Distribusi Kerusakan Komponen Blade Cutter
Tabel 5.9. Perhitungan Index of Fit dengan Distribusi Normal Komponen
Blade Cutter Lanjutan I
Xi=Ti Fti
Yi Xi
2
Yi
2
Xi.Yi
34 39
0.83416 0.97073
1521 0.94232
37.85844 35
42 0.85891
1.07544 1764
1.15657 45.16844
36 45
0.88366 1.19350
2025 1.42444
53.70754 37
45 0.90842
1.33106 2025
1.77173 59.89783
38 45
0.93317 1.49981
2025 2.24943
67.49150 39
51 0.95792
1.72705 2601
2.98271 88.07963
40 56
0.98267 2.11238
3136 4.46217
118.29354
Total 930
20 27686
36.53422 434.14491
Sumber : Hasil Pengolahan Data
Setelah didapat hasil perhitungan waktu antar kerusakan distribusi normal dari data ke 1 sampai dengan data ke 40, dilakukan perhitungan Index of Fit dimana
langkah-langkahnya adalah sebagai berikut: g.
Menghitung nilai Sxy Sxy
= = 40434.14491 - 200
= 17365.79648 h.
Menghitung nilai Sxx Sxx
= = 4027686 – 20
= 242540
2
i. Menghitung nilai Syy
Syy =
= 4036.53422 – 0 = 1461.36887
2
j. Menghitung nilai Index of Fit r
Index of Fit r = = 0,92241
2. Distribusi Lognormal
a. Xi = ln ti = ln 7 = 1.94591
b. Yi = Zi = Ф-1 Fti diperoleh nilai Y
1
Perhitungan waktu antar kerusakan distribusi lognormal data selanjutnya dapat dilihat pada Tabel 5.10.
= Ф-1 0,01733 = -2.11238
Tabel 5.10. Perhitungan Index of Fit dengan Distribusi Lognormal
Komponen Blade Cutter
I Ti
Fti Yi
Xi = ln ti Xi
2
Yi
2
Xi.Yi
1 7
0.01733 -2.11238 1.94591
3.78657 4.46217
-4.11051 2
11 0.04208 -1.72705
2.39790 5.74990
2.98271 -4.14129
3 11
0.06683 -1.49981 2.39790
5.74990 2.24943
-3.59639 4
12 0.09158 -1.33106
2.48491 6.17476
1.77173 -3.30757
5 13
0.11634 -1.19350 2.56495
6.57897 1.42444
-3.06127 6
13 0.14109 -1.07544
2.56495 6.57897
1.15657 -2.75845
7 13
0.16584 -0.97073 2.56495
6.57897 0.94232
-2.48987 8
13 0.19059 -0.87571
2.56495 6.57897
0.76687 -2.24615
9 13
0.21535 -0.78801 2.56495
6.57897 0.62095
-2.02120 10
14 0.24010 -0.70598
2.63906 6.96462
0.49841 -1.86313
11 14
0.26485 -0.62846 2.63906
6.96462 0.39496
-1.65854 12
15 0.28960 -0.55454
2.70805 7.33354
0.30752 -1.50173
13 15
0.31436 -0.48354 2.70805
7.33354 0.23381
-1.30945 14
16 0.33911 -0.41490
2.77259 7.68725
0.17214 -1.15034
15 16
0.36386 -0.34816 2.77259
7.68725 0.12121
-0.96529 16
17 0.38861 -0.28293
2.83321 8.02710
0.08005 -0.80161
17 18
0.41337 -0.21889 2.89037
8.35425 0.04791
-0.63268 18
18 0.43812 -0.15574
2.89037 8.35425
0.02426 -0.45015
19 19
0.46287 -0.09320 2.94444
8.66972 0.00869
-0.27443 20
20 0.48762 -0.03103
2.99573 8.97441
0.00096 -0.09295
Tabel 5.10. Perhitungan Index of Fit dengan Distribusi Lognormal
Komponen Blade Cutter Lanjutan
I Ti
Fti Yi
Xi = ln ti Xi
2
Yi
2
Xi.Yi
