ConclusionsCovariates (e.g., temperature, humidity, and electric current) are those factors affecting the outcome under study. Practitioners, such as reliability engineers, are often faced with measurement errors in covariates and/or unimportant covariates when collecting data on important variables. Such errors and unimportant covariates usually lead to low-quality estimation results and significantly increase computational efforts. To make the best use of data, it is essential to reduce the negative impact of measurement errors in covariates and eliminate those unimportant covariates, so that an adequate model with accurate and precise model parameter estimates can be obtained. A typical example involving measurement errors in covariates is accelerated life testing (ALT). Even in a laboratory testing environment, the exact measurements of covariates cannot be guaranteed. Moreover, the test conditions may not be perfectly controlled, and bringing the conditions back to the required levels may take some time. Consequently, these affect the reliability estimation for a product under investigation. Considering failure time data collected from the field, the negative impact of measurement errors in covariates is even more significant. Besides a number of known accelerating variables, it is beneficial to monitor some other conditions that might also be influential on the product's reliability. However, it is often difficult to tell which variables are actually important prior to data analysis. To overcome this challenge, variable selection needs to be considered in order to reduce the model complexity. In this work, both Weibull and Lognormal regression models are studied, for the first time, for modeling ALT data with measurement errors in covariates. The numerical results validate the proposed method for handling measurement errors in covariates and for eliminating unimportant covariates. Beyond ALT, the proposed method can be used to handle other types of data, such as healthcare data, where some environmental factors and human-related characteristics cannot be measured exactly.