Prior Distribution Screening and Risk Calculation for Reliability Qualification Test of the Exponential Product

This paper investigates the selection of prior distributions and risk calculations for the reliability qualification test (RQT) of exponential products under multiple imprecise prior information. By integrating historical data, expert judgments, and parameters from similar systems, a method based on the maximum entropy principle is proposed to transform diverse prior information into constrained optimization problems. The method employs Particle Swarm Optimization (PSO) to search for optimal test plans that minimize trial costs while ensuring reliability. Through case studies and simulation validation, the proposed approach shows significant improvements in reducing test time and failure counts compared to traditional methods. The research highlights the effectiveness of handling complex prior information and provides a robust framework for reliability test planning in engineering applications. Simultaneously, difference analysis based on three types of prior distributions is conducted, providing valuable insights for parameter estimation and distribution selection in future studies.