運用複式模擬法建構新製程個別值移動全距管制圖

Abstract

業界常使用Shewhart管制圖來監控製程，在建構Shewhart管制圖時，需要至少100筆以上的樣本資料才能準確地估計製程參數，以建構穩定之管制界限。但許多新開發產品之製程，因為生產初期只能生產少量產品進行測試，導致無法建構有效之Shewhart管制圖。本研究之主要目的是針對僅有少量資料的新製程，先利用Bootstrap模擬法來增生樣本量，再利用Bootstrap信賴區間中的Percentile Bootstrap(PB)與Biased-Corrected and Accelerated Percentile Bootstrap(BCa) 信賴區間來建構複式個別值與移動全距管制圖，並透過敏感度分析探討在不同參數組合下之Weibull分佈新製程時，本研究所提出之複式個別值移動全距管制圖之偵測能力。經由敏感度分析結果得知，以PB信賴區間法所建構之個別值移動全距管制圖偵測能力最佳。整體而言，符合Weibull分佈之新製程，不論製程之分佈是右偏、接近常態分佈或是呈現高狹峰，均可使用本研究提出之以PB信賴區間法所建構之個別值移動全距管制圖，其監控成效均會優於傳統的個別值移動全距管制圖和Q管制圖。

The most commonly used control chart in industry is Shewhart control chart, which requires at least 100 sample data to accurately estimate the parameters of process and then construct the Shewhart’s control chart. There are more and more start-up process now. Because the start-up process will only produce a small number of products for testing. There are not enough samples to construct the Shewhart’s control chart. The objective of this study is to utilize the Bootstrap simulation method and Bootstrap confidence intervals to construct the individual and moving range control charts for start-up process. The sensitivity analysis is utilized to demonstrate the effectiveness of the proposed method. When the process is stable, the result indicates that under various values of Weibull parameters and sample sizes the proposed bootstrap control charts using PB method performed better than the traditional individual-moving range control charts and Q chart in terms of the average run length. When the mean of process is shifted, the proposed bootstrap control chart is superior to the traditional individual-moving range control chart and Q chart. The bootstrap control chart constructed by the PB confidence interval is better than all the other control charts no matter the process distribution is right skewed、near normal distribution or raving high peak pattern.