An Alternative Method for Prediction Intervals of an Order Observation from One-Parameter Exponential Distribution Based on Censored Sample

於設限資料下對具有一個參數的指數分配求次序觀測值的預測區間

吳聰慧(Tsong-Huey Wu) ； 陸海林(Hai-Lin Lu)

《工業工程學刊》 23卷1期 (2006/01) Pp. 80-90

https://doi.org/10.29977/JCIIE.200601.0008

摘要

本文對於具有一個參數的指數分配中，樣本數為n的多元型二設限資料，提出適當的基準量，更精確地推估未來第j個元件次序觀測值的預測區間。另外，在相同之設限樣本下，討論其近似預測區間，最佳線性不偏估計，與近似最大概似估計。在實際應用上，對於壽命試驗的耐用時間，可以預測出系統大小為n之第j個元件的故障時間。最後，並以兩個實際例子說明。

關鍵字

基準量 ； 多元型二設限樣本 ； 指數分配 ； 近似最大概似估計

並列摘要

In the paper, we construct a more precise prediction interval of the jth order observation from some pivotal quantities for the one-parameter exponential distribution based on Type Ⅱ censored samples. Our method is more general in the sense that it can be applied to any data scheme. From the illustrated examples and the results of simulation, the performances of our method are better than the widely-used methods of Mann and Grubbs [12] and Kaminsky and Nelson [5,6]. For further study, our method is easily applied to other location and scale family distributions.

並列關鍵字

prediction intervals ； order statistics ； Monte Carlo simulation ； one-parameter exponential distribution

參考文獻

Balakrishnan, N.,C. A. Cohen(1991).Order statistics and inference: estimation methods.(Academic Press, Inc.).

Balasubramanian, K.,N. Balakrishnan(1992).Estimation for one-and two-parameter exponential distributions under multiple type-Ⅱ censoring.Statistische Hefte.(Statistische Hefte).

Fernandez, A. J.(2000).On maximum likehood prediction based on Type II doubly censored exponential data.Metrika.(Metrika).

Grubbs, F. E.(1971).Approximate fiducial bounds for the reliability of a series system for which each component has an exponential time-to-fail distribution.Technometrics.13,865-871.

Kaminsky, K.S.,P. I. Nelson(1974).Prediction intervals for the exponential distribution using subsets of the data.Technometrics.16,57-59.