21 20
0.51238 0.03103
2.99573 8.97441
0.00096 0.09295
22 20
0.53713 0.09320
2.99573 8.97441
0.00869 0.27921
23 20
0.56188 0.15574
2.99573 8.97441
0.02426 0.46656
24 21
0.58663 0.21889
3.04452 9.26912
0.04791 0.66643
25 21
0.61139 0.28293
3.04452 9.26912
0.08005 0.86140
26 21
0.63614 0.34816
3.04452 9.26912
0.12121 1.05997
27 22
0.66089 0.41490
3.09104 9.55454
0.17214 1.28246
28 23
0.68564 0.48354
3.13549 9.83132
0.23381 1.51613
29 24
0.71040 0.55454
3.17805 10.10003
0.30752 1.76236
30 26
0.73515 0.62846
3.25810 10.61519
0.39496 2.04758
31 27
0.75990 0.70598
3.29584 10.86254
0.49841 2.32681
32 36
0.78465 0.78801
3.58352 12.84161
0.62095 2.82384
33 38
0.80941 0.87571
3.63759 13.23203
0.76687 3.18547
34 39
0.83416 0.97073
3.66356 13.42168
0.94232 3.55633
35 42
0.85891 1.07544
3.73767 13.97017
1.15657 4.01964
36 45
0.88366 1.19350
3.80666 14.49068
1.42444 4.54326
37 45
0.90842 1.33106
3.80666 14.49068
1.77173 5.06691
38 45
0.93317 1.49981
3.80666 14.49068
2.24943 5.70927
39 51
0.95792 1.72705
3.93183 15.45925
2.98271 6.79047
40 56
0.98267 2.11238
4.02535 16.20346
4.46217 8.50309
Total 930
20 120.92366
375.00096 36.53422 18.12713
Sumber : Hasil Pengolahan Data
Setelah didapat hasil perhitungan waktu antar kerusakan distribusi lognormal dari data ke 1 sampai dengan data ke 40, dilakukan perhitungan Index of Fit
dimana langkah-langkahnya adalah sebagai berikut: c.
Menghitung nilai Sxy Sxy
= = 4018.12713 120.923660
= 725.0851 d.
Menghitung nilai Sxx
Sxx = = 40375.00096 120.92366
= 377.5059
2
e. Menghitung nilai Syy
Syy =
= 4036.53422 0 = 1461.3689
2
f. Menghitung nilai Index of Fit r
Index of Fit r = = 0,9762
3. Distribusi Eksponensial
a. Xi = ti = 7
b. Yi = ln11-Fti, maka Y
1
Perhitungan waktu antar kerusakan distribusi eksponensial untuk data selanjutnya dapat dilihat pada Tabel 5.11.
= ln 11-0.01733 = 0,01748
Tabel 5.11. Perhitungan Index of Fit dengan Distribusi Eksponenial
Komponen Blade Cutter
I Xi=Ti
Fti Yi = ln[11-
Fti] Xi
2
Yi
2
Xi.Yi
1 7
0.01733 0.01748
49 0.00031
0.12235 2
11 0.04208
0.04299 121
0.00185 0.47289
3 11
0.06683 0.06917
121 0.00478
0.76087 4
12 0.09158
0.09605 144
0.00923 1.15264
5 13
0.11634 0.12368
169 0.01530
1.60783 6
13 0.14109
0.15209 169
0.02313 1.97717
7 13
0.16584 0.18133
169 0.03288
2.35732
Tabel 5.11. Perhitungan Index of Fit dengan Distribusi Eksponenial
Komponen Blade Cutter Lanjutan
I Xi=Ti
Fti Yi = ln[11-
Fti] Xi
2
Yi
2
Xi.Yi
8 13
0.19059 0.21145
169 0.04471
2.74891 9
13 0.21535
0.24251 169
0.05881 3.15267
10 14
0.24010 0.27457
196 0.07539
3.84394 11
14 0.26485
0.30768 196
0.09467 4.30756
12 15
0.28960 0.34193
