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Modul 4. doe rcbd
- 1. Materi : DOE Minggu IV 1. Introduction 2. Simple Comparative Experiments 3. Experiments with a Single Factor 4. The Randomized Complete Block Design 5. The Latin Square Design 6. Factorial Design 7. The 2 k Factorial Design 8. Two-Level Fractional Factorial Design 9. Nested or Hierarchial Design 10. Response Surface Methods 10/22/12
- 2. Chapter 4. Randomized Blocks Controllable Factors X 1 , X 2 , , X q Input Process Output (Y) Randomization Z 1 , Z 2 , , Z q unknown Uncontrollable Factors known A A design factor that probably has an effect on the response, but we are Nuisance not interested in that effect 10/22/12 Factors
- 3. Chapter 4. Randomized Blocks (continued) A A design factor that probably has an effect on the response, but we are Nuisance not interested in that effect Factors unknown Controllable Factors known X 1 , X 2 , , X q blocking Input Process Output (Y) Z 1 , Z 2 , , Z q unknown Uncontrollable Factors known 10/22/12
- 4. The Randomized Complete Block Design (RCBD) When the nuisance source of variability is known and controllable, blocking can be used to systematically eliminate its effect on the statistical comparisons among treatments Situations for which the RCBD is appropriate: Units of test equipment or machinery (often different in their operating characteristics and would be a typical bloking factor) Batches of raw material, people, and time (common nuisane sources of variability in an experiment) 10/22/12
- 5. Desain penggunaan 4 merk mesin (Is it right ?) Hari Kerja atau Operator 1 2 3 4 A B C D Mesin yang A B C D digunakan A B C D (A,B,C,D) A B C D Tidak dapat dipisahkan antara rata-rata produktifitas mesin dari rata-rata produktifitas hari ataupun operator 10/22/12
- 6. Desain penggunaan 4 merk mesin (Right design ) Hari Kerja atau Operator -> BLOK 1 2 3 4 A B C D Mesin yang B C D A digunakan C D A B (A,B,C,D) D A B C Randomisasi secara lengkap dilakukan dalam BLOK yang sama, sehingga rata-rata produktifitas mesin dapat dipisahkan dari rata-rata produktifitas hari ataupun operator 10/22/12
- 7. The Randomized Complete Block Design (RCBD) Block 1 Block 2 Block 3 Block b Y11 Y12 Y13 Y1b Y21 Y22 Y23 Y2b Y31 Y32 Y33 Y3b Ya1 Ya2 Ya3 Yab There is one observation per treatment (1, 2, , a) in each block, and the order in which the treatments are run within each block is determined randomly. 10/22/12
- 8. The ANOVA: Structure Data and Model RCBD Treatment Block (j) Total Average (level i) 1 2 b Yi. Yi. 1 Y11 Y12 Y1n Y1. Y1. 2 Y21 Y22 Y2n Y2. Y2. ... a Ya1 Ya2 Yan Ya. Ya. Total Y.j Y.1 Y.2 Y.b Y.. Y.. Statistical model for the RCBD: yij = 袖ij + 竜ij, , i = 1, 2, , a; j = 1, 2, , b atau yij = 袖 + i + 硫j + 竜ij 10/22/12
- 9. The ANOVA Table for a RCBD Model Source of Sum of Mean DF F Variation Squares Square Treatments SST a1 MST FT = MST / MSE Blocks SSB b1 MSB FB = MSB / MSE Error SSE (a-1)(b-1) MSE Total SSTotal N1 a b Y..2 SS Total = 2 Yij N i =1 j =1 1 a 2 Y..2 1 b Y..2 SS T = Yi. ; SSB = Y j2. N b i =1 N a j =1 SSE = SS Total SS T SSB 10/22/12
- 10. Chapter 4. Randomized Blocks People, Machine, and other control- Type of Tip Controllable Factors able factors are inthe SAME conditions 1, 2, 3, 4 X 1 , X 2 , , X q Input Process Output (Y) Metal coupon Z 1 , Z 2 , , Z q The hardness testing machine Uncontrollable Factors We wish to determine whether or not four different tips produce different readings on a hardness testing machine ? 10/22/12
- 11. Data from the Hardness Testing Experiment Test Coupon (Block) Type of Tip 1 2 3 4 1 9.3 9.4 9.6 10.0 2 9.4 9.3 9.8 9.9 3 9.2 9.4 9.5 9.7 4 9.7 9.6 10.0 10.2 The metal coupon differ slightly in their hardness, as might happen if they are taken from ingots that are product in different heats, the experiment units (the coupon) will contribute to the variabiliy observed in the hardness data. 10/22/12
- 12. Graphical Analysis: Box-Plot Data 10/22/12
- 13. Graphical Analysis: Main Effect Plot 10/22/12
- 14. ANOVA of RCBD: MINITAB output 10/22/12
- 15. Wrong ANOVA : MINITAB output 10/22/12
- 16. Data, Fits and Residual: MINITAB output 10/22/12
- 17. Graphical comparison of means This plot indicates that tip 1, 2, and 3 probably produce identical average hardness measurements but that tip 4 produces a much higher mean hardness. Tip 3 Tip 1 Tip 2 Tip 4 9.4 9.6 9.8 10.0 10/22/12
- 18. Model Adequacy Checking: Normality test 10/22/12
- 19. Model Adequacy Checking: Equality variance Plot of residuals by tip type (treatment) and by coupon (block) 10/22/12
- 20. MINITAB command for RCBD Analysis 10/22/12