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| Presentation | 2019-05-24 16:00 [Invited Talk] Several inequalities used for construction of bar{X} and S control charts with unequal sample sizes Chanseok Park (PNU)  R2019-7 |
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| Abstract | (in Japanese) | (See Japanese page) |
| (in English) | The X-bar and S charts have been widely used in quality engineering. The usual requirement under these charts is that the sample sizes of subgroups are all equal. There exist several ad hoc methods to handle this issue. However, these methods are biased, which can result in underperformance. In this paper, we suggest several unbiased estimators and provide the rigorous proofs of the inequalities needed for selecting an estimator. The proofs reveal an interesting and useful connection between the statistical and mathematical theories. For example, the normal-consistency factor $c_4$ can be expressed using the Wallis' production formula calculating pi and the Watson representation. |
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| Keyword | (in Japanese) | (See Japanese page) |
| (in English) | Control Charts / unbiasedness / Wallis production formula / / / / / | |
| Reference Info. | IEICE Tech. Rep., vol. 119, no. 54, R2019-7, pp. 35-40, May 2019. | |
| Paper # | R2019-7 | |
| Date of Issue | 2019-05-17 (R) | |
| ISSN | Print edition: ISSN 0913-5685 Online edition: ISSN 2432-6380 | |
| Copyright and reproduction |
All rights are reserved and no part of this publication may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopy, recording, or any information storage and retrieval system, without permission in writing from the publisher. Notwithstanding, instructors are permitted to photocopy isolated articles for noncommercial classroom use without fee. (License No.: 10GA0019/12GB0052/13GB0056/17GB0034/18GB0034) | |
| Download PDF | R2019-7 |
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| Conference Information | |
| Committee | R |
| Conference Date | 2019-05-24 - 2019-05-24 |
| Place (in Japanese) | (See Japanese page) |
| Place (in English) | Aichi Institute of Technology, Motoyama Campus |
| Topics (in Japanese) | (See Japanese page) |
| Topics (in English) | Software Reliability, Overall reliability engineering |
| Paper Information | |
| Registration To | R |
| Conference Code | 2019-05-R |
| Language | English |
| Title (in Japanese) | (See Japanese page) |
| Sub Title (in Japanese) | (See Japanese page) |
| Title (in English) | Several inequalities used for construction of bar{X} and S control charts with unequal sample sizes |
| Sub Title (in English) | |
| Keyword(1) | Control Charts |
| Keyword(2) | unbiasedness |
| Keyword(3) | Wallis production formula |
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| 1st Author's Name | Chanseok Park |
| 1st Author's Affiliation | Pusan National University (PNU) |
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| Speaker | Author-1 |
| Date Time | 2019-05-24 16:00:00 |
| Presentation Time | 40 minutes |
| Registration for | R |
| Paper # | R2019-7 |
| Volume (vol) | vol.119 |
| Number (no) | no.54 |
| Page | pp.35-40 |
| #Pages | 6 |
| Date of Issue | 2019-05-17 (R) |
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