No. of Printed Pages: 4 IMSTL-002/S11 POST GRADUATE DIPLOMA IN APPLIED STATISTICS (PGDAST) CTI Term-End Examination ("..J June, 2016
I'll
1._.
IJ MSTL-002/S1 INDUSTRIAL STATISTICS LAB SET-1
Time Hours Maximum Marks: 50
Note: Attempt any two questions.
Solve the questions in Microsoft Excel.
Use ofFormulae and Statistical Tables Booklet for PGDAST is allowed.
Mention necessary steps, hypothesis, interpretation, etc.
Symbols have their usual meanings.

1. A new process of producing ball bearings is started. For monitoring the outside diameter of the ball bearings, the quality controller takes samples of four ban bearings at 10.00 AM., 12.00 Noon, 2.00 P.M.,4.00 P.M. and 6.00 P.M. The outside diameter (in mm) of each selected ball bearing is measured. The results of the measurement over a 5-day production period are as follows

Day Sample Number Time Observations
X1 X2 X3 X4
1 10.00 A.M. 52 52 50 51
2 12.00 Noon 50 53 52 53
Monday 3 2.00 P.M. 54 51 50 52
4 4.00 P.M. 62 65 60 62
5 6.00 P.M. 51 52 50 53

6 10.00 AM. 50 52 51 50
7 12.00 Noon 50 54 52 51
Tuesday 8 2.00 P.M. 52 51 53 50
9 4.00 P.M. 52 53 52 55
10 6.00 P.M. 51 51 50 51

11 10.00 A.M. 52 52 54 62
12 12.00 Noon 49 48 50 50
Wednesday 13 2.00 P.M. 52 53 54 49
14 4.00 P.M. 52 51 54 51
15 6.00 P.M. 51 51 52 52

Day Sample Number Time Observations
X1 X2 X3 X4
16 10.00 A.M. 50 50 51 52
17 12.00 Noon 50 51 53 51
Thursday 18 2.00 P.M. 52 50 49 53
19 4.00 P.M. 52 51 54 51
20 6.00 P.M. 45 43 50 52

21 10.00 A.M. 52 54 53 50
22 12.00 Noon 50 50 52 51
Friday 23 2.00 P.M. 54 52 50 52
24 4.00 P.M. 50 54 54 50
25 6.00 P.M. 51 51 50 52

Which control charts should be used to control the process mean and process variability of the process of producing ball bearings?

Construct these charts and check whether the process is under statistical control or not.

Also plot the revised control charts, if necessary.

An electronics firm is manufacturing computer memory chips. Statistical quality control methods are to be used to monitor the quality of the chips produced. Any chip that does not meet specifications is classified as defective. 250 chips are sampled on each of the 30 consecutive working days. The number of defective chips found each day are recorded in the following table

Working No. of Working No. of Working No. of
Day Defectives Day Defectives Day Defectives
1 12 11 20 21 15
2 8 12 15 22 16
3 18 13 11 23 7
4 14 14 14 24 14
5 9 15 7 25 12
6 13 16 15 26 8
7 10 17 12 27 14
8 14 18 8 28 12
9 8 19 22 29 8
10 12 20 9 30 10

Construct the appropriate control chart and state whether the process is under statistical control or not.

Calculate the revised centre line and control limits to bring the process under statistical control. Also plot the revised control chart.

2. The number of accidents on a particular stretch of highway seems to be related to the number of vehicles and the speed at which they are travelling. A city councillor has decided to examine the data statistically so that new speed laws, that will reduce traffic accidents, may be introduced. The data for 40 randomly selected days is given in the following table

No. of No. of Average Speed No. of No. of Average Speed
Accidents Vehicles Accidents Vehicles
2 2123 68 13 3484 75
6 2501 74 5 2400 60
12 2722 83 12 3220 71
3 2214 63 11 3092 78
17 2840 80 12 3200 75
8 2625 71 7 2901 66
12 2723 78 4 2682 68
4 2146 60 5 2880 59
8 2682 71 2 2102 60
14 3203 82 6 2943 55
10 3100 68 8 3012 76
11 2842 72 10 3407 78
12 3002 75 12 3450 60
20 3526 88 6 2703 58
6 2405 64 3 2260 72
7 3201 65 3 2406 60
2 2318 63 4 3012 77
10 2845 72 6 3210 62
8 3017 70 4 3121 60
11 3284 70 12 3429 68

Prepare a scatter matrix to get a rough idea about the relationship among the variables.

Develop a multiple linear regression model.

Test the significance of the fitted regression model and individual regression coefficient at level of significance.

Find the 99% confidence interval of the regression parameters.

Check the linearity and normality assumptions for regression analysis.

3. The following data refers to the sales of commercial vehicles at the All India level of a leading automobile company in the country during three financial years:

Month Year
2013 2014 2015

April 724 1414 1243
May 1440 2117 1818
June 1606 2199 2880
July 1656 2583 1693
August 1549 2358 2136
September 2285 3677 3707
October 1523 1823 1931
November 1856 2372 1637
December 2135 2301 1746
January 2119 2761 2638
February 2075 2110 2655
March 3850 3996 3576

Compute 12-monthly moving averages and plot the graph of the moving averages with the sales data.

Compute the seasonal indices for 12 months.

Obtain deseasonalised values.

Plot the given data along with deseasonalised values.