To achieve better product quality, the dual‐response surface has been widely used to simultaneously achieve targets for the mean and reduced variance. The general assumption is that the experimental data are normally distributed without censoring. However, reliability data are usually non‐normally distributed and censored. Consequently, the classical dual‐response surface method may not be suitable for handling reliability data. This study proposed a dual‐response surface method based on robust parameter design (RPD) for reliability data. First, a percentile lifetime and an interquartile range (IQR) were used for the location and dispersion effects, respectively. A two‐stage method was then developed to identify the effects of significant factors. During the first stage, the Boruta algorithm was employed for factor effect selection, and during the second stage, the least absolute shrinkage and selection operator (LASSO) dimension reduction method was used to determine the final significant factor effects. Finally, a modified standard particle swarm optimization (SPSO) algorithm was adopted to determine the optimal solution. The proposed method was demonstrated using an industrial thermostat experiment. Compared with other methods, the proposed method performed better over various warranty periods, particularly for the 10th percentile.