State whether the following statements are True or False. Give reason

Question

State whether the following statements are True or False. Give reason in support of your answer.
a) If the average number of defects in an item is 4, the upper control limit of the c-chart will be 12.
b) The specification limits and natural tolerance limits are same in statistical quality control.
c) If the probability of making a decision about acceptance or rejection of a lot on the first sample is 0.80 and the sizes of the first and second samples are 10 and 15, respectively, then the average sample number for the double sampling plan will be 25.
d) Two independent components of a system are connected in series configuration. If the reliabilities of these components are 0.1 and 0.30, respectively then the reliability of the system will be 0.65.
e) A point in the pictorial representation of a decision tree having states of nature as immediate sub-branches is known as decision point.

29 Feb 2024

Answer :

Word Count : 490

Let's analyze each statement carefully manually, step by step: --- a) If the average number of defects in an item is 4, the upper control limit of the c-chart will be 12. * For a c-chart (used for counting defects per item): $$ \text{UCL} = \bar{c} + 3\sqrt{\bar{c}}, \quad \text{LCL} = \bar{c} - 3\sqrt{\bar{c}} $$ Here, $\bar{c} = 4$. So, $$ \text{UCL} = 4 + 3\sqrt{4} = 4 + 3 \cdot 2 = 4 + 6 = 10 $$ ✅ Answer: _______ ____ __________ ______ _______ _______ _________.
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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

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