关键词: 产品可靠度, 排序集抽样, 极大似然估计量, 相对效率, Fisher信息

Abstract: In order to improve the estimation efficiency of the product reliability for exponential distribution, this paper considers the maximum likelihood estimator(MLE)based on ranked set sampling. The proposed MLE is shown to have existence, uniqueness and asymptotic normality, and its asymptotic variance is obtained by the Fisher information of ranked set sampte. However, the root of likelihood equation cannot be written in closed form. Therefore, the modified MLE having closed from is proposed using the technique replaced some terms in the likelihood equation by their expectations. The values of asymptotic relative efficiency and simulated relative efficiency show that the proposed MLE and modified MLE are always more efficient than the MLE using simple random sampling. Finally, the proposed method is applied to a clinical study on metastatic renal carcinoma.

Key words: product reliability, ranked set sampling, maximum likelihood estimator, relative efficiency, Fisher information