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# 9 10 kendali variabel xr

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• The following slide provides much of the data from Table S6.1.

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• 1. Peta KendaliVariabel
• 2. • Menggambarkan variasi atau penyimpanganyg terjadi pd kecenderungan data variabel• Kondisi in-out of control tapi tdk identik dgkepuasan pelanggan
• 3. Manfaat…• Perbaikan kualitas• Menentukan kemampuan proses• Membuat keputusan berkaitan dg prosesproduksi dan produk yg dihasilkan
• 4. Tahapan…1. Pemilihan karakteristik kualitas– panjang, berat, volume, waktu– Mempengaruhi kinerja produk– Pemilihan karakteristik dg Diagram Pareto
• 5. 2. Pemilihan Sub KelompokUkuran Sampel menurut Inspeksi Normal ANSI/ASQC Z1.9-1993Byknya produk yg dihasilkan Ukuran Sampel91 – 150151 – 280281 – 400401 – 500501 – 12001201 – 32003201 – 1000010001 – 3500035001 - 15000010152025355075100150
• 6. 3. Pengumpulan Data4. Penentuan Batas Kendali untuk pet X-Rdan Nilai Faktor Guna
• 7. X ChartRange forsample i# SamplesMean forsample iFromTable Nilai GunaRAxxLCLRAxxUCL2−=2+=nRRin1i=∑=nxinix1=∑=
• 8. Nilai Faktor GunaSampleSize, nMeanFactor, A2UpperRange, D4LowerRange, D32 1.880 3.268 03 1.023 2.574 04 0.729 2.282 05 0.577 2.115 06 0.483 2.004 07 0.419 1.924 0.0768 0.373 1.864 0.1369 0.337 1.816 0.18410 0.308 1.777 0.22312 0.266 1.716 0.2840.184
• 9. R ChartRange for Sample i# SamplesFrom Table Nilai GunanRRRDLCLRDUCLin1i3R4R=∑===
• 10. Process Capability Ratio, Cpprocesstheofdeviationstandard6σionSpecificatLowerionSpecificatUpper=−=σpC
• 11. Process Capability CpkpopulationprocesstheofdeviationstandardmeanprocessxwhereLimitionSpecificatLowerxor,xLimitionSpecificatUpperofminimum==− −=σσσ33pkCAssumes that the process is:• under control• normally distributed
• 12. Warning Conditions…..Western Electric :1. 1 titik diluar batas kendali ( 3σ)2. 2 dr 3 titik berurutan diluar bataskendali (2σ)3. 4 dr 5 titik berurutan jauh dari GT(1σ)4. 8 titik berurutan di satu sisi GT5. Giliran panjang 7-8 titik6. 1/beberapa titik dekat satu bataskendali7. Pola data TAK RANDOM
• 13. Examples: Compute the 3σ control charts for and R from 15 samples of size n=3. Plot thecontrol limits and the and R values and comment about the underlying process.Sample OBSERVED DIMENSIONS (cm)1 4.843 4.863 4.8592 4.925 4.882 4.8913 4.866 4.914 4.8734 4.852 4.883 4.885 4.92 4.884 4.8216 4.915 4.902 4.8987 4.887 4.892 4.8588 4.868 4.888 4.8429 4.904 4.863 4.86610 4.921 4.92 4.89411 4.914 4.884 4.89912 4.892 4.896 4.88713 4.866 4.829 4.8814 4.85 4.875 4.87215 4.867 4.9 4.885
• 14. Sample OBSERVED DIMENSIONS (cm) mean range1 4.843 4.863 4.859 4.855 0.0202 4.925 4.882 4.891 4.899 0.0433 4.866 4.914 4.873 4.884 0.0484 4.852 4.883 4.88 4.872 0.0315 4.92 4.884 4.821 4.875 0.0996 4.915 4.902 4.898 4.905 0.0177 4.887 4.892 4.858 4.879 0.0348 4.868 4.888 4.842 4.866 0.0469 4.904 4.863 4.866 4.878 0.04110 4.921 4.92 4.894 4.912 0.02711 4.914 4.884 4.899 4.899 0.03012 4.892 4.896 4.887 4.892 0.00913 4.866 4.829 4.88 4.858 0.05114 4.85 4.875 4.872 4.866 0.02515 4.867 4.9 4.885 4.884 0.0334.882 0.037
• 15. 844.4)037(.023.1882.4920.4)037(.023.1882.4=−==+=xxLCLUCLx Chart
• 16. Six Sigma Control Chart (x-bar)4.8404.8504.8604.8704.8804.8904.9004.9104.9204.9300 2 4 6 8 10 12 14 16ObservationcmSample MeanUpper Control LimitLower Control LimitCenter Line
• 17. R- Chart0951.037.57.24 =×=RD0037.03 =×=RD
• 18. 00.020.040.060.080.10.120 2 4 6 8 10 12 14 16range(cm)UppCenLowSam
• 19. ContohNo Hasil Pengukuran Xֿ R1234567891020,22,21,23,2219,18,22,20,2025,18,20,17,2220,21,22,21,2119,24,23,22,2022,20,18,18,1918,20,19,18,2020,18,23,20,2121,20,24,23,2221,19,20,20,20Jumlah/Rata-rata
• 20. n =A2 =D4 =D3 =• GT =• BKA =• BKB =
• 21. n = 5A2 = 0,577D4 = 2,115D3 = 0• GT =• BKA =• BKB =
• 22. No X1 X2 X3 X4 X5 X6 X7 X¯ R1234567891061191216101512167976111041614913108131089101613101510910971361512105107881311487512976131110Jumlah/Rata-rata
• 23. • X¯(rata-rata) = ni (Xi)/ni= n1X1 +n2X2 +……niXini• R¯ = ni (Ri)/ni= n1R1 +n2R2 +……niRini• BP-X¯ = X¯rata-rata ± A2.R¯• BPA-R = R¯D4• BPB-R = R¯D3
• 24. No X¯ BPA BPB R BPA BPB123456789108,578,1713,2510,0013,2513,7415,6513,256,756,264,356,751167614,9115,5317,6914,910,59000.59
• 25. • Xֿ(rata-rata) = GT peta kendali X= 7(8,57) +6(8,17)+…+4(13,25)+7(10)7+6+7+……+4+7=• Rֿ= GT peta kendali R=7(11)+6(6)+7(7)…+4(7)+7(6)7+6+7+…+4+7=Ada 10 macam BATAS KENDALI