Experiments for Reliability Achievement

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.

KEYWORDS:

• censoring
• design of experiments
• Weibull distribution
• Weibull probability plots
• Weibull regression

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