A small electronic device is designed to emit a timing signal of 200 m

Question

A small electronic device is designed to emit a timing signal of 200 milliseconds (ms) duration. In the production of this device, 10 subgroups of four units are taken at periodic intervals and tested. The results are shown in the following table:

Subgroup Number	Duration of Automatic Signal (in ms)
	a	b	c	d
1	195	201	194	201
2	204	190	199	195
3	195	197	205	201
4	211	198	193	180
5	204	193	197	200
6	200	202	195	200
7	196	198	197	196
8	201	197	206	207
9	200	202	204	192
10	203	201	209	192

i) Estimate the process mean and standard deviation.

ii) Determine the centre line and control limits for the process mean and process variability.

iii) By plotting the charts on graph paper, determine that the process is stable or not with respect to the process mean and process variability. If necessary, compute revised control limits

29 Feb 2024

Answer :

Word Count : 931

Let's solve this step by step manually. We are asked to analyze a control chart problem for a small electronic device with subgroups of size 4. We have 10 subgroups ($n=4$), each with 4 measurements of the signal duration. The tasks are: --- ## Step (i): Estimate the process mean and standard deviation ### Step 1: Compute the subgroup means $\bar{x}_i$ For each subgroup, the mean of 4 observations: #### Subgroup 1: 195, 201, 194, 201 $$ \bar{x}_1 = \frac{195 + 201 + 194 + 201}{4} = \frac{791}{4} = 197.75 $$ #### Subgroup 2: 204, 190, 199, 195 $$ \bar{x}_2 = \frac{204+190+199+195}{4} = \frac{788}{4} = 197.0 $$ #### Subgroup 3: 195, 197, 205, 201 $$ \bar{x}_3 = \frac{195+197+205+201}{4} = \frac{798}{4} = 199.5 $$ #### Subgroup 4: 211, 198, 193, 180 $$ \bar{x}_4 = \frac{211+198+193+180}{4} = \frac{782}{4} = 195.5 $$ #### Subgroup 5: 204, 193, 197, 200 $$ \bar{x}_5 = \frac{204+193+197+200}{4} = \frac{794}{4} = 198.5 $$ #### Subgroup 6: 200, 202, 195, 200 $$ \bar{x}_6 = \frac{200+202+195+200}{4} = \frac{797}{4} = 199.25 $$ #### Subgroup 7: 196, 198, 197, 196 $$ \bar{x}_7 = \frac{196+198+197+196}{4} = \frac{787}{4} = 196.75 _________ ________ ________ ________ _____.
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Failure Number			1	2	3	4	5		6	7		8	9	10
Operating Time (in hours)			3	5	31	51	76		116	140		182	250	302

Subgroup Number	Number of Mobile Phones Inspected	Number of Defective Mobile Phones
1	100	3
2	100	6
3	100	4
4	100	6
5	100	20
6	100	2
7	100	6
8	100	7
9	100	3
10	100	0
11	100	6
12	100	15
13	100	5
14	100	7
15	100	6

		Player B
		B₁	B₂	B₃	B₄	B₅
Player A	A₁	3	4	5	–2	3
Player A	A₂	1	6	–3	3	7