基於Weibull 產品的上記錄值樣本之壽命性能指標的計量值允收抽樣計劃

Variables acceptance sampling plan based on the lifetime performance index for Weibull products with upper record values

在生產過程中，允收抽樣計劃（acceptance sampling plan）是提供生產者和消費者針對一批產品達到兩者對其產品品質之要求的一項決策規則。而且壽命性能指標（lifetime performance index；LC）是被用來評估產品品質是否達到顧客所要求之水準的一項工具。另外，在某些現實狀況下，我們有興趣的是此次產品的壽命值是否比上一次產品的壽命值高，此種資料我們定義為記錄值。所以，在本文中主要探討假設產品壽命的上記錄值資料是來自於Weibull分配具有給定（或已知）的形狀參數β和未知的尺度參數γ，根據不同的允收品質水準（acceptance quality level；AQL）、不同的批容許不良率（lot tolerance percent defective；LTPD）、給定生產者風險和消費者風險的各種組合之下，基於壽命性能指標，我們推導出所要求檢驗的上記錄值之樣本大小m和其對應的臨界值0C並製成表格。最後，我們也列舉一實例來說明提出的計量值允收抽樣計劃是如何來評估產品是否被接受。

In the process of production, acceptance sampling plan is a decision rule that provides producers and consumers with a number of products that meet both of their product quality requirements. The lifetime performance index can be used to assess whether the product quality standard meets the level required by the customer. In addition, we need to record when the next products' life are higher than the previous products in some practical situations. Therefore, in this paper we assume that the data of the upper record values for lifetime of the products has a Weibull distribution with the given (or known) shape parameter β and unknown scale parameter γ and we derive the sample size of the upper record values m and the corresponding critical value 0 C and tabulated based on the lifetime performance index for various combinations of acceptance quality level (AQL), lot tolerance percent defective (LTPD), producer's risk, and consumer's risk. Finally, we use a practical example to illustrate how to implement this variables acceptance sampling plan for making a decision on product acceptance determination.