In this article, the stress–strength reliability (𝑆𝑆𝑅 = 𝑃 (𝑋 < 𝑌 )), where both stress 𝑋 and strength 𝑌 follow a new model called Marshall Olkin’s q extended generalized extreme value linear distribution (𝑀-𝑞) under type II progressive censoring, is investigated. The 𝑆𝑆𝑅 estimation is considered using both maximum likelihood estimation (𝑀𝐿𝐸) and Bayesian estimation (𝐵𝐸). Since the 𝑀𝐿𝐸 equations are extremely complex, a metaheuristic optimization technique called the Whale Optimization Algorithm (WOA) is utilized. The 𝐵𝐸 is considered for both informative and non informative cases using both Linex and square error loss functions. Temperature data from Sacramento and Los Angeles counties in California are also used to demonstrate the proposed statistical methodology, showing that the 𝑀-𝑞𝐺𝐸𝑉 𝐿 model provides a better fit than both 𝑞𝐺𝐸𝑉 𝐿 and 𝐺𝐸𝑉 𝐿 based on lower 𝑆𝐾, 𝐴𝐼𝐶, and 𝐵𝐼𝐶 values. Time series analysis, return level, and 𝑆𝑆𝑅 are applied to predict future temperatures, and the results consistently indicate higher predicted temperatures in Los Angeles than in Sacramento.