225 0.11692
5.12899 13
15 0.31436
0.37740 225
0.14243 5.66096
14 16
0.33911 0.41417
256 0.17153
6.62666 15
16 0.36386
0.45234 256
0.20461 7.23742
16 17
0.38861 0.49203
289 0.24209
8.36445 17
18 0.41337
0.53335 324
0.28447 9.60039
18 18
0.43812 0.57646
324 0.33231
10.37637 19
19 0.46287
0.62152 361
0.38628 11.80883
20 20
0.48762 0.66870
400 0.44715
13.37392 21
20 0.51238
0.71821 400
0.51583 14.36422
22 20
0.53713 0.77031
400 0.59337
15.40613 23
20 0.56188
0.82527 400
0.68106 16.50530
24 21
0.58663 0.88342
441 0.78043
18.55184 25
21 0.61139
0.94517 441
0.89334 19.84855
26 21
0.63614 1.01098
441 1.02209
21.23063 27
22 0.66089
1.08143 484
1.16950 23.79155
28 23
0.68564 1.15723
529 1.33918
26.61624 29
24 0.71040
1.23924 576
1.53572 29.74178
30 26
0.73515 1.32859
676 1.76514
34.54324 31
27 0.75990
1.42670 729
2.03548 38.52101
32 36
0.78465 1.53551
1296 2.35778
55.27824 33
38 0.80941
1.65761 1444
2.74767 62.98916
34 39
0.83416 1.79672
1521 3.22821
70.07217 35
42 0.85891
1.95836 1764
3.83519 82.25127
36 45
0.88366 2.15127
2025 4.62795
96.80703 37
45 0.90842
2.39050 2025
5.71448 107.57236
38 45
0.93317 2.70558
2025 7.32015
121.75101 39
51 0.95792
3.16820 2601 10.03750
161.57828 40
56 0.98267
4.05550 3136 16.44712
227.10826
Total 930
20 39.0027
27686 71.33604 1345.21040
Sumber : Hasil Pengolahan Data
c. Menghitung nilai Sxy
Sxy =
= 401345.21040 93039.0027 = 17535.90187
d. Menghitung nilai Sxx
Sxx =
= 4027686 930 = 242540
2
e. Menghitung nilai Syy
Syy =
= 4071.33604 39.0027 = 1332.23088
2
f. Menghitung nilai Index of Fit r
Index of Fit r = = 0,97554
4. Distribusi Weibull
a. Xi = ln ti = ln 7 = 1.94591
b. Yi = ln ln 11-Fti, maka Y
1
Perhitungan waktu antar kerusakan distribusi weibull untuk data selanjutnya dapat dilihat pada Tabel 5.12.
= ln ln 11-0.01733 = -4.04678
Tabel 5.12. Perhitungan Index of Fit dengan Distribusi Weibull Komponen
Blade Cutter
I Ti
Fti Xi = lnti
Yi = ln ln[1-FTi]
Xi
2
Yi
2
Xi.Yi
1 7
0.01733 1.94591
-4.04678 3.78657
16.37641 -7.87467
2 11
0.04208 2.39790
-3.14678 5.74990
9.90225 -7.54566
3 11
0.06683 2.39790
-2.67119 5.74990
7.13527 -6.40524
4 12
0.09158 2.48491
-2.34285 6.17476
5.48897 -5.82178
5 13
0.11634 2.56495
-2.09007 6.57897
4.36837 -5.36091
6 13
0.14109 2.56495
-1.88328 6.57897
3.54675 -4.83052
7 13
0.16584 2.56495
-1.70743 6.57897
2.91530 -4.37946
8 13
0.19059 2.56495
-1.55374 6.57897
2.41412 -3.98528
9 13
0.21535 2.56495
-1.41670 6.57897
2.00704 -3.63376
10 14
0.24010 2.63906
-1.29256 6.96462
1.67071 -3.41114
11 14
0.26485 2.63906
-1.17869 6.96462
1.38930 -3.11062
12 15
0.28960 2.70805
-1.07314 7.33354
1.15163 -2.90612
