Nilai Rata-rata Kesalahan Mean Square Error

4.11 Nilai Rata-rata Kesalahan Mean Square Error

MSE = n e i ∑ 2 1. Maka untuk α = 0,1 MSE = n e i ∑ 2 = 34 063 , 216627 = 6371,384 2. Maka untuk α = 0,2 MSE = n e i ∑ 2 = 34 504 , 119568 = 3516,720 3. Maka untuk α = 0,3 Universitas Sumatera Utara MSE = n e i ∑ 2 = 34 2303 , 63807 = 1876,683 4. Maka untuk α = 0,4 MSE = n e i ∑ 2 = 34 2305 , 34879 = 1025,859 5. Maka untuk α = 0,5 MSE = n e i ∑ 2 = 34 6979 , 24769 = 728,520 6. Maka untuk α = 0,6 Universitas Sumatera Utara MSE = n e i ∑ 2 = 34 0195 , 30495 = 896,912 7. Maka untuk α = 0,7 MSE = n e i ∑ 2 = 34 9486 , 51898 = 1526,439 8. Maka untuk α = 0,8 MSE = n e i ∑ 2 = 34 5913 , 90204 = 2653,076 9. Maka untuk α = 0,9 Universitas Sumatera Utara MSE = n e i ∑ 2 = 34 258 , 148271 = 4360,919 Untuk menentukan nilai α yang optimal, maka diambil dari nilai MSE yang paling minimum yaitu pada α = 0,5. Universitas Sumatera Utara Tabel 4.11 Nilai Pemulusan Eksponensial Periode Jumlah Nasabah α = 0,1 α = 0,2 α = 0,3 Forecast e 2 i Forecast e 2 i Forecast e 2 i 1 6895 - - - - - - 2 6812 - - - - - - 3 6730 6847.89 13898.0521 6805.76 5739.5776 6768.61 1490.7321 4 6815 6839 575.904004 6800.864 199.826496 6778.606 1324.52324 5 6919 6852.36 4441.42274 6839.896 6257.44282 6849.18 4874.8324 6 6820 6844.04 578.017764 6828.441 71.250481 6830.644 113.294736 7 6912 6855.47 3195.98009 6857.572 2962.40718 6875.804 1310.15042 8 6764 6835.69 5139.02597 6819.193 3046.26725 6812.39 2341.5921 9 6814 6828.95 223.442704 6812.422 2.490084 6806.962 49.533444 10 6902 6840.94 3728.3236 6843.352 3439.5879 6857.736 1959.3017 11 6955 6861.86 8674.3145 6886.694 4665.70964 6918.399 1339.6332 12 6962 6881.14 6537.69274 6919.964 1767.0253 6955.618 40.729924 13 6873 6879.77 45.819361 6907.339 1179.16692 6921.029 2306.78484 14 6914 6886.79 740.492944 6914.285 0.081225 6924.358 107.288164 15 6920 6893.95 678.863025 6921.119 1.252161 6928.657 74.943649 16 6838 6883.6 2079.63361 6892.648 2986.4039 6880.785 1830.55622 17 6799 6866.97 4619.9209 6856.641 3322.48488 6830.077 965.779929 18 6768 6846.62 6180.78992 6818.891 2589.89388 6783.833 250.683889 Universitas Sumatera Utara 19 6595 6794.75 39898.4645 6723.495 16510.965 6655.948 3714.6587 20 6606 6752.93 21589.3065 6661.702 3102.7128 6594.399 134.583201 21 6635 6723.39 7813.49924 6631.526 12.068676 6582.685 2736.85922 22 6788 6729.18 3459.32186 6673.553 13098.1158 6673.453 13121.0152 23 6794 6735.66 3403.20557 6707.427 7494.88433 6731.838 3864.11424 24 6820 6746.69 5373.91625 6742.97 5933.6209 6781.642 1471.33616 25 6878 6767.96 12108.5815 6791.999 7396.172 6844.298 1135.8248 26 6752 6761.09 82.591744 6776.417 596.189889 6802.432 2543.38662 27 6817 6768.43 2358.94776 6791.468 651.883024 