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系統識別號 U0002-1006200516242700
中文論文名稱 在截略壽命試驗下使用 Inverse Gaussian 和 Birnbaum-Saunders 分配的允收抽樣計畫
英文論文名稱 Acceptance Sampling Plans for Inverse Gaussian Distribution and Birnbaum-Saunders Distribution under Truncated Life Tests
校院名稱 淡江大學
系所名稱(中) 統計學系碩士班
系所名稱(英) Department of Statistics
學年度 93
學期 2
出版年 94
研究生中文姓名 吳政儒
研究生英文姓名 Cheng-Ju Wu
學號 692460610
學位類別 碩士
語文別 英文
口試日期 2005-05-27
論文頁數 51頁
口試委員 指導教授-蔡宗儒
委員-吳碩傑
委員-蘇聖珠
委員-廖敏治
委員-蘇懿
中文關鍵字 壽命試驗  Inverse Gaussian分配  Birnbaum-Saunders分配  消費者風險  生產者風險 
英文關鍵字 Life test  Inverse Gaussian distribution  Birnbaum-Saunders distribution  Comsumer's risk  Producer's risk 
學科別分類 學科別自然科學統計
中文摘要 在統計品質管制中,若有興趣的問題是查驗產品以決定是否接受或者拒絕此產品,我們將這類的查驗程序稱之為允收抽樣。如果產品的品質特性是產品壽命,則允收抽樣的問題就轉變成壽命試驗的問題。壽命試驗的目地在於當壽命試驗顯示產品壽命超過期望標準時,我們選擇接受此批產品;相對地,當壽命試驗顯示產品壽命未到達標準時,我們將會拒絕此批產品。假如產品的壽命很長,則等待直到全部產品壽命結束以完成壽命試驗可能將會相當費時。因此,在本篇論文中,我們規劃出當產品壽命服從Inverse Gaussian分配與Birnbaum-Saunders分配時的截略壽命試驗,以降低完成試驗所需的時間,並說明如何推算出此允收抽樣計劃的相關參數值。在每個抽樣計劃之後,本論文也提供部份實用的表列值以供當產品壽命服從Inverse Gaussian分配與Birnbaum-Saunders分配時,使用者可以直接使用本文建議的允收抽樣計劃。
英文摘要 In statistical quality control, the type of inspection procedure is usually called acceptance sampling when the inspection of products is for the purpose of acceptance or rejection a product. If the quality characteristic is the lifetime of product, the problem of accepance sampling becomes the life test. One objective of the test is to accept the lot when the test shows that the mean life of products exceeds the standard; otherwise, we reject the lot if the test shows that the mean life of products below the standard. Frequently, it might time consuming to wait until all the products fail in a life test if the lifetimes of products are high. In this thesis, a truncated life test is proposed to the Inverse Gaussian and Birnbaum-Saunders life data, which can save the testing time. An algorithm is provided to obtain the sampling plans based on the truncated life test. Moreover, some useful tables are provided for the sampling plans under those two lifetime distributions.
論文目次 1 Introduction 1
2 Sampling Plan Based on Inverse Gaussian Distribution 3
2.1 Inverse Gaussian Distribution and Its Moments . . . . . . . . 3
2.2 The Sampling Plan . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.3 Steps for Constructing Tables . . . . . . . . . . . . . . . . . . . . 11
2.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
3 Sampling Plan Based on Birnbaum-Saunders Distribution 26
3.1 Birnbaum-Saunders Distribution and Its Moments . . . . . . 26
3.2 The Sampling Plan . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.3 Steps for Constructing Tables . . . . . . . . . . . . . . . . . . . . 33
3.4 Example . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
4 Conclusions 48
Bibliography 49

List of Figures
1 IG distribution c.d.f. for β =1,2,4, and θ =1. . . . . . . . . . . . 6
2 IG distribution p.d.f. for β =1,2,4, and θ =1. . . . . . . . . . . . 7
3 Curves of the IG c.d.f. versus t/θ when β =1,2,3,4. . . . . . . . . 10
4 BS distribution c.d.f. for γ =0.5,0.6,1.0, and δ =1. . . . . . . . . 28
5 BS distribution p.d.f. for γ =0.5,0.6,1.0, and δ =1. . . . . . . . . 29
6 Curves of the BS c.d.f. versus t/δ when γ =0.5,0.6,0.7,1. . . . . . 32


List of Tables
1 Minimum sample sizes necessary to assert the average life to exceed a
given value, μ0, with probability P_ and the corresponding acceptance
number, c, for the IG lifetime distribution with β =1.. . . . . . . . . 14

