X ̅-R管制圖誤判機率之模擬研究

The Simulation Study of the False Alarm Rates for X ̅-R Control Chart

范玉如(Yu-Ju Fan)

指導教授 ： 沈群英

健行科技大學/商管學院/企業管理系碩士班/碩士(2018年)

摘要

統計製程管制 (Statistical Process Control, SPC)為工業界最常使用的工業統計技術，其主要的功能為利用SPC管制圖判斷製程是否持續維持在穏定狀態，但有其誤判機率過高的缺點，造成業界使用上極大的困擾。
本研究係以五顆骰子總點數所形成之近似常態分配群組作為樣本，將其導入取樣數為5的「平均值(X ̅)-全距(R)管制圖」，分別以電腦模擬數值分析及擲骰實驗的方式，進行其誤判機率之量化計算。
在電腦模擬數值分析之結果顯示，5次擲骰平均值確為極近似常態分配，然其全距則為較左傾之非對稱鐘型分配，針對「點超出管制界限」、「連續7點位於管制中心的單側」及「連續7點依次上升/下降」等3項判讀法則，X ̅-R管制圖每次判讀的總誤判機率為3.646118%。
本研究另以1,000筆5次擲骰數據，代入X ̅-R管制圖中，以實際實驗的方式，量化計算其誤判機率。針對「點超出管制界限」、「連續7點位於管制中心的單側」及「連續7點依次上升/下降」等3項判讀法則，X ̅-R管制圖每次判讀的總誤判機率為4.625957%。
對於工業上的應用，總誤判機率3.646118%顯然是太高，其中又以「連續7點位於管制中心的單側」這項判讀法則佔最高比率，因此建議後續可進一步研討該判讀法則之修正方法。

關鍵字

統計製程管制 ； 誤判機率 ； 假警報 ； 管制圖 ； 平均值管制圖 ； 全距管制圖 ； 平均值(X)-全距(R)管制圖

並列摘要

Summary of statistical process control (Statistical Process Control, SPC) most frequently used techniques of industrial statistics, its main function for the use of SPC control chart to determine whether process continue in stablity, but has its disadvantages of false alarm rates probability are too high, causing great hardship on an industrial use.
Total points to five dice for this study, the formation of an approximate normal distribution groups as samples, import it into a sample size for the average value (X ̅)-range (R) control chart, numerical analysis with computer simulation and rolling experiments individually, to make the quantitative calculation of false alarm rates.
Numerical analysis with computer simulation results show 5 rolling average values are approximately normally distributed, but its ranges are more left-leaning non-symmetrical bell-shaped distribution. The false alarm rates for the X ̅-R control chart of 3 interpretation rules of "points exceed the control limit", "7 consecutive points in the control center's unilateral" and "7 points in a row and then click up/down" total likely to be 3.646118%.
This research also use the data of 1,000pcs of 5 dice to make the X ̅-R control chart and calculate its false alarm rates, based on actual experimental approach,. The false alarm of 3 interpretation rules for the X ̅-R control charts of "points exceed the control limit", "7 consecutive points in the control center's unilateral" and "7 points in a row and then click up/down" is 4.625957% totally.
The total false alarm rates 3.646118% is obviously too high for industrial applications. Among them, the interpretation rule "7 consecutive points in the control center's unilateral" is accounted for the highest percentage, therefore suggest that further discussion of the interpretation of the laws of the correction method.

並列關鍵字

SPC ； Statistical Process Control ； False Alarm Rates ； False Signals ； X ̅control chart ； R control chart ； X ̅-R control chart

參考文獻

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