Question

a TiW layer is deposited on a substrate using a sputtering tool. the following table presents data, in Angstroms, from 20 subgroups of n=4. (a) Plot an x-bar and R control chart for the process. Perform run tests to western Electric rules 1 thru 5. Is the Process in Control? Revise the control limits as necessary. (b) Estimate the mean and standard deviation of the revised process. (c) Is the layer thickness of the revised process normally distributed? (d) if the specifications are 450 + - 30 Angstroms, estimate the process capability.  

Subgroup x1 x2 x3 x4

1 459 449 435 450

2 443 440 442 442

3 457 444 449 444

4 469 463 453 438

5 443 457 445 454

6 444 456 456 457

7 445 449 450 445

8 446 455 449 452

9 444 452 457 440

10 432 463 463 443

11 445 452 453 438

12 456 457 436 457

13 459 445 441 447

14 441 465 438 450

15 460 453 457 438

16 453 444 451 435

17 451 460 450 457

18 422 431 437 429

19 444 446 448 467

20 450 450 454 454

Answer 1

For the given data

a)

Now the process in control.

b)

Mean = = 449.68

We can obtain the d₂ value from the variable control chart table..

see in the subgroup size and d₂ column , we get the d₂ value.

= 16.74

Standard deviation (S)

= 2.059

S =  16.74 / 2.059 = 8.13

c)

Yes , The revised process is in control.., so the process is normally distributed.

d)

USL = 480 , LSL = 420

Process capability = C_P = (USL - LSL) / 6*S

C_P = (480 - 420) / (6 * 8.13)

C_P = 1.23

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