Statistical Testing for Assessing Lifetime Performance index of the Rayleigh Lifetime Products

Rayleigh壽命產品的壽命績效指標評估之統計檢定

10.29977/JCIIE.200811.0001

李汶娟(Wen-Chuan Lee)

商品績效 ； 型Ⅱ多重設限樣本 ； Rayleigh分配 ； 均勻最小變異數不偏估計量 ； 檢定程序 ； Product performance ； type Ⅱ multiply censored sample ； Rayleigh distribution ； uniformly minimum variance unbiased estimator ； testing procedure

工業工程學刊

25卷6期（2008 / 11 / 01）

433 - 445

英文

在服務（或製造）業中製程能力指標就是用來衡量製程產出商品之品質是否達到規格要求水準。而且壽命績效指標(lifetime performance index)（或望大型製程能力指標(larger-the-better process capability index)）C(下标 L)常常被用來當作測量商品績效的標準，其中L是已知下規格界限。因此，這個研究利用來自Rayleigh分配的型Ⅱ多重設限樣本來建立一個C(下标 L)的均勻最小變異數不偏估計量(uniformly minimum variance unbiased estimator; UMVUE)。這個C(下标 L)的UMVUE被利用去發展一個具有已知L的新假設檢定。最後，我們給一個關於滾珠軸承的耐久力檢定的例子去說明在給定的顯著水準下此檢定程序如何進行商品的績效評估。而且透過此檢定程序，業者也可以了解所提供的商品壽命是否達到規格要求，並藉此檢定程序來提升商品品質，以更能符合顧客的需求。

In the service (or manufacturing) industries, process capability indices (PCIs) are utilized to assess whether product quality meets the required level. And the lifetime performance index (or larger-the-better process capability index) C(subscript L) is frequently used as a means of measuring product performance, where L is the lower specification limit. Hence, this study constructs an uniformly minimum variance unbiased estimator (UMVUE) of C(subscript L) based on the type Ⅱ multiply censored sample from the Rayleigh distribution. The UMVUE of CL is then utilized to develop a novel hypothesis testing procedure in the condition of known L. Finally, we give an example regarding the ball bearing in endurance test to illustrate the use of the testing procedure under given significance level. Moreover, the purchasers can then employ the testing procedure to determine whether the product performance adheres to the required level. Manufacturers can also utilize this testing procedure to improve the process capability.

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