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# On the design of variable sample size and sampling intervals charts under non-normality - PowerPoint PPT Presentation

On the design of variable sample size and sampling intervals charts under non-normality. 作者 :Yu-Chang Lina, Chao-Yu Choub 學生 : 吳志權 指導教授 : 童超塵教授. 1. Introduction 2. Review of the VSSI charts 3. The Burr distribution 4. Performance indicators 5. The VSSI charts under non-

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### On the design of variable sample size andsampling intervals charts under non-normality

• 1. Introduction

• 2. Review of the VSSI charts

• 3. The Burr distribution

• 4. Performance indicators

• 5. The VSSI charts under non-

normality

• 6. Conclusions

• standard Shewhart (SS) control chart is to take

samples of equal size from the process at fixed

length sampling interval

• variable sampling interval (VSI),

• variable sample size (VSS),

• variable sample size and sampling intervals (VSSI)

• 以上4種 管制圖的資料都來自於常態分配,所以此篇利用

Burr distribution去設計非常態資料,去探討這四種管制圖在

非常態資料下的表現

• 用 the symmetric-limit chart and the asymmetric-limit

這2種 VSSI X charts under non-normality 去探討其偵測能

力

• 抽樣的點接近中心線，則使用小抽樣n1和長抽樣區間h1；如果抽樣的點在管制界限內，但是接近管制界限，則使用大抽樣n2和短抽樣區間h2

• 抽樣點落在the central region (LWLi ;UWLi)，則下一個抽樣子群使用n1和h1；如果抽樣的點落在warning region ( LCLi ；LWLi or UWLi;UCLi)，則下一個抽樣子群使用n2和h2；如果抽樣的點落在action region (LCLi以下orUCLi以上)，則超出管制界限

• CDF:

• C , q>1 ;不同c , q可以涵蓋廣範圍的偏態係數和

峰態係數,不同的偏態係數和峰態係數可以去近似常

態，Gamma，Beta分配

• The sampling distribution of under the

Burr population

的樣本平均偏態係數跟峰態係數為:

• VSSI chart的一些指標:

• 1.ANSS—the average number of samples to

signal

• 2.ANOS—the average number of observations to signal

• 3.ATS—the average time to signal

• ATS如果是大的，則有低的誤警率

• ANOS和AATS小的話，則管制圖有好的偵測能力，而且有較低的抽樣成本

• 計算ANSS,ANOS,ATS,AATS

• Normal distribution

• Burr distribution

• The VSSI X charts with symmetric limits

• ATS values for various X charts under normality大概都是370，而ATS values for various symmetric-limit X charts with k =3 under the Burr distributions在310-63之間，所以非常態下的誤警率太頻繁了

• 為了降低非常態下的誤警率，降低k值，使ATS大約370，比較AATS，結果看出VSSI和VSS的偵測能力是比SS和VSI來的有效率

• VSS和VSSI管制圖比VSI和SS管制圖更有效

率去偵測小偏移，且比較適合用於非常態資料

• 如果使用非常態資料（偏態和峰態係數是

大），則如果使用傳統管制界限和警告界限去做

偵測，則誤警率或偵測能力會變的不合理；此篇

所使用的非對稱的管制界限似乎是比較好的選擇

• 未來可以研究　管制圖在非常態下的經濟性設

計的探討

7.感想

• VSSI的管制方法是否可以應用在Ｔｕｋｅｙ管制圖上面？

• Markov chain approach是否可以用來估計Ｔｕｋｅｙ管制圖的ＡＲＬ？

• Burr distribution雖然在傳統的管制界限表現不是很好，但是在非對稱的管制界限表現比較好，是否可以應用非對稱的管制界限？