6816.379 0.385641 28 6897 6790.86 11264.8505 6834.122 3953.64288 6871.269 662.084361 29 6949 6820.5 16513.278 6884.736 4129.8617 6931.681 299.947761 30 6922 6840.38 6661.33469 6908.899 171.636201 6946.642 607.228164 31 6890 6850.91 1528.26265 6912.088 487.879744 6932.555 1810.92803 32 6953 6872.42 6492.65293 6938.445 211.848025 6959.622 43.850884 33 6869 6873.86 23.590449 6922.296 2840.46362 6921.889 2797.24632 34 6795 6860.17 4247.1289 6880.228 7263.81198 6854.24 3509.3776 35 6815 6852.43 1401.07976 6857.896 1840.06682 6827.76 162.8176 36 6985 6879.79 11069.3545 6909.888 5641.81254 6915.637 4811.22577 Jumlah - 216627.063 - 119568.504 - 63807.2303 Periode Jumlah α = 0,4 α = 0,5 α = 0,6 Universitas Sumatera Utara Nasabah Forecast e 2 i Forecast e 2 i Forecast e 2 i 1 6895 - - - - - - 2 6812 - - - - - - 3 6730 6736.44 41.4736 6709.25 430.5625 6687.04 1845.5616 4 6815 6770.23 2004.3529 6773.75 1701.5625 6787.17 774.5089 5 6919 6872.76 2138.1376 6904.188 219.395344 6938.01 361.3801 6 6820 6837.87 319.265424 6841.5 462.25 6836.5 272.25 7 6912 6896.05 254.434401 6912.453 0.205209 6924.718 161.747524 8 6764 6801.15 1379.82532 6782.078 326.814084 6756.655 53.949025 9 6814 6801.04 168.039369 6794.965 362.331225 6792.409 466.171281 10 6902 6873.47 813.846784 6890.945 122.213025 6911.502 90.288004 11 6955 6946.51 72.029169 6970.704 246.615616 6990.736 1277.0617 12 6962 6979.77 315.630756 6993.718 1006.03152 6998.949 1365.2286 13 6873 6917.69 1997.55364 6902.542 872.729764 6880.161 51.279921 14 6914 6921 48.958009 6913.362 0.407044 6907.777 38.725729 15 6920 6925.87 34.421689 6922.227 4.959529 6921.636 2.676496 16 6838 6861.08 532.732561 6841.886 15.100996 6824.864 172.554496 17 6799 6802.87 14.938225 6781.83 294.8089 6767.31 1004.2561 18 6768 6756.49 132.503121 6740.108 777.963664 6732.31 1273.7761 19 6595 6603.24 67.831696 6563.651 982.759801 6531.958 3974.29376 20 6606 6555.55 2545.50521 6538.374 4573.27588 6535.797 4928.46121 21 6635 6569.65 4270.4918 6577.961 3253.44752 6596.484 1483.48226 Universitas Sumatera Utara 22 6788 6707.58 6466.73306 6755.118 1081.22592 6803.66 245.2356 23 6794 6774.91 364.542649 6813.627 385.219129 6838.37 1968.6969 24 6820 6823 8.988004 6849.348 861.305104 6859.151 1532.8008 25 6878 6886.23 67.749361 6908.941 957.345481 6917.981 1598.48036 26 6752 6806.88 3011.59488 6790.104 1451.91482 6761.801 96.059601 27 6817 6821.53 20.5209 6815.869 1.279161 6811.284 32.672656 28 6897 6890.08 47.8864 6902.593 31.281649 6917.259 410.427081 29 6949 6957.47 71.673156 6974.876 669.567376 6989.322 1625.86368 30 6922 6958.77 1352.0329 6959.477 1404.52553 6953.936 1019.9081 31 6890 6927.76 1425.51554 6914.258 588.450564 6898.377 70.174129 32 6953 6960.95 63.2025 6959.889 