製程能力指標估計式的準確度評估

Abstract

製程能力指標（Process Capability Index）在品質管理這個領域中是一個已經普及並且好用的工具之一。工程人員可藉著在製程中得出的指標數值瞭解一製程產出符合預設規格的能力，進而發現製程的問題，達成有效監控製程、改善品值的目標。這個領域從1986年發展至今已有許多不同的製程能力指標相繼被提出，然而在準確度評估的議題中，大部分的研究並沒有提出完整的探討。因此本研究將在假設製程遵循常態分配並且規格區為對稱的前題下，整理四個最常用的指標估計式的統計特性，並且對各指標估計式在不同型態製程中之準確度表現作一完整的計算及分析，提出如相對誤差、相對均方誤以及 a % 信賴度之相對誤差等表格，讓使用者可對照並瞭解在實際製程所得出的指標估計值的精準程度，以達到實用的目標。

The process capability indices have been widely used in the manufacturing industry to provide numerical measures on process performance. The most useful four indices are Cp, Cpk, Cpm, and Cpmk. They combine two important factors- process spread and process centering in one number and make it easy to judge whether a process is acceptable. In this research the statistical properties of the four natural estimated indices will be presented, and the accuracy analysis of the estimated indices will be analyzed by the computational results using relative bias (BIASR), relative mean square error (MSER), and □-level confidence relative error (CRER). The computational results are tabled, and the investigation is useful to the practitioners in determining the sample sizes required in their applications for the estimations good to the desired accuracy. 英文摘要 ....................................................II 誌謝 ......................................................III LIST OF CONTENT ............................................IV LIST OF TABLES .............................................VI LIST OF FIGURES ............................................XI CHAPTER 1 INTRODUCTION .....................................1 CHAPTER 2 THE INDICES Cp and Ca ............................3 2.1 Definition .........................................3 2.2 The Estimation of Cp ...............................4 2.3 The Performance of .................................5 2.4 The Estimation of Ca ...............................7 2.5 The Performance of .................................8 2.6 Conclusion ........................................10 CHAPTER 3 THE INDEX Cpk ...................................24 3.1 Definition ........................................24 3.2 The Estimation of Cpk .............................25 3.3 The Accuracy of ...................................28 3.4 Conclusion ........................................31 CHAPTER 4 THE NDEX Cpm ....................................43 4.1 Definition ........................................43 4.2 The Estimation of Cpm .............................44 4.3 The Reliability of ................................46 4.4 Conclusion ........................................48 CHAPTER 5 THE INDEX Cpmk ..................................63 5.1 Definition ........................................63 5.2 Estimation of Cpmk ................................64 5.3 The Probability Density Function of ...............66 5.3 Accuracy of .......................................66 5.4 Conclusion ........................................67 REFERENCE ..................................................75