Journal of Quality Engineering Society

Mathematics for Quality Engineering

18. Likelihood and Probability

Genichi Taguchi

1999 Volume 7 Issue 1 Pages 5-9
Published: February 01, 1999
Released on J-STAGE: December 24, 2016

DOIhttps://doi.org/10.18890/qes.7.1_5

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R.A.Fisher studied the concept of Likelihood in stead of the methods of Mathematical Statistics given by Neyman and Pearson. The writer also studied likelihood as the measure of odds or its measure of guessing error instead of distribution of unknown parameter. Fisher made a mistake introducing Lebesgue measure in parameter space. There is no such Lebesgue measure in parameter space. Likelihood should be used for comparing the odds among each value of parameter values instead of distribution of parameter values.
This paper introduced the new ideas to compare only likelihood among each value of parameter.

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Improvement　of　print　position　accuracy

Improvement　of　print　position　accuracy　of　Continuous　multipart with inpact-dot-printer

Junichi Deguchi, Hiroshi Ishida

1999 Volume 7 Issue 1 Pages 27-31
Published: February 01, 1999
Released on J-STAGE: June 10, 2016

DOIhttps://doi.org/10.18890/qes.7.1_27

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Improvement　of　the　Printing　Position　Accuracy　for　an　Impact-dot-printer　to Print　on　the　Continuous　Multi-layer　Paper. The　impact　printers　used　with　computers　can　use　continuous　multi-layer　paper for　printout.　But　when　the　paper　is　fed　improperly,　the　printing　position　on　the top　sheet　of　multi-layer　paper　slips　off　from　the　position　of　tile　bottom　sheet. A　study　was　made　to　improve　the　function　of　the　paper　feeding　mechanism.　As the　paper　feeding　function,　the　input　was　the　indicated　amount　of　paper　feeding and　the　output　was　the　actual　fed　amount　of　paper.　For　the　noise　factor,　the positions　of　top　and　bottom　layers　was　considered.　Zero　Point　Proportional equation　was　used　for　SN　ratio　calculations.　A　gain　of　3.5　db　was　estimated　and 4.0　db　was　confirmed.

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Evaluation　of　the　Falling　Strength　of　Remote　Controlling　Units

Nobuhide Naruko, Kimikazu Hatou

1999 Volume 7 Issue 1 Pages 32-37
Published: February 01, 1999
Released on J-STAGE: June 10, 2016

DOIhttps://doi.org/10.18890/qes.7.1_32

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Liquid　crystal　panels　are　installed　in　the　remote　controlling　units　for　airconditioners.　The　panels　are　made　of　glass　:　the　weakest　component　parts　by　impact. These　controlling　units　are　purchased　from　suppliers.　In　the　evaluation　of　falling strength,　destructive　tests　had　been　used　by　measuring　the　height　at　which　the unit　breaks.　Since　there　is　a　large　measurement　error,　a　large　number　of　samples are　required　for　the　test. In　this　study,　"buffering"　was　considered　as　the　function　of　remote　control　units and　this　function　was　evaluated　in　the　study.　As　a　result,　the　time　spent　for evaluation　was　greatly　reduced.

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Quality　improvement　of　electro-deposited　Magnets

Hayato Shirai, Yukihiko Shiohara

1999 Volume 7 Issue 1 Pages 38-42
Published: February 01, 1999
Released on J-STAGE: June 10, 2016

DOIhttps://doi.org/10.18890/qes.7.1_38

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In　the　electro-deposition　process　for　a　magnet　production,　pin-hole　type　defectives　are　frequently　produced　due　to　the　variation　of　magnet　material　used in　the process.　To　reduce　the　pin-hole　problem,　a　study　was　conducted　to　improve　the function　of　electro-deposition.　In　the　study,　the　cumulated　amount　of　coulomb was　used　as　the　input,　the　deposit　thickness　was　used　as　the　output　and　their relationship　was　considered　as　the　generic　function.　Deterioration　of　solution　was used　as　a　noise　factor.　Zero-point　Proportional　equation　was　used　for　the analysis. The　gain　of　the　optimum　condition　was　estimated　as　5.48　db　whereas　the　gain from　the　confirmation　was　4.28　db,　indicating　a　good　reproducibility.　These results　were　applied　to　the　mass　production　process,　and　the　number　of　pin-hole related　defectives　was　significantly　reduced.

