ABSTRACT
Design of experiments is used extensively to achieve quality, but applications to reliability are less common. This is due to a number of reasons but mainly to the fact that the normal distribution, which underlies most experimental designs, is not a reasonable distribution for lifetimes. In this review article, we describe the problem of using designed experiments to model the distribution of lifetimes and, in particular, how the lifetimes depend on a set of predictor variables. We discuss a number of examples and present results using the most common statistical software packages.
Notes
Scale = 0.303
Weibull distribution
Loglik(model) = −30.8 Loglik(intercept only) = −37.6
Chisq = 13.73 on 3 degrees of freedom, p = 0.0033
Number of Newton-Raphson Iterations: 8
n = 8
Scale = 0.408
Weibull distribution
Loglik(model) = −611.9 Loglik(intercept only) = −670.2
Chisq = 116.56 on 3 degrees of freedom, p = 0
Number of Newton-Raphson Iterations: 6
n = 90
Scale = 0.375
Scale = 0.402
Scale = 0.364
Weibull distribution
Loglik(model) = −244.2 Loglik(intercept only) = −254.5
Chisq = 20.57 on 2 degrees of freedom, p = 3.4e-05
Number of Newton-Raphson Iterations: 5
n = 64