基於排序集合樣本對Weibull 產品的壽命性能指標做貝氏評估

Bayesian Evaluation for the Lifetime Performance Index of Weibull Products Based on the Ranked Set Sample

製程能力指標（Process Capability Indices; PCIs）常為一個有效且方便的品質性能評估工具，並被用來評估產品是否達到業者所要求水準，而望大型製程能力指標（或壽命性能指標）（LC）是其中一個靈活且有效的指標，用來評估產品性能。事實上，許多產品之壽命並非來自常態分配，因此我們假設壽命來自Weibull分配且取排序集合樣本對壽命性能指標（LC）做貝氏評估，其中L是給定（或已知）的下規格界限（lower specification limit）。接著，我們也發展出一套貝氏檢定程序。最後，我們列舉一個實例，在給定顯著水準α之下，針對符合Weibull分配的產品來說明此貝氏檢定程序並且提供業者檢驗產品是否符合要求水準。

Process Capability Indices (PCIs) are often an effective and convenient quality performance assessment tool and are used to assess whether the product meets the required level of the industry, while the larger-the-better type process capability index (or lifetime performance index) ( L C ) is one of the flexible and effective index and is used to evaluate product performance. In fact, the lifetime of many products is not from the normal distribution, so we assume that the lifetime of the products has the Weibull distribution and use the ranked set sample to do Bayesian assessment for the lifetime performance index ( L C ), where L is the given (or known) lower specification limit. Then, we also developed a set of Bayesian test procedure. Finally, we illustrate an example to explain this Bayesian test procedure for the Weibull product under a given significance level α and provide the manufacturer with a test of whether the product meets the required level.