Inspection Plan Based on the Process Capability Index Using the Neutrosophic Statistical Method
Abstract
:1. Introduction
2. Design of a Neutrosophic Plan Based on PCI
- Step 1:
- Select a random sample of size from the product lot. Compute the statistic ; ,.
- Step 2:
- Accept a product lot of ; , otherwise reject a product lot, where is the neutrosophic acceptance number. An acceptance number is also called the action number/boundary number. A product lot is rejected if the statistic is smaller than , otherwise, the product lot is accepted.
Research Methodology
- Specify the values of AQL, LQL, and .
- Specify the suitable ranges for such that and such that .
- Perform the simulation by the grid search method and select those values of the neutrosophic plan parameters where and satisfy the conditions given in Equations (7)–(9).
3. Comparison Study
4. Application of the Proposed Plan
- Step 1:
- Select a random sample of size = from a product lot. Compute the statistic .
- Step 2:
- Accept a product lot as .
5. Concluding Remarks
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
References
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p1 | p2 | ||||
---|---|---|---|---|---|
0.001 | 0.002 | [602, 643] | [1.093, 1.095] | [0.9500, 0.95033] | [0.0441, 0.0891] |
0.003 | [218, 228] | [1.052, 1.054] | [0.9500, 0.9505] | [0.06223, 0.0898] | |
0.004 | [128, 133] | [1.022, 1.024] | [0.9506, 0.9513] | [0.0700, 0.0914] | |
0.006 | [69, 71] | [0.978, 0.980] | [0.9513, 0.9517] | [0.0807, 0.0969] | |
0.008 | [47, 49] | [0.946, 0.948] | [0.9506, 0.9528] | [0.0848, 0.0977] | |
0.010 | [36, 38] | [0.921, 0.923] | [0.9502, 0.9504] | [0.0849, 0.0958] | |
0.015 | [24, 28] | [0.874, 0.876] | [0.9541, 0.9675] | [0.0914, 0.0959] | |
0.020 | [18, 20] | [0.842, 0.844] | [0.9521, 0.9614] | [0.0761, 0.0823] | |
0.0025 | 0.030 | [21, 23] | [0.793, 0.795] | [0.9529, 0.9606] | [0.0923, 0.0995] |
0.050 | [13, 15] | [0.731, 0.735] | [0.9567, 0.9674] | [0.0607, 0.0754] | |
0.005 | 0.050 | [19, 21] | [0.730, 0.732] | [0.9512, 0.9599] | [0.0897, 0.0967] |
0.100 | [9, 11] | [0.631, 0.633] | [0.9575, 0.9740] | [0.0957, 0.0961] | |
0.01 | 0.020 | [274, 290] | [0.854, 0.856] | [0.9500, 0.9504] | [0.0513, 0.0881] |
0.030 | [95, 99] | [0.803, 0.805] | [0.9504, 0.9512] | [0.0696, 0.0918] | |
0.03 | 0.060 | [165, 174] | [0.718, 0.720] | [0.9503, 0.9509] | [0.0581, 0.0903] |
0.090 | [55, 57] | [0.659, 0.661] | [0.9505, 0.9511] | [0.0756, 0.0950] | |
0.05 | 0.100 | [123, 129] | [0.647, 0.649] | [0.9502, 0.9505] | [0.0690, 0.0986] |
0.150 | [41, 43] | 0.584, 0.586 | 0.9509, 0.9530 | 0.0736, 0.0911 |
p1 | p2 | Proposed Plan | Plan Based on Classical Statistics |
---|---|---|---|
0.001 | 0.002 | [602, 643] (R = 41) | 1134 (R = 1134) |
0.003 | [218, 228] (R = 10) | 351 (R = 351) | |
0.004 | [128, 133] (R = 5) | 161 (R = 161) | |
0.006 | [69, 71] (R = 2) | 74 (R = 74) | |
0.008 | [47, 49] (R = 2) | 47 (R = 47) | |
0.01 | 0.020 | [274, 290] (R = 16) | 449 (R = 449) |
0.030 | [95, 99] (R = 4) | 132 (R = 132) | |
0.03 | 0.060 | [165, 174] (R = 9) | 240 (R = 240) |
0.090 | [55, 57] (R = 2) | 68 (R = 68) | |
