Q1. A TiW layer is deposited on a substrate using a sputtering tool. Table contains layer thickness measurements (in Angstroms) on 20 subgroups of four substrates.

(a) Set up and R control charts on this process. Is the process in control? Revise the control limits as necessary.

(b) Estimate the mean and standard deviation of the process.

(c) If the specifications are at 450 30, estimate fraction defectives.

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

(d) Table below contains 10 new subgroups of thickness data. Plot this data on the control charts constructed earlier. Is the process in statistical control?

Subgroup	x1	x2	x3	x4
21	454	449	443	461
22	449	441	444	455
23	442	442	442	450
24	443	452	438	430
25	446	459	457	457
26	454	448	445	462
27	458	449	453	438
28	450	449	445	451
29	443	440	443	451
30	457	450	452	437