Reliability Analysis of Cyclic Accelerated Life Test Data Using Log-Location-Scale Family of Distributions Under Censoring With Application to Solder Joint Data

Accelerated life testing is widely employed due to the high cost involved in testing high-quality products under normal operating conditions. For products exposed to continuously fluctuating stress in the working environment, cyclic stress tests become necessary. The Coffin–Manson model is commonly used when product failure is solely attributed to temperature changes (<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\Delta T$</tex-math></inline-formula>). However, this assumption does not always hold in many practical situations. The Norris–Landzberg model, which considers both maximum temperature and cyclic change frequency, offers much flexibility in modeling fatigue life due to cyclic temperature fluctuations. Several studies have been conducted based on the Norris–Landzberg model. However, using the multiple linear regression method without any distributional assumption may fail to provide satisfactory inferential results. This article assumes the log-location-scale family of distributions and then shows that the weighted least-squares method based on order statistics of failure times yields the best linear unbiased estimators (BLUEs) of parameters based on complete as well as Type-II censored data. We then study some properties of these BLUEs using both theory and Monte Carlo simulations. Next, we present an illustrative example involving solder joint data to demonstrate the model and the associate inferential results developed here. Finally, the optimal design procedure is discussed.