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Optimization　for　thermal　oxidation　of　silicon

Kiyokazu Toiyama, Hiroyuki Yamashita, Norio Nawachi

1999 Volume 7 Issue 1 Pages 43-49
Published: February 01, 1999
Released on J-STAGE: June 10, 2016

DOIhttps://doi.org/10.18890/qes.7.1_43

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The　thermal　oxidation　of　silicon　is　a　basic　process　in　micro-sensor　fabrication.　In this　study,　Quality　Engineering(Taguchi-Methods)was　applied to improve the uniformity　and　controllability　of　SiO₂　thickness.　Two　Zero-point　Proportional equations　were　used　for　analyses　: (1)Y=βM　(Y:SiO₂　thickness,　β　:　constant,　M　:　oxidation　time) (2)Y^*=βM　(Y^*:square　of　SiO₂　thickness) As　a　result,　excellent　uniformity　of　SiO₂　thickness　was　obtained　under　the optimum　condition　when　generic function(2)Y^*=βM　was　used.

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A　Study　on　a　Drill　Groove　Grinding　Process　for　Productivity　Improvement Using　Energy　Related　Evaluation Method

Masanori Toda, Shinichi Kazashi, Kazuyoshi Takagi, [in Japanese], [in ...

1999 Volume 7 Issue 1 Pages 50-58
Published: February 01, 1999
Released on J-STAGE: June 10, 2016

DOIhttps://doi.org/10.18890/qes.7.1_50

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In　order　to　the　improve　the　productivity　of　a　drill　grooving　process　technology development　was　efficiently　conducted　by　optimizing　a　function　which　is　defined by　the　energy　input/output　relationship. Two　generic　functions　were　observed　:　the　function　which　relates　to　processing stability　and　the　one　relates　to　sharpness.　The　power　consumption　of　the grinding　axle　motor　was　observed　as　the　output.　The　type　of　material　processed was　used　as　the　noise　factor　and　test　pieces　were　used　in　the　experiment.　The grinding　related　control　factors　were　assigned　to　an　L₁₈　orthogonal　array. From　the　analysis,　the　issues　on　the　reproducibility　of　conclusions　was　discussed. There　was　a　2　decibel　gain　in　sensitivity,　which　led　to　establish　new　grinding conditions　and　resulted　a　significant　productivity　improvement.　The　same　result were　also　applied　to　other　production　lines. After　the　process　was　stabilized,　On-Line　process　control　techniques　were applied　to　further　reduce　the　total　loss　of　the　process.

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A　Study　of　Human　Factors　which　Affect　on　Software　Design

Takayuki Suzuki, Muneo Takahashi, Hiroshi Yano

1999 Volume 7 Issue 1 Pages 59-64
Published: February 01, 1999
Released on J-STAGE: June 10, 2016

DOIhttps://doi.org/10.18890/qes.7.1_59

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The　improvement　of　software　duality　is　an　extremely　important　subject　in software　related　industries.　In　this　study,　software　production　was　viewed　as　the production　of　industrial　products　where　Quality　Engineering　methods　can　be applied.　The　software　design　related　control　factors　and　the　types　of　design　errors were　assigned　in　the　study　and　the　problems　in　the　software　design　process　were discussed　and　clarified.

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A　Prediction　on　Ability　of Programming　from　Questionnaire　Using　MTS　Method

Kei Takada, Kazuhito Takahashi, Hiroshi Yano

1999 Volume 7 Issue 1 Pages 65-72
Published: February 01, 1999
Released on J-STAGE: June 10, 2016

DOIhttps://doi.org/10.18890/qes.7.1_65

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Historically,　there　have　been　no　quantitative　methods　of　evaluating　the　ability　of the　human.　In　this　study,　a　trial　was　made　to　use　the　MTS　method　based　on　the results　of　questionnaires.　In　the　experiment,　evaluated　People　each　wrote　a simple　program　and　answered　60　questions.　A　Mahalanobis　space　was　constructed　from　the　results　and　Mahalanobis　distance　was　used　for　evaluation. Although　the　number　of　data　was　insufficient,　the　study　showed　a　good　possibility　of　using　this　approach　to　forecast　programming　abilities.

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