duration of testing in weeks (8 levels)
	Temperature		Temperature in degrees Celsius (4 levels)

Download

Data File (tab-delimited text)

Source

Nelson, W. (1981). Analysis of performance-degradation data. IEEE Transactions on Reliability, 2, R-30, 149-155.

NIST Standard Reference Data Sets.

Analysis

Co-plot (10507 bytes)

The reference analysis according to NIST gives

log[Stength] = b1 - b2*Time * exp[-b3*Temperature]  +  e

            Certified Values
        Parameter     Standard Deviation
b1   2.5906836021E+00  1.9149996413E-02
b2   5.6177717026E-09  6.1124096540E-09
b3  -5.7701013174E-02  3.9572366543E-03

The data is actually slightly better modelled as gamma or Poisson-gamma rather than log-normal:

> dglm(log(Strength)~ordered(Time)*ordered(Temperature),family=tweedie(var.power=0,link.power=1),method="ml")$m2loglik+2*sum(log(Strength))
[1] 309.5124
> dglm(Strength~ordered(Time)*ordered(Temperature),family=tweedie(var.power=2,link.power=0),method="ml")$m2loglik
[1] 309.2368
> dglm(Strength~ordered(Time)*ordered(Temperature),family=tweedie(var.power=1.8,link.power=0),method="ml")$m2loglik
[1] 303.5884