0.05 | 0.100 | [123, 129] (R = 6) | 167 (R = 167) |
0.150 | [41, 43] (R = 2) | 46 (R = 46) |
[1.9422,1.9422] | [1.9651, 1.9651] | [2.0230, 2.0435] | [1.9712,1.9712] | [1.9975,1.9975] | [2.0164,2.0164] | [1.9927,1.9927] | [1.9566,1.9566] |
[1.9738, 1.9738] | [1.9541, 1.9541] | [1.9800, 1.9800] | [1.9596, 1.9596] | [1.9811, 1.9811] | [2.0088, 2.0088] | [1.9858, 1.9858] | [1.9677, 1.9677] |
[2.0001, 2.0001] | [1.9659, 1.9659] | [1.9955, 1.9955] | [1.9842, 1.9842] | [1.9909,2.0512] | [1.9829, 1.9829] | [1.9684, 1.9684] | [1.9942, 1.9942] |
[1.9897, 1.9897] | [1.9836, 1.9836] | [1.9891, 1.9891] | [1.9608, 1.9608] | [2.0109, 2.0109] | [1.9912, 1.9912] | [2.0077, 2.0077] | [1.9803, 1.9803] |
[2.0106, 2.0106] | [1.9885, 1.9885] | [1.9704, 1.9704] | [1.9882, 1.9882] | [1.9689, 1.9689] | [1.9553, 1.9553] | [1.9741, 1.9741] | [1.9825, 1.9825] |
[1.9640, 1.9640] | [2.0187, 2.0187] | [1.9616, 1.9616] | [1.9865, 1.9865] | [1.9556, 1.9556] | [1.9817, 1.9817] | [1.9774, 1.9774] | [1.9316, 1.9316] |
[1.9841, 1.9841] | [1.9919, 1.9919] | [1.9737, 1.9737] | [1.9958, 1.9958] | [2.0121, 2.0121] | [2.0021, 2.0521] | [1.9665, 1.9665] | [1.9773, 1.9773] |
[1.9841, 1.9841] | [1.9570, 1.9875] | [1.9610, 1.9610] | [2.0015, 2.0015] | [1.9750, 1.9750] | [1.9825, 1.9825] | [1.9758, 1.9758] | [1.9682, 1.9682] |
[1.9668, 1.9668] | [1.9696, 1.9696] | [2.0334, 2.0334] | [1.9656, 1.9656] | [1.9819, 1.9819] | [2.0116, 2.0116] | [1.9754, 1.9754] | [1.9986, 1.9986] |
[2.0114, 2.0114] | [1.9861, 1.9861] | [1.9743, 1.9743] | [1.9594, 1.9594] | [1.9712,1.9914] | [1.9849, 1.9849] | [1.9711, 1.9711] | [1.9486, 1.9486] |
[1.9837, 1.9837] | [1.9424, 1.9424] | [1.9744, 1.9744] | [1.9605, 1.9605] | [1.9719, 1.9719] | [1.9656, 1.9656] | [1.9549, 1.9549] | [2.0174, 2.0174] |
[1.9779, 1.9779] | [2.0072, 2.0072] | [1.9875, 1.9875] | [1.9781, 1.9781] | [1.9834, 1.9834] | [1.9893, 1.9893] | [1.9276, 1.9276] | [1.9513, 1.9513] |
[1.9971, 1.9971] | [1.9963, 1.9963] | [1.9375, 1.9375] | [1.9941, 1.9941] | [1.9763, 1.9763] | [2.0108, 2.0108] | [1.9687, 1.9687] | [1.9559, 1.9559] |
[1.9611, 1.9611] | [1.9729, 1.9729] | [1.9992, 1.9992] | [1.9925, 1.9925] | [2.0073, 2.0073] | [1.9742, 1.9742] | [1.9557, 1.9557] | [1.9726, 1.9726] |
[1.9964, 1.9964] | [1.9614, 1.9614] | [1.9768, 1.9768] | [1.9991, 1.9991] | [1.9832, 1.9832] | [1.9847, 1.9847] | [1.9849, 1.9849] | [1.9918, 1.9918] |
[1.9748, 1.9748] | [1.9664, 1.9664] | [2.0035, 2.0245] | [1.9822, 1.9822] | [1.9882,1.9999] | [1.9809, 1.9809] | [1.9920, 1.9920] | [1.9994,2.0512] |
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Aslam, M.; Albassam, M. Inspection Plan Based on the Process Capability Index Using the Neutrosophic Statistical Method. Mathematics 2019, 7, 631. https://doi.org/10.3390/math7070631
Aslam M, Albassam M. Inspection Plan Based on the Process Capability Index Using the Neutrosophic Statistical Method. Mathematics. 2019; 7(7):631. https://doi.org/10.3390/math7070631
Chicago/Turabian StyleAslam, Muhammad, and Mohammed Albassam. 2019. "Inspection Plan Based on the Process Capability Index Using the Neutrosophic Statistical Method" Mathematics 7, no. 7: 631. https://doi.org/10.3390/math7070631