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How Rao's Orthogonal arrays helps in developing Taguchis Design of Experiments.

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- 1. Rao-Taguchi-Rao-Taguchi-MahalanobisLife and Research Alex Thumba alexthumba@gmail.com
- 2. Prof. Calyampudi Radhakrishna Rao C.R. Rao, Sc.D. (Cantab), F.R.S Member, National Academy of Sciences, USA. National Medal of Science Laureate,USA Eberly Professor Emeritus of Statistics, PSU, USA Distinguished Professor Emeritus and Advisor CR Rao AIMSCS Padma Vibhushan Awardee, India
- 3. C R Rao was born in Hadagali, Karnataka, India. His Parents were CDaraiswamy Naidu, a police inspector, and A Laxmikanthamma. He was theeighth of his parents. His name Radhakrishna comes from the god Krishna (whowas the eighth of his parents children and, for that reason, the custom was toname the eighth child after Krishna). In 1931 CRs father retired and the familysettled down in Visakhapatnam, on the coast of Andhra Pradesh. CR studiedthere for ten years, first at high school, then mathematics, physics, and chemistryat the intermediate Mrs A V N College before attending Andhra University. Atthe intermediate college he won the Chandrasekara Iyer Scholarship in each ofhis two years. He has had the unique distinction of knocking off the most covetedprizes throughout his school career.
- 4. He graduated M.A. with First Class Honours in Mathematics from Andhra University in1940. He applied for a research scholarship from Andhra University but his applicationwas rejected on the grounds that it had been received after the deadline. At this stage,encouraged by his family, he decided to sit the competitive Indian Civil Serviceexaminations but, being only twenty years old, he had to wait eighteen months beforebeing allowed to take the examinations. He applied for job as a mathematician in anarmy survey unit to fill out the time before taking the Civil Service examinations. Hewas called to Calcutta for an interview but failed to get the job. However, this was aturning point for CR, for he stayed in the South Indian Hotel before his interview andthere he met a young man who was being trained in statistics at the Indian StatisticalInstitute. CR had taken a course on probability while studying for his Masters degree atAndhra University but he had never heard of the Indian Statistical Institute. The youngman took CR to visit the Institute, at that time located in the Physics Department ofPresidency College. It seemed to provide both a job and a chance to test whether hewould like research so CR applied for the one-year training course in statistics.
- 5. The family were in some financial difficulties by this time since CRs father had died inthe previous year. However, one of his brothers and his mother managed to finance himthrough the year at the Institute. The training course was rather a disappointment, taughtby people with little understanding of statistical theory. However, there was the head ofthe Institute P C Mahalanobis, as well as other top researchers working at the Institutesuch as K Raghavan Nair, Samarendra Nath Roy and Raj Chandra Bose. CR beganundertaking research with Nair and they published a joint paper Confounded designs forasymmetrical factorial experiments(1941). In the following year he published six experiments(1941)papers, four of them joint publications with Nair, for example A general class of quasi- quasi-factorial designs leading to confounded designs for factorial experiments and A note onpartially balanced incomplete block designs. designs.CR was appointed as a Technical Apprentice at the Indian Statistical Institute beginningin November 1943 and, a few months later, in June 1944, he also worked as a part-timelecturer at Calcutta University. By the end of 1946 he had over thirty papers in print
- 6. Way to success M.A. degree in mathematics with a first class and first rank at the Andhra University in Waltair, , Andhra Pradesh-(1941) M.A. degree in statistics from Calcutta University in Kolkata, West Bengal with a first class, first rank and a record of marks unbeaten till now, and a gold medal- (1943) Ph.D. in 1948 from Cambridge University with R.A. Fisher, the father of modern statistics, as his thesis advisor. Sc.D (Doctor of science) degree in 1965 from the same university 31 Honorary Doctoral Degrees from universities in 18 countries spanning six continents.
