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。 ;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.
