雙邊規格Cpk之多條生產線製程信賴下界與允收抽樣計畫

Abstract

製程能力指標常被用來衡量製程重複製造產品符合規格的能力，不僅是提供品質保證的工具，也是提供品質改善方面的一個方針。製程能力針對單條生產線的製程已被廣泛研究，因此，本研究探討了多條生產線的製程能力指標CpkM。我們探討CpkMhat的常態近似分配和信賴下界。透過資料模擬來檢驗泰勒展開後近似的常態分配與真實分配的準確性，且計算信賴下界的涵蓋率，並做出修正。此外，本研究提出CpkM的允收抽樣計畫，我們列出在不同生產者風險及消費者風險下，所需抽樣之產品樣本數及產品允收臨界值。工程師或實務界可依據本篇研究之成果，來決定多條生產線製程下，所需之抽樣產品樣本數及產品允收臨界值，並做出可靠有效之決策。

Process capability indices (PCIs) have been proposed in the manufacturing industry to provide numerical measures in process capability, which are effective tools for quality assurance and guidance for process improvement. Methods for measuring yield for processes with single manufacturing line have been investigated extensively, but comparatively neglected for processes with multiple independent manufacturing lines. Therefore, in this thesis, we consider the process capability index CpkM with multiple independent manufacturing lines. We explore the approximate normal distribution of CpkMhat by Taylor expansion approximate and lower confidence bound. We verify the accuracy between the Taylor expansion approximate normal distribution and the simulated distribution through simulation data. The lower confidence bound is calculated, and make corrections. In addition, we consider the product acceptance sampling plan based on CpkM to deal with product acceptance determination for processes with multiple independent manufacturing lines. We tabulate the required sample size and the corresponding critical acceptance value for various vendor’s risks with the capability requirement average requirement average quality level (AQL) and lot tolerance percent defective (LTPD). The computational results are useful to the practitioners for their in-plant applications.