47.458321 6962.072 82.301184 33 6869 6904.43 1255.14318 6885.575 274.730625 6868.197 0.644809 34 6795 6819.21 586.220944 6788.852 37.797904 6764.666 920.151556 35 6815 6800.66 205.6356 6786.209 828.921681 6783.021 1022.65644 36 6985 6932.28 2779.82018 6962.746 495.240516 7001.471 271.293841 Jumlah - 34879.2305 - 24769.6979 - 30495.0195 Universitas Sumatera Utara Periode Jumlah Nasabah α = 0,7 α = 0,8 α = 0,9 Forecast e 2 i Forecast e 2 i Forecast e 2 i 1 6895 - - - - - - 2 6812 - - - - - - 3 6730 6669.81 3622.8361 6657.56 5247.5536 6650.29 6353.6841 4 6815 6808.49 42.328036 6835.736 429.981696 6866.902 2693.8176 5 6919 6969.76 2576.9837 6995.992 5927.76806 7014.228 9068.3719 8 6 6820 6820.8 0.646416 6794.727 638.724529 6760.366 3556.2139 6 7 6912 6935.8 566.582809 6950.051 1447.8786 6971.731 3567.7923 6 8 6764 6727.29 1347.6241 6695.111 4745.69432 6659.063 11011.774 9 6814 6796.51 305.830144 6809.003 24.970009 6830.935 286.79422 5 10 6902 6934.51 1056.96512 6957.557 3086.58025 6977.336 5675.5129 11 6955 7005.2 2520.04 7012.743 3334.25405 7013.178 3384.6796 8 12 6962 6996.76 1208.5357 6989.195 739.568025 6979.012 289.40814 4 13 6873 6854.37 347.039641 6828.448 1984.8807 6804.691 4666.1194 8 14 6914 6908.08 34.999056 6916.131 4.541161 6932.078 326.81408 4 15 6920 6924.22 17.783089 6927.875 62.015625 6929.509 90.421081 Universitas Sumatera Utara 16 6838 6808.8 852.464809 6792.105 2106.35103 6774.181 4072.8647 6 17 6799 6758.12 1671.01088 6753.647 2056.89461 6754.121 2014.1246 4 18 6768 6730.19 1429.52048 6731.535 1329.69623 6734.472 1124.1267 8 19 6595 6504 8280.27202 6477.188 13879.6673 6450.033 21015.431 1 20 6606 6543.64 3889.39322 6560.014 2114.7122 6584.412 466.04174 4 21 6635 6618.36 276.856321 6639.158 17.288964 6655.442 417.87536 4 22 6788 6847.44 3532.99472 6884.463 9305.11037 6914.994 16127.476 23 6794 6847.33 2844.19556 6842.139 2317.36332 6825.524 993.76257 6 24 6820 6857.59 1412.93292 6851.237 975.750169 6845.895 670.55102 5 25 6878 6921.29 1874.37044 6924.409 2153.79528 6929.524 2654.7225 8 26 6752 6729.41 510.172569 6696.034 3132.19316 6661.826 8131.3502 8 27 6817 6814.21 7.778521 6826.717 94.420089 6849.19 1036.1961 28 6897 6935.21 1460.0041 6953.726 3217.83908 6968.99 5182.5601 29 6949 7000.18 2619.08533 7005.702 3215.1168 7005.476 3189.5385 8 30 6922 6943.15 447.195609 6928.292 39.589264 6911.495 110.35502 5 Universitas Sumatera Utara 31 6890 6882.85 51.093904 6869.969 401.240961 6861.464 814.30329 6 32 6953 6969.13 260.112384 6981.256 798.401536 6997.478 1978.2924 8 33 6869 6851.39 310.1121 6833.224 1279.92218 6811.611 3293.4973 2 34 6795 6745.82 2418.37733 6731.799 3994.3664 6723.037 5178.6733 7 35 6815 6788.42 706.602724 6800.191 219.306481 6816.441 2.076481 36 6985 