Question

A company is manufacturing integrated circuits. The design specifies the nominal thickness of the IC resistance layer to be 100 units. If the thickness strays too far from 100 units IC performance may be degraded. Assume the process is in control when 25 samples of IC resistance layer thickness (each of size 4) were taken off the production line. Using the methods of Control Charts for Variables, we want to achieve statistical control of the resistance layer thickness using X-bar and R charts.

The 25 sample values are provided in the following table.

Sample No.	Sample Values
1	90.42	90.92	98.98	93.26
2	91.91	86.45	103.18	103.58
3	110.85	96.96	98.19	102.65
4	125.56	106.68	105.53	97.33
5	111.84	100.27	93.82	111.41
6	98.12	97.76	90.02	112.4
7	107.87	87.01	106.06	119.58
8	100.17	100.93	80.77	88.77
9	94.02	100.77	107.21	101.69
10	93.49	112.24	100.73	95.44
11	89	91.44	104.04	98.09
12	94.12	93.56	95.84	102.98
13	107.21	86.29	97.46	122.98
14	95.35	100.9	106.59	100.73
15	101.66	109.1	92.83	86.62
16	103.35	80.3	117.23	93.92
17	103.31	94.49	115.74	103.28
18	103.87	118.35	111.11	91.97
19	106.45	105.86	108.14	97.13
20	89	98.45	112.17	111.68
21	115.88	108.87	104.21	91.71
22	106.19	96.96	102.49	103.81
23	99.48	107.25	92.07	101.53
24	99.35	90.06	72.8	94.88
25	96.87	101.96	101.92	105.49

Calculate an R chart based on these data.

Calculate an X-bar chart based on these data.

Can the R chart and the X-bar chart just calculated be employed to monitor the process? Explain your answer.

Explain the significance of the Central Limit Theorem to Statistical Process Control.

Answer 1

Answer:

The design specifies the nominal thickness of the IC resistance layer to be 100 units. If the thickness strays too far from 100 units IC performance may be degraded. The process is control when 25 samples of IC resistance layer thickness were taken off the production line.

a. The center line value for R chart (\overline{R}) is 19.6096

And the respective control limits are:For subgroup size 4

LCL = D_{3}*\overline{R} = 0* 19.6096 = 0

UCL = D_{4}*\overline{R} = 2.282 * 19.6096 =44.74911

b. The center line value for X-Bar chart (\overline{X}) is 100.5121

And the respective control limits are:For subgroup size 4

LCL = \overline{\overline{X}}-A_{2} \overline{R} = 100.5121-0.729 19.6096 = 86.2167

UCL =\overline{\overline{X}}+A_{2} \overline{R} = 100.5121+0.729 19.6096 = 114.8105

c.

c. The contol limits, here, may be employed to monitor the process, however other process improvement tools should be used along with the control charts.Control charts only depicts any special causes of variation, if any.

d.Contol charts:

In R chart, Since point corresponding to sample 37 lie outside the control limit, the process is out of control

Similarly, in X-bar chart,samples after 30 lie outside the control limits which implies process is out of control.