13 15
0.31436 2.70805
-0.97446 7.33354
0.94957 -2.63888
14 16
0.33911 2.77259
-0.88149 7.68725
0.77702 -2.44400
15 16
0.36386 2.77259
-0.79332 7.68725
0.62936 -2.19956
16 17
0.38861 2.83321
-0.70922 8.02710
0.50300 -2.00938
17 18
0.41337 2.89037
-0.62857 8.35425
0.39510 -1.81680
18 18
0.43812 2.89037
-0.55084 8.35425
0.30343 -1.59213
19 19
0.46287 2.94444
-0.47559 8.66972
0.22619 -1.40035
20 20
0.48762 2.99573
-0.40243 8.97441
0.16195 -1.20556
21 20
0.51238 2.99573
-0.33099 8.97441
0.10956 -0.99156
22 20
0.53713 2.99573
-0.26097 8.97441
0.06810 -0.78179
23 20
0.56188 2.99573
-0.19205 8.97441
0.03688 -0.57533
24 21
0.58663 3.04452
-0.12395 9.26912
0.01536 -0.37738
25 21
0.61139 3.04452
-0.05639 9.26912
0.00318 -0.17169
26 21
0.63614 3.04452
0.01092 9.26912
0.00012 0.03325
27 22
0.66089 3.09104
0.07829 9.55454
0.00613 0.24199
28 23
0.68564 3.13549
0.14603 9.83132
0.02132 0.45787
29 24
0.71040 3.17805
0.21450 10.10003
0.04601 0.68169
30 26
0.73515 3.25810
0.28412 10.61519
0.08072 0.92567
31 27
0.75990 3.29584
0.35537 10.86254
0.12629 1.17123
32 36
0.78465 3.58352
0.42886 12.84161
0.18392 1.53683
33 38
0.80941 3.63759
0.50538 13.23203
0.25541 1.83835
Tabel 5.12. Perhitungan Index of Fit dengan Distribusi Weibull Komponen
Blade Cutter Lanjutan
I Ti
Fti Xi = lnti
Yi = ln ln[1-FTi]
Xi
2
Yi
2
Xi.Yi
34 39
0.83416 3.66356
0.58596 13.42168
0.34335 2.14672
35 42
0.85891 3.73767
0.67211 13.97017
0.45173 2.51212
36 45
0.88366 3.80666
0.76606 14.49068
0.58684 2.91612
37 45
0.90842 3.80666
0.87150 14.49068
0.75951 3.31751
38 45
0.93317 3.80666
0.99532 14.49068
0.99065 3.78883
39 51
0.95792 3.93183
1.15316 15.45925
1.32979 4.53404
40 56
0.98267 4.02535
1.40008 16.20346
1.96021 5.63579
Total 930
20 120.92366
-22.31584 375.00096 69.68683
-45.73154
Sumber : Hasil Pengolahan Data
c. Menghitung nilai Sxy
Sxy =
= 40-45.73154 120.92366-22.31584 = 869.25196
d. Menghitung nilai Sxx
Sxx =
= 40375.00096120.92366 = 377.50591
2
e. Menghitung nilai Syy
Syy =
= 4069.68683 -22.31584 = 2289.47629
2
f. Menghitung nilai Index of Fit r
Index of Fit r = = 0,93501
Rekapitulasi perhitungan Index of Fit untuk pola distribusi selang waktu kerusakan komponen Blade Cutter mesin Slab Cutter dapat dilihat pada Tabel
5.13.
Tabel 5.13. Rekapitulasi Perhitungan Index of Fit Komponen Blade Cutter
Distribusi Index of Fit
Normal 0.94224
Lognormal 0.97622
Eksponensial 0.97554
Weibull 0.93501
Sumber : Hasil Pengolahan Data
Dari hasil perhitungan Index of Fit komponen Blade Cutter mesin Slab Cutter, distribusi yang terpilih adalah distribusi lognormal dengan Index of Fit r
terbesar 0,97622.