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. 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 and sampling intervals charts under non normality

On the design of variable sample size andsampling 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


On the design of variable sample size and sampling 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
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
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
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
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

  • 4.AATS—the adjusted average time to signal,又叫steady state ATS (SSATS).

  • 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


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

  • 計算ANSS,ANOS,ATS,AATS

  • Normal distribution

  • Burr distribution


5 the vssi x charts under non normality
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


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


6 conclusions
6. Conclusions

  • 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


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