You are a third year technical apprentice and you have been asked by your supervisor to contribute to the quality standards for particular products because your company feel that they need to develop their quality processes. The company feel that using statistics will enable them to enhance the quality of their product and so they are considering statistics to examine processes and wish you to evaluate what is available and then to apply the best methods to a particular product. The company produce a small component that has a hole in it that is critical and checked with a plug gauge. The company produce these in batches of 50 and initially carries out 100% inspection. The company are concerned that the process is not in control and have asked you to investigate. Table One gives the defects for 50 batches which you need to use to produce attribute control charts, np and p charts. Table Two gives the next 100 batches. You are expected to: 1. construct the control charts np and p using table one, 2. document your research into ways in which the data can be used to inform the company about the process; 3. determine the extent that the process is under control using that data in table two The tables on following pages give the actual sizes of the diameter "A" and length "B" of a stud that the company produces on one of their CNC machines. Design statistical variable control charts involving the mean and range, X and R charts for diameter A. The measurements were taken in batches of 5 and recorded on the table as 1-5 first batch, 6-10 second batch etc. Use the first 50 entries [10 batches] to do this. 1. construct the control charts X and R using this data, 2. document your research into ways in which the data can be used to inform the company about the process; 3. determine the extent that the process is under control using the rest of the data in the table for diameter A, remember these are in batches of 5. Using the data in the table for the length B of the stud produce: 1. a statistical process capability chart for length B for the first 100 studs. 2. an evaluation regarding the machine's capability based on a calculation of Cp and Cpk for the length of the stud, and how the process can be improved. 3. produce a modified control chart and plot the rest of the data from the table for the length B of the stud Produce a report that includes: An evaluation of the use of the statistical methods possible and how they have influenced the design and successful use of process control charts. A Process Capability Study based on your outcomes from the data used from the table for the length B of the stud. The size for dimension A is 12.5mm ±0.3. The sizes given in the table are in millimetres. The size for dimension B is 20.2mm ±0.2. The sizes given in the table are in millimetres. Table One Batch Batch Number Output 100 100 100 1 2 3 4 5 6 7 8 9 23 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Batch Defects 17 19 11 3 2 17 15 13 14 5 2NFRAREamonn Hagang 12 19 14 18 17 14 20 20 15 19 16 14 11 9 3 6 5 20 20 17 5 18 8 4 6 18 17 7 11 9 19 19 20 7 5 9 7 20 Table Two Batch Number 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 Batch Output 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 100 Batch Defects 19 20 12 15 12 18 17 15 18 15 19 11 4 12 11 3 17 5 13 15 17 7 10 14 17 5 15 11 4 11 4 14 16 11 14 2 16 6 12 16 9 10 16 9 3 13 15 13 15 8 Batch Number 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 Batch Output 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 106 107 109 111 104 110 103 108 112 111 106 107 109 111 104 110 103 108 112 111 106 107 119 111 104 110 113 108 112 111 Batch Defects 2 10 21 13 3 3 6 2 10 5 14 12 14 16 7 14 6 2 9 19 8 14 12 17 13 13 9 18 18 5 7 17 12 16 12 13 9 12 18 5 8 14 12 17 18 17 9 18 17 6 TABLE 3 Dimension A 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 0 u 2 3 44 45 46 47 48 49 50 40 41 42 43 12.488 12.685 12.636 12.448 12.470 12.381 12.383 12.403 12.611 12.520 12.666 12.404 12.627 12.580 12.414 12.636 12.538 12.553 12.424 12.681 12.365 12.675 12.413 12.624 12.617 12.324 12.537 12.446 12.610 12.622 12.370 12.499 12.342 12.515 12.573 12.444 12.348 12.553 12.359 12.365 12.652 12.359 12.522 12.362 12.643 12.348 12.423 12.432 12.603 12.696 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 12.613 12.678 12.475 12.643 12.539 12.669 12.699 12.410 12.551 12.612 12.390 12.520 12.697 12.324 12.429 12.405 12.587 12.545 12.441 12.402 12.390 12.708 12.355 12.357 12.528 12.534 12.693 12.353 12.714 12.459 12.490 12.496 12.611 12.476 12.510 12.403 12.629 12.518 12.551 12.492 12.366 12.496 12.506 12.364 12.403 12.692 12.343 12.627 12.581 12.412 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 12.717 12.618 12.359 12.453 12.383 12.663 12.345 12.391 12.696 12.501 12.383 12.409 12.606 12.591 12.604 12.668 12.658 12.521 12.466 12.458 12.389 12.408 12.506 12.447 12.555 12.441 12.447 12.484 12.595 12.467 12.612 12.432 12.636 12.570 12.404 12.401 12.516 12.401 12.330 12.647 12.351 12.660 12.625 12.487 12.692 12.711 12.388 12.543 12.343 12.551 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 12.358 12.437 12.699 12.570 12.565 12.628 12.469 12.451 12.582 12.355 12.611 12.542 12.707 12.652 12.498 12.657 12.646 12.559 12.551 12.699 12.495 12.365 12.602 12.613 12.445 12.488 12.702 12.489 12.525 12.355 12.355 12.359 12.557 12.471 12.550 12.585 12.592 12.572 12.349 12.478 12.582 12.731 12.685 12.533 12.520 12.422 12.654 12.693 12.663 12.709 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 12.359 12.711 12.617 12.719 12.444 12.397 12.730 12.692 12.413 12.474 12.537 12.527 12.646 12.467 12.601 12.549 12.395 12.671 12.474 12.556 12.385 12.515 12.391 12.468 12.542 12.496 12.536 12.389 12.491 12.372 12.584 12.623 12.426 12.559 12.677 12.475 12.628 12.579 12.457 12.383 12.663 12.462 12.493 12.536 12.607 12.569 12.609 12.675 12.450 12.719