On the design of variable sample size and sampling intervals charts under non-normality

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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
1. Introduction
• 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

2. Review of the VSSI charts
• 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
3. The Burr distribution
• 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:

4. Performance indicators
• 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

• Normal distribution
• Burr distribution
5. The VSSI X charts under non-normality
• 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
The VSSI X charts with asymmetric limits
• 用非對偁的管制界限所計算出來的ATS和AATS的偵測能力比對稱的管制界限來的好
6. Conclusions
• VSS和VSSI管制圖比VSI和SS管制圖更有效

• 如果使用非常態資料（偏態和峰態係數是

• 未來可以研究　管制圖在非常態下的經濟性設

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？