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Problem Statement A hard-bake process is used in conjunction with photolithography in semiconductor manufacturing We wish to establish statistical control of the flow width of the resist in this process using i and R charts. Twenty-five samples, each of size five wafers, have been taken when we think the process is in control. The interval of time between samples or subgroups is one hour. The flow width measurement data (in microns) from these samples are shown in Table 6.1. Draw i and R charts. - TABLE 6.1 Flow Width Measurements (mierons) for the Hard-Bake Process Wafers Sample Number 3. R. 0.3679 13235 14128 1,6744 14573 1.6914 1.5119 14314 1.3592 1.6075 1.4666 16109 1.4951 0.2517 3. 14284 1.4871 14932 1.4324 1.5674 1.4817 0.1390 4. 1.5028 1.6352 13841 1.2831 1.5507 14712 03521 15604 1.2735 15265 14363 1.6441 14882 0.3706 13955 1.5451 13574 1.3281 L4198 14492 0.2674 1.6274 1.5064 1.8366 LA177 13144 1.58OS 04189 14190 1.4303 1.6637 1.6067 1.5519 L.5343 02447 1.3884 1.7277 1.5355 15176 13688 1.5076 0.3589 10 14039 1.6697 1.509 1.4627 15220 L5134 0.2658 14IS8 1.7667 14278 1.5928 LAI8I 1.5242 0.3509 12 1.5821 1.3355 15777 1.3908 1.7559 1.5284 04201 1.2856 13 1.4106 1.4447 1.6398 1.1928 1.3947 0.4470 14 14951 1.4036 1.5893 1.6458 1.4969 1.5261 02422 15 1.3589 1.2863 1.5996 1.2497 1.4083 1.5471 0.349 16 15747 1.5301 15171 L.1839 18662 1.5344 0,6823 17 1.3680 1.7269 1.3957 15014 14874 1.4449 0.3589 18 14163 1.3864 13057 1.6210 1.5573 1.4573 0.3153 19 1.5796 1.4185 1,6541 1.5116 1.7247 0.3062 1.5777 20 1.7106 1.4412 1.2361 1.3820 1.7601 1.5060 0.5240 21 14371 1.5051 3485 1491 1.4880 02185 22 1.5936 1.6583 0.1863 02533 14738 1.4973 14720 1.5390 23 15917 1.4333 1.5295 1.5551 1.5592 L6866 24 16399 1.5243 1.5705 1.5563 15530 1.5688 0.1156 13797 25 0.3224 1.3663 1.6240 13732 16887 1.5264 EN,.1302 R=0.32521 EX, = 37.6400 = 1.5056