To monitor the manufacturing process of mobile phones, a quality controller randomly selected 100 mobile phones from the production line, each day over 15 days. The mobile phones were inspected for defectives and the number of defective mobile phones found each day was recorded. The data are given below:

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

 i) Determine the trial centre line and control limits for the fraction defective using the above data. 

ii) Contract the control chart on graph paper and determine that the process is stable or not. If there is any out-of-control point, determine the revised centre line and control limits.

Word Count : 893

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To construct a control chart for the fraction defective, we need to calculate the proportion defective for each subgroup. The formula for the proportion defective is:

p = (number of defective mobile phones) / (number of mobile phones inspected)

Using the data provided, we can calculate the proportion defective for each subgroup as follows:

Subgroup 1: p1 = 3/100 = 0.03
Subgroup 2: p2 = 6/100 = 0.06
Subgroup 3: p3 = 4/100 = 0.04
Subgroup 4: p4 = 6/100 = 0.06
Subgroup 5: p5 = 20/100 = 0.2
Subgroup 6: p6 = 2/100 = 0.02
Subgroup 7: p7 = 6/100 = 0.06
Subgroup 8: p8 = 7/100 = 0.07
Subgroup 9: p9 = 3/100 = 0.03
Subgroup 10: p10 = 0/100 = 0
Subgroup 11: p11 = 6/100 = 0.06
Subgroup 12: p12 = 15/100 = 0.15
Subgroup 13: p13 = 5/100 = 0.05
Subgroup 14: p14 = 7/100 = 0.07
Subgroup 15: p15 = 6/100 = 0.06

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Subgroup Number

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

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The failure density function of a random variable T is given by

Calculate, the
i) reliability of the component. 
ii) reliability of the component for a 100 hour mission time. 
iii) mean time to failure (MTTF). 
iv) median of the random variable T. 
v) life of the component, if the reliability of 0.96 is desired. 

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To monitor the manufacturing process of mobile phones, a quality controller randomly selected 100 mobile phones from the production line, each day over 15 days. The mobile phones were inspected for defectives and the number of defective mobile phones found each day was recorded. The data are given below:

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

 i) Determine the trial centre line and control limits for the fraction defective using the above data. 

ii) Contract the control chart on graph paper and determine that the process is stable or not. If there is any out-of-control point, determine the revised centre line and control limits.

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A shirt manufacturing company supplies shirts in lots of size 250 to the buyer. A single sampling plan with n = 20 and c = 1 is being used for the lot inspection. The company and the buyer decide that AQL = 0.04 and LTPD = 0.10. If there are 15  defective in each lot, compute the
i) probability of accepting the lot. 
ii) producer’s risk and consumer’s risk. 
iii) average outgoing quality (AOQ), if the rejected lots are screened and all defective shirts
are replaced by non-defectives. 
iv) average total inspection (ATI). 

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The failure data of 10 electronic components are shown in the table given below:

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

Estimate, the
i) reliability. 
ii) cumulative failure distribution.
iii) failure density. 
iv) failure rate functions.