- 7. C.R.Rao With Prof. P.C. Mahalanobis
- 8. C. R. Rao with R.A. Fisher
- 9. C.R.Rao With S. N. Bose of Bose Einstein
- 10. Positions Held worked in India at the Indian Statistical Institute for 40 years before he took mandatory retirement at the age of 60 Director of the Indian Statistical Institute President of the International Statistical Institute President of the Institute of Mathematical Statistics (USA) President of the International Biometric Society Professor at the University of Pittsburgh and Eberly Professor and Director of the Center for Multivariate Analysis at Pennsylvania State University C.R. Rao Advanced Institute for Mathematics, Statistics and Computer Science as an honour ,for his outstanding achievements
- 11. Areas of research contributions Estimation theory Statistical inference and linear models Multivariate analysis Combinatorial design Biometry Statistical genetics Generalized matrix inverses Functional equations
- 12. Awards and medalsGuy Medal in Gold (2011) , Silver (1965) of the Royal Statistical Society[India Science Award 2010International Mahalanobis Prize (2003) of the International Statistical InstituteSrinivasa Ramanujan Medal (2003) of the Indian National Science AcademyPresident George W. Bush, on June 12, 2002, honored him with the National Medal ofScience, the highest award in U.S. in the scientific fieldPadma Vibhushan (2001) by the Government of IndiaMahalanobis Centenary Gold Medal (1993?) of the Indian Science CongressWilks Memorial Award (1989) of the American Statistical AssociationMegnadh Saha Medal (1969) of the Indian National Science AcademyS. S. Bhatnagar Award (1963) of Council of Scientific and Industrial ResearchJC Bose Gold Medal of the Bose Institute
- 13. Technical Terms Bearing Raos NameWidely quoted in statistical and engineering literatureCramer – Rao InequalityRao-Black wellizationRao’s Score TestRao’ s Orthogonal ArrayGeneralized Inverse of matrix /Khatri-Rao ProductQuoted in recent research papersQuatum Cramer-Rao BoundRao’s Quadratic EntropyFisher–Rao Metric/Rao Distance/Rao MeasureFisher–Rao Theorem/Cramer-Rao FunctionalRao-Rubin Theorem/ Rao’ s Damage ModelLau, Rao and Shanbhag Theorems/Lau-Rao TheoremKagan, Linnik, Rao TheoremRao’ s Paradox in Sample Surveys/Multivariate AnalysisQuoted in specialized literature
- 14. Dr. Genichi Taguchi (1924-2012) (1924-Taguchi was born and raised in the textile town of Tokamachi, in Niigata prefecture. Heinitially studied textile engineering at Kiryu Technical College with the intention ofentering the family kimono business.However, with the escalation of World War II in1942, he was drafted into the Astronomical Department of the Navigation Institute ofthe Imperial Japanese Navy.After the war, in 1948 he joined the Ministry of Public Health and Welfare, where hecame under the influence of eminent statistician Matosaburo Masuyama, whokindled his interest in the design of experiments. He also worked at the Institute ofStatistical Mathematics during this time,and supported experimental work on theproduction of penicillin at Morinaga Pharmaceuticals, a Morinaga Seika company.
- 15. In 1950, he joined the Electrical Communications Laboratory (ECL) of the NipponTelegraph and Telephone Corporation just as statistical quality control was beginning tobecome popular in Japan, under the influence of W. Edwards Deming and the JapaneseUnion of Scientists and Engineers. ECL was engaged in a rivalry with Bell Labs todevelop cross bar and telephone switching systems, and Taguchi spent his twelve yearsthere in developing methods for enhancing quality and reliability. Even at this point, hewas beginning to consult widely in Japanese industry, with Toyota being an early adopterof his ideas.During the 1950s, he collaborated widely and from 1954 he was visiting professor at 1950s,the Indian Statistical Institute, He worked under C. R. Rao, Ronald Fisher and Walter A.Shewhart.Shewhart. While working at the SQC Unit of ISI, he was introduced to the orthogonalarrays invented by C. R. Rao - a topic which was to be instrumental in enabling him todevelop the foundation blocks of what is now known as Rao-Taguchi methods Rao-
- 16. Taguchi’s Works at Indian StatisticalInstitute Visiting professor at ISI from 1954 Taguchi Worked under C. R. Rao , Ronald Fisher and Walter A. Shewhart at Indian Statistical Institute. He was introduced to the orthogonal arrays invented by C. R. Rao from SQC & OR unit of ISI which is the foundation block of well known Taguchi methods C.R. Rao &G. Taguchi made extensive use of OA’s in industrial experimentation. (described by Forbes Magazine as “new mantra” for industries),
- 17. L.H.C. Tippet, C.R. Rao, W.R. Deming (With Mrs. Deming) andG. Taguchi
- 18. Letter from Dr. Krishna kumar- kumar- 2 Trail House CourtConsultant in Business Analytics and Economist Rockville,MD. 20850, U.S.A. Rockville,MD.Dear ISI Friends,One of my relatives recently visited us here in Rockville, MD. She is Nalini Prakash Magal. Duringa ourconversation she mentioned that her father HS Narayana Rao, former CEO of Hindustan Photo Films, Ooty,and before that Chief Engineer, HAL, knew Prof PC Mahalanobis very well. She said she must have apicture of them together some place. Here is one picture she and her husband Prakash (my wife, Nirmalascousin)sent me. This photo may be of some interest to ISI, Karnataka Branchand its Life Members like me.I also recall here the speech delivered in Bangalore around 1990-95 by Dr me. 1990-Taguchi at the International Conference on Statistical Quality Control. He said that he conceived of optimal Control.manufacturing designs for quality improvement using Orthogonal Latin Squares and Dr CR Raos paperswhen he was visiting ISI, Calcutta in 50s and when Prof PC Mahalanobis sent him to Mysore Lamps for 50sSQC projects. Some of you perhaps have the history of ISI, Karnataka Branch and this photograph may projects.have been taken during the visit of Prof PC Mahalanobis to Bangalore to establish that branch with theassistance of Prof Ranganath of Information Science fame. Taguchis work must be one of the earliestworks at Bangalore centre. Are there any other similar pictures that may be of historical interest to ISI centre.Karnataka Branch? Can others in my contact list above throw some light on this history?
