DESAIN EKSPERIMEN INTRODUCTION. Semester Genap 2017/2018 Jurusan Teknik Industri Universitas Brawijaya

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1 DESAIN EKSPERIMEN INTRODUCTION Semester Genap Jurusan Teknik Industri Universitas Brawijaya

2 OUTLINE Introduction to DOX Four Eras in the History of DOX Engineering Experiments Typical Applications of Experimental Design Strategy of Experimentation Factorial Design Factorial Designs with Several Factors and Fractional Factorial The Basic Principles of DOX Planning, Conducting & Analyzing an Experiment 2

3 Introduction to DOX (1/2) An experiment is a test or a series of tests Experiments are used widely in the engineering world Process characterization & optimization Evaluation of material properties Product design & development Component & system tolerance determination All experiments are designed experiments, some are poorly designed, some are well-designed 3

4 Introduction to DOX (2/2) Experimentation is a vital part of scientific (or engineering) method For any experiment, questions to be asked: Are only these methods available? Are there any other factors that might affect the results? How many samples are needed for the experiment? How should the samples be assigned to each experiment? What is the order that the data should be collected? What method of data analysis should be used? What difference in average observed results between method, material, machines,? 4/33

5 Four Eras in the History of DOX The agricultural origins, s W.S. Gossett and the t-test (1908) R. A. Fisher & his co-workers Profound impact on agricultural science Factorial designs, ANOVA The first industrial era, 1951 late 1970s Box & Wilson, response surfaces Applications in the chemical & process industries The second industrial era, late 1970s 1990 Quality improvement initiatives in many companies Taguchi and robust parameter design, process robustness The modern era, beginning circa 1990 R. A. Fisher ( ) George E. P. Box 5

6 Engineering Experiments (1/2) In general, experiments are used to study the process and systems. The process can be the combination of operations, machines, methods, people, and other resources (often materials) that transfer some input into output that has one or more observable response variables y. Some of the process variables and material properties, x 1,, x p are controllable. Some of them are uncontrollable (although they may be controllable for purposes of a test). 6/33

7 Engineering Experiments (2/2) Determining which variables are most influential on the response y Determining where to set the influential x s so that y is almost always near the desired nominal value. Determining where to set the influential x s so that variability in y is small. Determining where to set the influential x s so that the effects of the uncontrollable variables z 1,., z q are minimized. 7

8 Typical Applications of Experimental Design Improve process yield Reduce variability and closer conformance to nominal or target requirements Reduce development time Reduce overall costs Evaluate and compare basic design configurations Evaluate material alternatives Select design parameters Determine key product design parameters Formulate new product 8/33

9 Strategy of Experimentation (1/4) Golf example-factor to influence the score Driver oversized or regular Ball balata or three piece Mode of travel walking or riding a golf cart Beverage water or beer. 9/33

10 Strategy of Experimentation (2/4) Best-guess experiments Used a lot More successful than you might suspect, but there are disadvantages One-factor-at-a-time (OFAT) experiments Sometimes associated with the scientific or engineering method Devastated by interaction, also very inefficient Statistically designed experiments Based on Fisher s factorial concept 10

11 Strategy of Experimentation (3/4) 11/33

12 Strategy of Experimentation (4/4) 12/33

13 Factorial Design (1/3) In a factorial experiment, all possible combinations of factor levels are tested The golf experiment: Type of driver Type of ball Walking vs. riding Type of beverage Time of round Weather Type of golf spike Etc, etc, etc 13/33

14 Factorial Design (2/3) 14/33

15 Factorial Design (3/3) 15/33

16 Factorial Designs with Several Factors 16/33

17 Factorial Designs with Several Factors A Fractional Factorial 17/33

18 The Basic Principles of DOX Randomization Running the trials in an experiment in random order Notion of balancing out effects of lurking variables Replication Sample size (improving precision of effect estimation, estimation of error or background noise) Replication versus repeat measurements? Replication reflects sources of variability both between runs and within runs Blocking Dealing with nuisance factors 18

19 Planning, Conducting & Analyzing an Experiment 1. Recognition of & statement of problem 2. Choice of factors, levels, and ranges 3. Selection of the response variable(s) 4. Choice of design 5. Conducting the experiment 6. Statistical analysis 7. Drawing conclusions, recommendations 8. Get statistical thinking involved early 9. Your non-statistical knowledge is crucial to success 10. Pre-experimental planning (steps 1-3) vital Pre-experimental planning 11. Think and experiment sequentially (use the KISS principle) 19

20 Tambahan: Kekeliruan Eksperimen Menyatakan kegagalan dari dua unit eksperimen identik yang dikenai perlakuan untuk memberikan hasil yang sama. Contoh: kekeliruan waktu menjalankan eksperimen, kekeliruan pengamatan, variasi bahan eksperimen, variasi antara unit eksperimen dan pengaruh gabungan semua faktor tambahan Untuk mengurangi kekeliruan dapat menggunakan bahan eksperimen yang homogen, menggunakan informasi yang sebaikbaiknya tentang variabel yang telah ditentukan dengan tepat, melakukan eksperimen dengan teliti, menggunakan DE yang lebih efisien 20

21 Tambahan: Efek dan interaksi Dalam keperluan desain eksperimen, variabel bebas dinamakan faktor, dan nilai-nilai atau klasifikasiklasifikasi dari sebuah faktor dinamakan taraf faktor. Faktor-faktor dinyatakan dengan huruf kecil a, b, c, d, dst.., sedangkan taraf faktor dinyatakan dengan angka 1, 2, 3, dst yang dituliskan sebagai indeks untuk faktor yang bersangkutan. 21

22 Tambahan: Kontrol Lokal Pengelompokan Pemblokan Penyeimbangan Penempatan sekumpulan unit eksperimen ke dalam kelompokkelompok agar kelompok yang berbeda memungkinkan untuk mendapatkan perlakuan yang berbeda pula. Contohnya ketika meneliti pengaruh tiga macam cara penyampaian materi terhadap mahasiswa. Terdapat 11 mahasiswa, yang dibagi menjadi 3 kelompok, (4-4-3). Penempatan atau pemilihan mahasiswa ke dalam kelompokkelompok dilakukan secara acak. Masing-masing kelompok diberikan materi dengan cara berbeda (A-B- C) Pengalokasian unit-unit eksperimen ke dalam blok sehingga unit-unit dalam blok secara relatif bersifat homogen sedangkan sebagian besar dari variasi yang dapat diperkirakan di antara unit-unit telah terbaur dengan blok. Variasi yang dapat diduga tidak menjadi bagian daripada kekeliruan eksperimen, sehingga desain lebih efisien. Contohnya:: Ada 12 komponen mesin. Enam jenis X, tiga jenis Y, dan tiga jenis Z. Jenis diambil sebagai blok. Blok pertama terdiri dari 6 buah komponen jenis X. Blok kedua terdiri dari 3 buah komponen jenis Y. Blok ketiga terdiri dari 3 buah komponen jenis Z. Usaha memperoleh unit eksperimen, usaha pengelompokan, pemblokan dan penggunaan perlakuan sedemikian sehingga dihasilkan konfigurasi formasi yang seimbang 22