基於最大期望算法之分析陶瓷基板機器暗裂破片率

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黃培凱(Pei-Kai Huang) 查詢紙本館藏

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資訊工程學系

論文名稱

基於最大期望算法之分析陶瓷基板機器暗裂破片率
(Analyze the micro-crack rate of PCB based on Expectation-Maximization algorithm)

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摘要(中)

針對陶瓷基板(Ceramic PCB, Ceramic Substrate)交織生產的複雜狀況，以及生產過程中暗裂破片責任歸咎與觀測數據失真問題：如破片產生不一定是由單一機器造成，可能是多臺機器互相作用之結果；不明顯的暗裂破片容易混入良片中進入後續生產以及機器限制使得某些機器不能及時觀測產出結果，這些都導致了生產數據與實際存在一定偏差。以上原因皆導致了維護人員在定位異常機器存在困難，而在定位異常機器期間，異常機器又會持續生產造成更多破片。
針對上述問題，本文收集連續半年因暗裂導致破片的生產資料，設計相應的似然函數(Likelihood Function)並使用最大期望值算法(Expectation-Maximization Algorithm)求解，評估分析機器暗裂破片率。將分析所得的機器暗裂破片率，代入Markov Chain與實際批次生產結果相比較，其平均誤差為6.705%。在22987個生產批次中，誤差在6%以内的超過70%，誤差在8%以内的超過80%，證明分析所得的機器暗裂破片率是準確的。此外，可將分析所得的機器暗裂破片率與機器異常維護資料結合分析。通過在機器在高暗裂破片率期間確切有發生異常維修，佐證分析所得的機器暗裂破片是符合實際生產表現的。

摘要(英)

In view of the complex situation of interwoven production of ceramic substrates, and the blame of micro-crack broken pieces and the distortion of observation data in the production process，that is，broken pieces may be caused by multiple machines more than by a single machine; unobvious micro-crack broken pieces are easily mixed into good pieces for subsequent production and some machines fail to observe the production results promptly due to machine limitations. All of these result in some deviation between production data and practice. All these reasons lead to the difficulty for maintenance personnel in locating the abnormal machine, and during which time, the abnormal machine will continue to produce more broken pieces.
To solve the above problems, this paper collected the production data of broken pieces caused by micro-crack in six months, designed the corresponding likelihood function and used the maximum expectation algorithm to solve it for evaluation and analysis of the micro-crack rate of the machine. We compare the actual production rate and the production rate obtained by analysis with Markov Chain. The average error was 6.705% by comparing the rate with the actual batch production results. In 22,987 production batches, the error within 6% was over 70% and within 8% over 80%. The results showed that the micro-crack rate of the machine obtained by analysis was accurate. In addition, the micro- crack rate can be analyzed again by combining with the abnormal maintenance data of the machine. Through the actual abnormal maintenance of the machine during the period of high micro-crack rate, it proved that the micro-crack broken pieces of the machine obtained by the analysis were consistent in the actual production performance.

關鍵字(中)

★ 陶瓷基板
★ 暗裂破片
★ 似然函數
★ 最大期望值算法

關鍵字(英)

★ Ceramic substrates
★ Micro-crack broken pieces
★ Likelihood function
★ EM

論文目次

摘要 i
Abstract ii
致謝 iii
目錄 iv
圖目錄 vi
表目錄 viii
第一章緒論 1
1-1 研究背景 1
1-2 研究動機與目的 2
1-3 研究貢獻 3
1-4 論文架構 3
第二章背景知識 4
2-1 生產背景 4
2-2-1 GBOM與LOT 4
2-2-2 破片成因 5
2-2-3 暗裂問題 5
2-2-4 隧道問題 6
2-2最大期望值算法 7
第三章問題定義與研究 8
3-1 目標式定義 8
3-2 似然函數設計 9
3-3 破片責任分擔 10
3-4 預估暗裂妥善率 11
3-5 評估改良 12
3-6 生產資訊前處理 13
第四章實驗設計 18
4-1 實驗流程 18
4-2 實驗數據 19
4-3 EM預估分析求平均暗裂妥善率 19
4-4 精確時段内分析 20
4-5 驗證機器暗裂妥善率 20
4-6 EM不同評估方式效能之比較 22
第五章實驗結果與分析 23
5-1 Markov Chain 驗證結果 23
5-2 暗裂妥善率趨勢與維修資料 24
5-3 EM不同評估方式效能 26
第六章結論與未來展望 29
6-1 結論 29
6-2 未來展望 29
參考文獻 31
附錄 33
1.Symbols Definition and Problem Description 33
2.Problem Objective 36
3.Solution Methodology 37
4.Likelihood 38
5.Cost function 39
6.Theta’, the next iteration answer 42

參考文獻

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指導教授

梁德容(Deron Liang)

審核日期

2019-7-9

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