Power approximations for failure‐time regression models

• Published in: Quality and reliability engineering international 2019-10, Vol.35 (6), p.1666-1675
• Main Authors: Johnson, Thomas H., Medlin, Rebecca M., Freeman, Laura
• Format: Article
• Language: English
• Subjects: censored data; Computer simulation; Design of experiments; Experiments; Likelihood ratio; Mathematical analysis; power analysis; Product reliability; Regression analysis; Regression models; reliability; Reliability aspects; sample size determination; Statistical analysis; Statistical methods
• ISSN: 0748-8017; 1099-1638
• DOI: 10.1002/qre.2467

Reliability experiments determine which factors drive product reliability. Often, the reliability or lifetime data collected in these experiments tend to follow distinctly non‐normal distributions and typically include censored observations. The experimental design should accommodate the skewed nature of the response and allow for censored observations, which occur when products do not fail within the allotted test time. To account for these design and analysis considerations, Monte‐Carlo simulations are frequently used to evaluate experimental design properties. Simulation provides accurate power calculations as a function of sample size, allowing researchers to determine adequate sample sizes at each level of the treatment. However, simulation may be inefficient for comparing multiple experiments of various sizes. We present a closed‐form approach for calculating power, based on the noncentral chi‐squared approximation to the distribution of the likelihood ratio statistic for large samples. The solution can be used to rapidly compare multiple designs and accommodate trade‐space analyses between power, effect size, model formulation, sample size, censoring rates, and design type. To demonstrate the efficiency of our approach, we provide a comparison to estimates from simulation.