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利用相互删失方法联合估计系统与部件可靠性AI 解读

Let $F$ denote the life distribution of a coherent structure of independent components. Suppose that we have a sample of independent systems, all having the same structure. Each system is continuously observed until it fails. For every component in each system, either a failure time or a censoring time is recorded. A failure time is recorded if the component fails before or at the time of system failure; otherwise a censoring time is recorded. We introduce a method for…

指数性与平均剩余寿命趋势转折的检验AI 解读

Given that an item is of age $t$, the expected value of the random remaining life is called the mean residual life (MRL) at age $t$. We propose two new nonparametric classes of life distributions for modeling aging based on MRL. The first class of life distributions consists of those with "increasing initially, then decreasing mean residual life" (IDMRL). The IDMRL class models aging that is initially beneficial, then adverse. The second class, "decreasing, then increasing…

用于刻画老化的一类寿命分布AI 解读

We introduce a new better than used of age t 0 (NBU-t 0) class of life distributions, where the survival probability at age 0 is greater than or equal to the conditional survival probability at specified age t 0 > 0. The dual class of new worse than used of age t 0 (NWU-t 0) life distributions is defined by reversing the direction of inequality. Preservation and nonpreservation properties of the two classes under various reliability operations are presented. We also show how…

随机变量的负关联及其应用AI 解读

Random variables, $X_1, \cdots, X_k$ are said to be negatively associated (NA) if for every pair of disjoint subsets $A_1, A_2$ of $\{1, 2, \cdots, k\}, \operatorname{Cov}\lbrack f(X_1, i \in A_1), g(X_j, j \in A_2) \rbrack \leq 0$, for all nondecreasing functions $f, g$. The basic properties of negative association are derived. Especially useful is the property that nondecreasing functions of mutually exclusive subsets of NA random variables are NA. This property is shown…

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多元指数分布的参数估计AI 解读

Parameter estimation for a (k + 1)-parameter version of the k-dimensional multivariate exponential distribution (MVE) of Marshall and Olkin is investigated. Although not absolutely continuous with respect to Lebesgue measure, a density with respect to a dominating measure is specified, enabling derivation of a likelihood function and likelihood equations. In general, the likelihood equations, not solvable explicitly, have a unique root which is the maximum likelihood…

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平均剩余寿命的检验AI 解读

In this paper we develop tests for alternatives representing decreasing mean residual life and the property ‘new better than used in expectation’. The decreasing mean residual life test statistic, V*, is new, and critical constants and a large-sample approximation are obtained to make the test readily applicable. The new better than used in expectation statistic, K*, is shown to be equivalent to the total time on test statistic; the latter is ordinarily viewed as a test…

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平均剩余寿命的检验AI 解读

In this paper we develop tests for alternatives representing decreasing mean residual life and the property ‘new better than used in expectation’. The decreasing mean residual life test statistic, V*, is new, and critical constants and a large-sample approximation are obtained to make the test readily applicable. The new better than used in expectation statistic, K*, is shown to be equivalent to the total time on test statistic; the latter is ordinarily viewed as a test…

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