Rigel Kent

To fully appreciate the math we are about to discuss, we must first rewind our clock to 1911. Udny Yule was enrolled into University College London at the young age of 16, where he remained from 1887 to 1890. Among his teachers were Karl Pearson (then Professor of Applied Mathematics), Alexander Kennedy (Professor of Engineering), J. A. Fleming (Professor of Electrical Engineering), J. M. Hill (Professor of Mathematics), C. Foster (Professor of Physics). While Yule was working with Heinrich Hertz in Bonn, Pearson offered him a role as demonstrator at UCL which he accepted, and he occupied this position from 1893 to 1896 (the year he was promoted to Assistant Professor of Applied Mathematics). 1911 is an important year for students of statistics. For one, the world's first statistics department was founded by Karl Pearson (1857 – 1936) in UCL. And two, the world's first statistics textbook was published by Udny Yule (1871 – ...

The following example is taken from Dalgaard (2008, p. 97), who, in turn, got his data from Altman (1991, p. 183). In 1986, Manocha and his colleagues studied eleven healthy female subjects (aged 22 to 30) for ten days, and took careful measurements of their daily calorie intakes, \(\varepsilon_{k,j}\), where \(j\) is the day index. Here, \(\varepsilon\) is energy intake data. But it can be anything numeric depending on your use case. In the table, we see that Manocha condensed 110 data points (\(\varepsilon_{k,j}\)) into 11 data points (\(\varepsilon_k\)). See Peter Dalgaard (2008) Introductory statistics with R 2nd edition, Springer Science + Business Media, LLC, New York. And also Douglas G. Altman (1991) Practical statistics for medical research , Chapman & Hall/CRC, Boca Raton. S. Manocha, G. Choudhuri, B. N Tandon (1986) A study of dietary intake in pre- an...

In 1887, John Venn published a letter John Venn (1887) The law of error, Nature 36(931), pp. 411 - 412 (September 1, 1887) in Nature criticising Adolphe Quetelet (1796 - 1874) for naively believing that normal distribution is the only viable probability density function in nature. Venn's opening paragraph is reproduced as follows: Everyone interested in the theory of statistics is aware how strongly Quetelet was under the conviction that there is only one law of error prevalent for the departure from the mean of a number of magnitudes or measurements of any natural phenomonon. I have done what I can to protest against this doctrine as a theoretic assumption; and recently Galton and Edgeworth have shown how untenable it is, and how great is the importance of studying the properties of other laws of error than the symmetrical binomial, and its limiting form the exponential. Karl Pearson supported the notions of Venn and Galton an...

A composite metric named overall equipment effectiveness (OEE, 設 備 総 合 効 率 ) was first proposed by Seiichi Nakajima ( 中 嶋 清 一 ) in early seventies. In his 1982 book (Deploying TPM At at the time when the book was written, the M in TPM means maintenance and not management. Program for Reforming Manufacturing, 生 産 革 新 のためのTPM 展 開 プログラム), the following formulation was given: \begin{align} {\small 設備総合効率} &＝ {\small 時間稼働率} \times {\small 性能稼働率} \times {\small 良品率}\\ \eta_{\rm oee} &= \eta_{\rm time} \times \eta_{\rm rate} \times \eta_{\rm quality} \end{align} The first ratio, 時 間 稼 is a kanji formed from the semioglyph 禾 (meaning rice or other cash crops) and the audioglyph 家, while 働 is a kanji formed from the two semioglyphs: 人/亻 (people) and 動 (move). Together, 稼働 can be taken to mean people working in the paddy field. When the context is changed from human to machine, the word 稼働 means that the equipment is in running or operating mode. 稼 働 率 , \beg...