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指定使用年龄下“新品优于旧品”的生存曲线估计AI 解读

Suppose that the survival function S of a random variable X is a member of the new-better-than-used-at-age-t 0 (NBU-{t 0}) class. As defined by Hollander, Park, and Proschan (1986), S must satisfy the condition S(x + t 0) ≤ S(x)S(t 0) for all x ≥ 0. Given a random sample from S, an estimator is sought that itself belongs to the NBU-{t 0} class and has the same asymptotic optimality properties as the empirical survival curve S n . The estimator S of S, given implicitly by…

可靠性分析中一类多项分布的最大似然估计AI 解读

Summary Let Xi, i = 1, …,k be independent Bernoulli variables, with Xi ~ B(1, pi). Let Y = σ Xi, and consider a multinomial experiment based on n independent, identically distributed observations Y 1,…, Yn. This model is identifiable in the ordered parameter vector (p (1),…, p (k)), where p(i -1) ≤ p(i), and arises in reliability experiments in which k components in parallel have potentially different probabilities of failure. The family of multinomial distributions with the…