Confidence Intervals in Optimized Response Surface Designs for Accelerated Lifetime Testing

Accelerated Lifetime Testing (ALT) evaluates product reliability under increased loads to expedite lifetime assessments and reduce costs. Using Response Surface Methodology (RSM) with Design of Experiments (DOE) principles enables robust multivariate exploration and modeling but faces challenges like increased prediction variance, just as in one-dimensional W¨ohler models, when extrapolating to field level. Here optimized response surface designs (RSDs) are discussed that minimize extrapolation variance by strategically relocating runs while balancing model accuracy, size and test time. This paper examines Confidence Interval (CI) behavior in ALT optimized RSDs. A synthetic lifetime model generates testing times for RSDs, facilitating parameter estimation and variance analysis under efficiency-driven modifications. Numerical evaluations reveal CI properties of model responses, complemented by analysis of a central composite design (CCD) dataset to assess the impact of design manipulations. By integrating CI behavior with extrapolation variance and parameter deviations, this study advances the understanding of efficient Lifetime-RSDs in ALT.

Keywords: DOE, RSD, ALT, Reliability, Confidence interval, Weibull-GLM.