LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.Sc. DEGREE EXAMINATION – STATISTICS
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FOURTH SEMESTER – APRIL 2007
ST 4808 – STATISTICAL COMPUTING – III
Date & Time: 23/04/2007 / 9:00 – 12:00 Dept. No. Max. : 100 Marks
Answer Any three Questions:
- Analyse the following 23 Confounded factorial design
Replication -1
| Block-1 | N 120 | P 121 | K 141 | Npk 151 |
| Block-2 | (1) 121 | Nk 145 | Np 167 | Kp 211 |
Replication -2
| Block-1 | Knp 131 | K 101 | Np 141 | (1) 51 |
| Block-2 | Nk 62 | N 83 | P 43 | Pk 32 |
Replication -3
| Block-1 | Knp 142 | Pk 123 | N 195 | (1) 143 |
| Block-2 | Np 143 | Nk 105 | P 165 | K 212 |
- 2) Analyse the following Repeated Latin Square design, stating all the Hypotheses, Anova and Inferences. The data represent the Production in Millions of five different soft drinks in five seasons at five different Companies( for the first two weeks).
WEEK-1
| Company/Season | 1 | 2 | 3 | 4 | 5 |
| S1 | A125 | B338 | C345 | D563 | E233 |
| S2 | B635 | C453 | D634 | E784 | A345 |
| S3 | C455 | D901 | E344 | A124 | B466 |
| S4 | D781 | E443 | A235 | B 948 | C452 |
| S4 | E245 | A378 | B565 | C712 | D344 |
WEEK-2
| Company/Season | 1 | 2 | 3 | 4 | 5 |
| S1 | A255 | B385 | C455 | D156 | E273 |
| S2 | B165 | C454 | D645 | E748 | A734 |
| S3 | C475 | D903 | E354 | A124 | B456 |
| S4 | D078 | E432 | A253 | B498 | C455 |
| S5 | E485 | A782 | B556 | C142 | D534 |
3 a). The data given below are temperature readings from a chemical process in a
degrees centigrade, taken every two minutes.
853 985 949 937 959
945 973 941 946 939
972 955 966 954 948
945 950 966 935 958
975 948 934 941 963
The target value for the mean is m0 = 950
i). Estimate the process standard deviation.
ii). Set up and apply a tabular CUSUM for this process, using standardized values
h = 5 and k = 0.5. Interpret this chart.
Reconsider the above data. Set up and apply an EWMA control chart to these
data using l = 0.1 and L =2.7.
b). Find a single sampling plan for which p1 = 0.05, a = 0.05, p2 =0.15 and
b = 0.10.
- a). A paper mill uses a control chart to monitor the imperfections in finished rolls of paper. Production output is inspected for 20 days, and the resulting data are shown below. Use these data to set up a control chart for nonconformities per roll of paper. Does the process appear to be in statistical control? What center line and control limits would you recommend for controlling current production?
Day: Number of rolls produced Total number of imperfection
1 18 12
2 18 14
3 24 20
4 22 18
5 22 15
6 22 12
7 20 11
8 20 15
9 20 12
10 20 10
11 18 18
12 18 14
13 18 9
14 20 10
15 20 14
16 20 13
17 24 16
18 24 18
19 22 20
20 21 17
- (b) Solve the following IPP :
Maximize
Subject to
are nonnegative integers
- Consider the design of an electronic device consisting of three main components. The three components are arranged in series so that the failure of one component will result in the failure of the entire device. The reliability of the device can be enhanced by installing standby units in each component. The design calls for using one or more standby units, which means that each main component may include upto three units in parallel. The total capital available for the design of the device is $10,000. The data for the reliability, cost for various components for given number of parallel units are summarized below. Determine the number of parallel units for each component that will maximize the reliability of the device without exceeding the allocated capital. You should use dynamic programming technique to solve the given problem.
| 1 | 0.6 | 1 | 0.7 | 3 | 0.5 | 3 |
| 2 | 0.8 | 2 | 0.8 | 5 | 0.7 | 4 |
| 3 | 0.9 | 3 | 0.9 | 6 | 0.9 | 5 |
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