| 講演名 | 2019-05-24 [Invited Talk] Several inequalities used for construction of bar{X} and S control charts with unequal sample sizes Chanseok Park(PNU), |
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| PDFダウンロードページ |  PDFダウンロードページへ |
| 抄録(和) | 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 providethe 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. |
| 抄録(英) | 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 providethe 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. |
| キーワード(和) | Control Charts / unbiasedness / Wallis production formula |
| キーワード(英) | Control Charts / unbiasedness / Wallis production formula |
| 資料番号 | R2019-7 |
| 発行日 | 2019-05-17 (R) |
| 研究会情報 | |
| 研究会 | R |
|---|---|
| 開催期間 | 2019/5/24(から1日開催) |
| 開催地（和） | 愛知工業大学 本山キャンパス |
| 開催地（英） | Aichi Institute of Technology, Motoyama Campus |
| テーマ（和） | ソフトウェアの信頼性, 信頼性一般 |
| テーマ（英） | Software Reliability, Overall reliability engineering |
| 委員長氏名（和） | 安里 彰(富士通) |
| 委員長氏名（英） | Akira Asato(Fujitsu) |
| 副委員長氏名（和） | 土肥 正(広島大) |
| 副委員長氏名（英） | Tadashi Dohi(Hiroshima Univ.) |
| 幹事氏名（和） | 田村 信幸(法政大) / 平栗 滋人(鉄道総研) |
| 幹事氏名（英） | Nobuyuki Tamura(Hosei Univ.) / Shigeto Hiraguri(RTRI) |
| 幹事補佐氏名（和） | 井上 真二(関西大) / 岡村 寛之(広島大) |
| 幹事補佐氏名（英） | Shinji Inoue(Kansai Univ.) / Hiroyuki Okamura(Hiroshima Univ.) |
| 講演論文情報詳細 | |
| 申込み研究会 | Technical Committee on Reliability |
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| 本文の言語 | ENG |
| タイトル（和） | |
| サブタイトル（和） | |
| タイトル（英） | [Invited Talk] Several inequalities used for construction of bar{X} and S control charts with unequal sample sizes |
| サブタイトル（和） | |
| キーワード(1)（和/英） | Control Charts / Control Charts |
| キーワード(2)（和/英） | unbiasedness / unbiasedness |
| キーワード(3)（和/英） | Wallis production formula / Wallis production formula |
| 第 1 著者 氏名（和/英） | Chanseok Park / Chanseok Park |
| 第 1 著者 所属（和/英） | Pusan National University(略称：PNU) Pusan National University(略称：PNU) |
| 発表年月日 | 2019-05-24 |
| 資料番号 | R2019-7 |
| 巻番号（vol） | vol.119 |
| 号番号（no） | R-54 |
| ページ範囲 | pp.35-40(R), |
| ページ数 | 6 |
| 発行日 | 2019-05-17 (R) |