7043.28 3396.20873 7084.404 9881.15522 7122.208 18826.035 3 Jumlah - 51898.9486 - 90204.5913 - 148271.25 8 6000 6200 6400 6600 6800 7000 7200 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 Periode Ju m lah N asab ah 0,1 0,2 0,3 0,4 0,5 0,6 0,7 0,8 0,9 Universitas Sumatera Utara Gambar 4.2 Grafik Pemulusan Eksponensial Forecast untuk 2008 : Bulan 1 = 6935,302 + 27,443 1 = 6962,745 Bulan 2 = 6935,302 + 27,443 2 = 6990,188 Bulan 3 = 6935,302 + 27,443 3 = 7017,631 Bulan 4 = 6935,302 + 27,443 4 = 7045,074 Bulan 5 = 6935,302 + 27,443 5 = 7072,517 Bulan 6 = 6935,302 + 27,443 6 = 7099,96 Bulan 7 = 6935,302 + 27,443 7 = 7127,403 Bulan 8 = 6935,302 + 27,443 8 = 7154,846 Bulan 9 = 6935,302 + 27,443 9 = 7182,289 Bulan 10 = 6935,302 + 27,443 10 = 7209,732 Bulan 11 = 6935,302 + 27,443 11 = 7237.175 Bulan 12 = 6935,302 + 27,443 12 = 7264,618 Universitas Sumatera Utara Untuk forecast tahun 2009, maka m yang digunakan adalah m=13 karena untuk satu kali peramalan m merupakan nilai berkelanjutan dari m sebelumnya. Bulan 1 = 6935,302 + 27,443 13 = 7292,061 Bulan 2 = 6935,302 + 27,443 14 = 7319,504 Bulan 3 = 6935,302 + 27,443 15 = 7346,947 Bulan 4 = 6935,302 + 27,443 16 = 7374,39 Bulan 5 = 6935,302 + 27,443 17 = 7401,833 Bulan 6 = 6935,302 + 27,443 18 = 7429,276 Bulan 7 = 6935,302 + 27,443 19 = 7456,719 Bul an 8 = 6935,302 + 27,443 20 = 7484,162 Bulan 9 = 6935,302 + 27,443 21 = 7511,605 Bulan 10 = 6935,302 + 27,443 22 = 7539,048 Bulan 11 = 6935,302 + 27,443 23 = 7566,491 Bulan 12 = 6935,302 + 27,443 24 = 7593,934 Universitas Sumatera Utara Dan untuk forecast tahun 2010, maka m yang digunakan adalah m = 25. Dapat kita hitung sebagai berikut : Bulan 1 = 6935,302 + 27,443 25 = 7621,377 Bulan 2 = 6935,302 + 27,443 26 = 7648,82 Bulan 3 = 6935,302 + 27,443 27 = 7676,263 Bulan 4 = 6935,302 + 27,443 28 = 7703,706 Bulan 5 = 6935,302 + 27,443 29 = 7731,149 Bulan 6 = 6935,302 + 27,443 30 = 7758,592 Bulan 7 = 6935,302 + 27,443 31 = 7786,035 Bulan 8 = 6935,302 + 27,443 32 = 7813,478 Bulan 9 = 6935,302 + 27,443 33 = 7840,921 Bulan 10 = 6935,302 + 27,443 34 = 7868,364 Bulan 11 = 6935,302 + 27,443 35 = 7895,807 Bulan 12 = 6935,302 + 27,443 36 = 7923,25 Universitas Sumatera Utara Tabel 4.12 Forecast dengan Double Exponensial Smoothing α = 0,5 Bulan 2008 2009 2010 1 6,962,745 7,292,061 7,621,377 2 6,990,188 7,319,504 7648,82 3 7,017,631 7,346,947 7,676,263 4 7,045,074 7374,39 7,703,706 5 7,264,618 7,401,833 7,731,149 6 7099,96 7,429,276 7,758,592 7 7,127,403 7,456,719 7,786,035 8 7,154,846 7,593,934 7,813,478 9 7,182,289 7,511,605 7,840,921 10 7,209,732 7,539,048 7923,25 11 7237.175 7,566,491 7,895,807 12 7,072,517 7,484,162 7,923,25 Universitas Sumatera Utara BAB 5 IMPLEMENTASI SISTEM

5.1 Tahapan Implementasi