在現實生活中,我們常會遇到無法取得完整樣本的情況,例如因為時間、成本的限制或人為疏失而不能獲得所有的觀察值,而在實際應用上,可靠度分析或存活分析的壽命資料就常有這種問題產生,面對此種不完整資料,我們無法利用一般應用於完整樣本的統計方法來做推論分析。因此,我們所要討論的即為多重型Ⅱ設限樣本的統計分析方法。 在工業生產中許多產品的故障率函數會呈現浴缸型(bathtub shape)的曲線模式,例如電子、電鍍及機械等的產品。另外生物的壽命模式亦是呈現此種曲線。事實上,在產品生產完之後,我們通常會使用預燒(burn-in)來改善產品的品質,因為預燒的主要目的是提早除去初期會故障的零件(零組件、半成品及成品),進而提高產品的可靠度,而這些經維修後的產品,其壽命模式會呈現浴缸型的故障率曲線模式。因此,我們在描述這種情況時,利用具有浴缸型故障率函數之雙參數分配會比Weibull分配,Extreme value分配及Normal分配等等來得適合。所以,本文的主要研究目的為探討利用產品壽命來自於一個具有浴缸型或遞增的故障率函數(failure rate function)的壽命分配之多重型II設限樣本對其形狀參數提出最適當的檢定及區間估計。 在本篇文章中,我們可以發現當其樞紐量檢定力較高的情況下,則所對應之信賴區間長度則較短,而未加權樞紐量與加權樞紐量在不同的設限及不同的總樣本數下,大部分以第4、5及11個樞紐量表現較好,但加權樞紐量不只在檢定力和區間長度的表現又較未加權樞紐量好,因此我們可以提供給讀者新的樞紐量,使得能較為準確的去估計形狀參數。
In real life, we often encounter the situation of getting censored sample, for example, because of the restriction of time and cost or human mistake, we can’t get all observations. In practice, there are often these issues concerned in the data of the reliability or survival. In face of this censored data, we can’t apply traditional statistical inference to perform our analysis on it. Therefore, what we discuss in this paper is statistical inference with multiply type Ⅱ censored sample. In this paper, we discuss the lifetime distribution with the shape parameter of the bathtub-shaped or increasing failure rate function under the multiply type Ⅱ censored sample. First we provide 12 unweighted and weighted pivotal quantities to test the shape parameter of the bathtub-shaped or increasing failure rate function and establish confidence interval of the shape parameter under the multiply type Ⅱ censored sample. Secondly, we also find the best test statistic based on their most power of test among all test statistics. In addition, we obtain the best pivotal quantities with the shortest tolerance length. Finally, we give two examples and the Monte Carlo simulation to assess the behavior (including higher power and more shorter length of confidence interval) of these pivotal quantities for testing null hypotheses under given significance level and establishing confidence interval of shape parameter under the given confidence coefficient.