- 19. ORTHOGONAL ARRAYSOrthogonal Arrays (referred to Rao-Taguchi Methods) are often employed in industrialexperiments to study the effect of several control factors.An orthogonal array is a type ofexperiment where the columns for the independent variables are “orthogonal” to one another.Benefits:1. Conclusions valid over the entire region spanned by the control factorsand their settings2. Large saving in the experimental effort3. Analysis is easyTo define an orthogonal array, one must identify:1. Number of factors to be studied2. Levels for each factor3. The specific 2-factor interactions to be estimated4. The special difficulties that would be encountered in running theExperimentAfter the visit to ISI, working under prof. C.R.Rao, the sensitivity andUse of OA’s was followed in the following example in Arc welding process in Japan
- 20. An arc welding experiment performed by national railway cooperation ofJapan in 1959. Nine variables were studied as shown in the table:
- 21. OA design
- 22. CONCLUSION • Idea of publishing a standard set of designs (orthogonal arrays is a great idea) – C.R. Rao and Taguchi brought the field of DOE to the masses • Select variables that don’t interact -- interesting!! Assuming that interactions do not exist doesn’t mean they aren’t there! • As a precaution select design generators that give best design Design resolution and that provide desirable confounding structure.
- 23. C. R. Rao ’s orthogonal polynomial (RMM table)
- 24. Taguchi Methods Taguchis work includes three principal contributions to statistics: A specific loss function — Taguchi loss function The philosophy of off-line quality control and Innovations in the design of experiments. Taguchi’s Product development three stages: System design stage Non statistical stage for engineering, marketing and customer knowledge. Parameter stage: How the product should perform against defined parameters. The robust solution of cost effective manufacturing irrespective of the operating parameters. Tolerance design stage: Tolerance round the desired settings. Finding the balance between manufacturing cost and loss.
- 25. Honors Indigo Ribbon from the Emperor of Japan Willard F. Rockwell Medal of the International Technology Institute Honorary member of the Japanese Society of Quality Control and of the American Society for Quality Honorary member of American society of Mechanical engineers 3 times winner of Deming Application prize Shewhart Medal of the American Society for Quality (1995) Honored as a Quality Guru by the British Department of Trade and Industry (1990)
- 26. Prof. P.C. Mahalanobis (1893 – 1972) Prasanta Chandra Mahalanobis FRS founder of Indian Statistical Institute scientist and applied statistician Mahalanobis distance, a statistical measure
- 27. HonoursWeldon Medal from Oxford University (1944)Fellow of the Royal Society, London (1945)President of Indian Science Congress (1950)Fellow of the Econometric Society, U.S.A. (1951)Fellow of the Pakistan Statistical Association (1952)Honorary Fellow of the Royal Statistical Society, U.K. (1954)Foreign member of the Academy of Sciences of the USSR (1958)Honorary Fellow of Kings College, Cambridge (1959)Fellow of the American Statistical Association (1961)Padma Vibhushan (1968)Srinivasa Ramanujam Gold Medal (1968)
- 28. The government of India decided in 2006 to celebrate his birthday,29 June, as National Statistical Day

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