Application of Hyper-geometric Distribution in Reliability Qualification Test and Evaluation of Binomial Products

FENG Lei; XIE Long; LI Yugang; LIU Xi; HE Xuan

doi:10.7643/issn.1672-9242.2026.07.007

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Equipment Environmental Engineering ›› 2026, Vol. 23 ›› Issue (7) : 63-69. DOI: 10.7643/issn.1672-9242.2026.07.007

Weapons Equipment

Application of Hyper-geometric Distribution in Reliability Qualification Test and Evaluation of Binomial Products

FENG Lei, XIE Long, LI Yugang, LIU Xi^*, HE Xuan

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Abstract

The work aims to study the application of hyper-geometric distribution in the reliability qualification test of binomial products to address the issues regarding the unscientific formulation of reliability qualification test plans and inaccurate reliability evaluation for current binomial products such as missiles. Based on the hyper-geometric distribution, missile reliability qualification test plans were formulated to evaluate the one-sided confidence lower bound of reliability. Additionally, the producer's risk and consumer's risk for each test plan were calculated and compared with test plans based on the binomial distribution and their corresponding reliability evaluation results. The results indicated that, given the same maximum allowable number of failures, the sample size required by the hyper-geometric distribution test plans was consistently smaller than that of the binomial distribution, with a maximum reduction of 16%. When considering only the consumer's risk, the producer's risk associated with the hyper-geometric distribution test plans was lower than that of the binomial distribution; specifically, plan 4 showed a 13.16% reduction in producer's risk. Furthermore, the one-sided confidence lower bounds for reliability evaluated based on the hyper-geometric distribution were consistently higher than the binomial distribution evaluation results, converging to the binomial distribution results as the sample size increased. This study provides a more scientific methodology for the reliability qualification and production qualification of other binomial products.

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hyper-geometric distribution / binomial distribution / binomial products / reliability qualification test / risk of producer / risk of consumer

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FENG Lei, XIE Long, LI Yugang, LIU Xi, HE Xuan. Application of Hyper-geometric Distribution in Reliability Qualification Test and Evaluation of Binomial Products[J]. Equipment Environmental Engineering. 2026, 23(7): 63-69 https://doi.org/10.7643/issn.1672-9242.2026.07.007

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