Word Count : 696

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To estimate the reliability, we can use the following formula: R(t) = exp(-λt) where R(t) is the reliability at time t, and λ is the failure rate. To estimate λ, we can use the following formula: λ = (n - 1) / Σ(ti - ti-1) where n is the number of failures, ti is the operating time of the i-th failure, and ti-1 is the operating time of the (i-1)-th failure.

Using the given data, we can compute the values as follows:

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i	ti	ti-1	ti - ti-1	λ	R(t)
1	3	0	3	0.003333	0.996675
2	5	3	2	0.003333	0.993362
3	31	5

What is the system reliability if R1 = R 3 = R 5 = R 7 = R 9 = 0.85 and R 2 = R 4 = R 6 = R 8 = R10 = 0.95

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.

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.

Solve the two-person zero-sum game having the following payoff matrix for player A

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

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. 

 

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). 

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