2 Minimum sample sizes necessary to assert the average life to exceed a
given value, μ0, with probability P_ and the corresponding acceptance
number, c, for the IG lifetime distribution with β =2.. . . . . . . . . 15

3 Minimum sample sizes necessary to assert the average life to exceed a
given value, μ0, with probability P_ and the corresponding acceptance
number, c, for the IG lifetime distribution with β =3.. . . . . . . . . 16

4 Minimum sample sizes necessary to assert the average life to exceed a
given value, μ0, with probability P_ and the corresponding acceptance
number, c, for the IG lifetime distribution with β =4.. . . . . . . . . 17

5 Operating characteristic values of the sampling plan (n, c, t/μ0) for a
given P_, under the IG lifetime distribution with β =1. . . . . . . . . 18

6 Operating characteristic values of the sampling plan (n, c, t/μ0) for a
given P_, under the IG lifetime distribution with β =2. . . . . . . . . 19

7 Operating characteristic values of the sampling plan (n, c, t/μ0) for a
given P_, under the IG lifetime distribution with β =3. . . . . . . . . 20

8 Operating characteristic values of the sampling plan (n, c, t/μ0) for a
given P_, under the IG lifetime distribution with β =4. . . . . . . . . 21

9 Minimum ratio of true mean life to specified mean life for the acceptability
of a lot, for the IG lifetime distribution with parameter β = 1
and producer’s risk of 0.05. . . . . . . . . . . . . .. . . . . . . . . 22

10 Minimum ratio of true mean life to specified mean life for the acceptability of a lot, for the IG lifetime distribution with parameter β = 2 and producer’s risk of 0.05. . . . . . . . . . . .. . . . . . . . . 23

11 Minimum ratio of true mean life to specified mean life for the acceptability of a lot, for the IG lifetime distribution with parameter β = 3 and producer’s risk of 0.05. . . . . . . . . . . . . . . . . . . . 24

12 Minimum ratio of true mean life to specified mean life for the acceptability of a lot, for the IG lifetime distribution with parameter β = 4 and producer’s risk of 0.05. . . . . . . . . . . . . . . . . . . . 25

13 Minimum sample sizes necessary to assert the average life to exceed a
given value, μ0, with probability P_ and the corresponding acceptance
number, c, for the BS lifetime distribution with γ = 0.5. . . . . . . . 36

14 Minimum sample sizes necessary to assert the average life to exceed a
given value, μ0, with probability P_ and the corresponding acceptance
number, c, for the BS lifetime distribution with γ = 0.6. . . . . . . . 37

15 Minimum sample sizes necessary to assert the average life to exceed a
given value, μ0, with probability P_ and the corresponding acceptance
number, c, for the BS lifetime distribution with γ = 0.7. . . . . . . . 38

16 Minimum sample sizes necessary to assert the average life to exceed a
given value, μ0, with probability P_ and the corresponding acceptance
number, c, for the BS lifetime distribution with γ = 1.0. . . . . . . . 39

17 Operating characteristic values of the sampling plan (n, c, t/μ0) for a given P_, under the BS lifetime distribution with γ = 0.5. . . . . . 40

18 Operating characteristic values of the sampling plan (n, c, t/μ0) for a given P_, under the BS lifetime distribution with γ = 0.6. . . . . . 41

19 Operating characteristic values of the sampling plan (n, c, t/μ0) for a given P_, under the BS lifetime distribution with γ = 0.7. . . . . . 42

20 Operating characteristic values of the sampling plan (n, c, t/μ0) for a given P_, under the BS lifetime distribution with γ = 1.0. . . . . . 43

21 Minimum ratio of true mean life to specified mean life for the acceptability of a lot for the BS lifetime distribution with parameter γ = 0.5 and producer’s risk of 0.05. . . . . . . . . . . . . . . . . . . 44

22 Minimum ratio of true mean life to specified mean life for the acceptability of a lot for the BS lifetime distribution with parameter γ = 0.6 and producer’s risk of 0.05. . . . . . . . . . . . . . . . . . 45

23 Minimum ratio of true mean life to specified mean life for the acceptability of a lot for the BS lifetime distribution with parameter γ = 0.7 and producer’s risk of 0.05. . . . . . . . . . . . . . . . . . 46

24 Minimum ratio of true mean life to specified mean life for the acceptability of a lot for the BS lifetime distribution with parameter γ = 1.0 and producer’s risk of 0.05. . . . . . . . . . . . . . . . . . 47

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