Research Article
A Compound Class of Unit Burr XII Model: Theory, Estimation, Fuzzy, and Application
Table 4
ML and Bayesian estimations of parameters and reliability based on nonfuzzy and fuzzy: II.
| | | Parameter | Nonfuzzy | Fuzzy |
| | n | | | | | | | | | α = 0.25 | α = 0.55 | α = 0.9 | 0.5 | 50 | ML | AAB | 0.1580 | 0.7828 | 1.1471 | 0.0899 | 0.0394 | 0.0208 | 0.0140 | 0.0336 | 0.0605 | MSE | 0.0417 | 0.6823 | 1.5926 | 0.0094 | 0.0061 | 0.0061 | 0.0004 | 0.0020 | 0.0058 | LACI | 0.5074 | 1.0342 | 2.0632 | 0.1405 | 0.2634 | 0.2949 | 0.0600 | 0.1175 | 0.1824 | Bayesian | AAB | 0.2302 | 0.2097 | 0.0966 | 0.0861 | 0.0504 | 0.0349 | 0.0084 | 0.0224 | 0.0439 | MSE | 0.0693 | 0.1201 | 0.0884 | 0.0085 | 0.0060 | 0.0056 | 0.0002 | 0.0011 | 0.0035 | LCCI | 0.4788 | 1.0885 | 0.9865 | 0.1293 | 0.2310 | 0.2544 | 0.0477 | 0.0960 | 0.1522 | 150 | ML | AAB | 0.1255 | 0.7586 | 0.9303 | 0.0896 | 0.0354 | 0.0204 | 0.0135 | 0.0320 | 0.0574 | MSE | 0.0191 | 0.6320 | 1.2799 | 0.0084 | 0.0032 | 0.0025 | 0.0003 | 0.0013 | 0.0040 | LACI | 0.2262 | 0.6996 | 1.2413 | 0.0789 | 0.1528 | 0.1721 | 0.0351 | 0.0689 | 0.1065 | Bayesian | AAB | 0.2142 | 0.1840 | 0.0268 | 0.0833 | 0.0407 | 0.0234 | 0.0082 | 0.0218 | 0.0415 | MSE | 0.0668 | 0.0642 | 0.0573 | 0.0074 | 0.0031 | 0.0024 | 0.0002 | 0.0010 | 0.0034 | LCCI | 0.3499 | 0.6730 | 0.8217 | 0.0824 | 0.1518 | 0.1709 | 0.0328 | 0.0648 | 0.1041 | 1 | 50 | ML | AAB | 0.1733 | 0.9256 | 1.2260 | 0.0845 | 0.0467 | 0.0293 | 0.0081 | 0.0231 | 0.0470 | MSE | 0.0635 | 0.9712 | 2.0088 | 0.0082 | 0.0065 | 0.0066 | 0.0003 | 0.0015 | 0.0048 | LACI | 0.7173 | 1.3270 | 2.7892 | 0.1282 | 0.2580 | 0.2976 | 0.0601 | 0.1214 | 0.1982 | Bayesian | AAB | 0.2291 | 0.2502 | 0.0699 | 0.0757 | 0.0506 | 0.0370 | 0.0042 | 0.0143 | 0.0322 | MSE | 0.0724 | 0.1463 | 0.0974 | 0.0066 | 0.0055 | 0.0053 | 0.0001 | 0.0008 | 0.0026 | LCCI | 0.5122 | 1.0624 | 1.1128 | 0.1178 | 0.2166 | 0.2480 | 0.0443 | 0.0912 | 0.1494 | 150 | ML | AAB | 0.1292 | 0.9068 | 1.0418 | 0.0840 | 0.0419 | 0.0234 | 0.0077 | 0.0215 | 0.0428 | MSE | 0.0238 | 0.9070 | 1.9314 | 0.0074 | 0.0038 | 0.0029 | 0.0001 | 0.0007 | 0.0026 | LACI | 0.3298 | 0.8845 | 2.1541 | 0.0697 | 0.1434 | 0.1647 | 0.0330 | 0.0663 | 0.1059 | Bayesian | AAB | 0.2144 | 0.2122 | 0.0411 | 0.0748 | 0.0441 | 0.0288 | 0.0036 | 0.0138 | 0.0319 | MSE | 0.0690 | 0.0782 | 0.0674 | 0.0060 | 0.0032 | 0.0025 | 0.0001 | 0.0006 | 0.0022 | LCCI | 0.3660 | 0.7166 | 0.9822 | 0.0751 | 0.1395 | 0.1624 | 0.0298 | 0.0618 | 0.1031 |
| 2 | 50 | ML | AAB | 0.3160 | 1.3071 | 1.4667 | 0.0761 | 0.0536 | 0.0330 | 0.0010 | 0.0085 | 0.0329 | MSE | 0.1959 | 1.9614 | 3.1583 | 0.0061 | 0.0053 | 0.0052 | 0.0001 | 0.0008 | 0.0035 | LACI | 1.2153 | 1.9728 | 3.9364 | 0.0693 | 0.1945 | 0.2522 | 0.0470 | 0.1033 | 0.1926 | Bayesian | AAB | 0.2566 | 0.3206 | 0.0656 | 0.0572 | 0.0480 | 0.0375 | 0.0018 | 0.0024 | 0.0145 | MSE | 0.0953 | 0.1974 | 0.0953 | 0.0037 | 0.0039 | 0.0039 | 0.0001 | 0.0003 | 0.0014 | LCCI | 0.6091 | 1.1230 | 1.1810 | 0.0738 | 0.1544 | 0.1901 | 0.0316 | 0.0704 | 0.1273 | 150 | ML | AAB | 0.2353 | 1.2388 | 1.3620 | 0.0757 | 0.0509 | 0.0329 | 0.0010 | 0.0064 | 0.0249 | MSE | 0.0707 | 1.9101 | 2.9109 | 0.0058 | 0.0043 | 0.0033 | 0.0001 | 0.0003 | 0.0014 | LACI | 0.4857 | 1.1502 | 2.0969 | 0.0417 | 0.1170 | 0.1473 | 0.0278 | 0.0609 | 0.1092 | Bayesian | AAB | 0.2480 | 0.2895 | 0.0627 | 0.0509 | 0.0472 | 0.0352 | 0.0011 | 0.0024 | 0.0138 | MSE | 0.0916 | 0.1275 | 0.0795 | 0.0035 | 0.0030 | 0.0025 | 0.0000 | 0.0002 | 0.0010 | LCCI | 0.5293 | 0.8067 | 1.0771 | 0.0512 | 0.1053 | 0.1310 | 0.0228 | 0.0523 | 0.0994 |
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