Statistical Adjustment Methods for Sample Size Reduction in Guided Missile Reliability Demonstration

Purpose: This study re-examines the conventional 11-shot zero-failure criterion used in the Ammunition Stockpile Reliability Program (ASRP) for guided missiles. The objective is to determine whether the sample size in the 2nd-4th ASRP tests can be reduced while still guaranteeing a reliability level of 0.8 with a confidence level of 0.9.<br/>Methods: First, the 11-shot requirement is derived from a binomial reliability demonstration test framework. Subsequently, three complementary approaches are proposed: (1) a sequential testing plan, (2) a Bayesian updating scheme, and (3) a calibration-factor method.<br/>Results: Numerical analysis indicates that, given 11 zero-failure shots in the 1st phase, a 2nd-phase plan with up to seven shots can achieve a posterior probability P(p≥0.8) of approximately 0.91. Extending the Bayesian updating approach to the 3rd-4th phases shows that three-shot tests per phase can maintain the target confidence level when combined with prior information. The calibration factor (approximately 1.1 for seven shots) restores the reliability lower bound to a level comparable to that of the original 11-shot criterion.<br/>Conclusion: The proposed framework demonstrates that guided-missile ASRP testing can reduce live-round consumption in later phases without sacrificing statistical rigor. Furthermore, it provides a practical basis for redesigning reliability test plans that better balance resource constraints with required assurance levels.