LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

SUPPLEMENTARY SEMESTER EXAMINATION – JUN 2006

B.Sc. DEGREE EXAMINATION

                                           ST 6602 – STATISTICAL PROCESS CONTROL

 

 

 

Date & Time : 28/06/2006/9.00 – 12.00        Dept. No.                                                       Max. : 100 Marks

 

 

Section A

Answer all questions                                                                         ( 10 x 2 = 20 )

 

1. Define the term ‘quality of a product’.
2. Give an example each for physical and sensory quality characteristics.
3. What are control charts?
4. How are Type I and Type II errors defined with reference to control charts?
5. If the LCL and UCL of a p – chart are 5.6 and 10.3 respectively, find the corresponding control limits for np – chart (assume that n = 100).
6. Comment on the following: “Histogram can be used to study about the process capability”.
7. What is the need for variable control charts?
8. The sum of means and ranges for 20 different samples each of size 3 are obtained as 40 and 100 respectively. Find the control limits for the  and R charts.
9. Define: Process Capability Ratio’.
10. What is ‘lot sentencing’?

Section B

Answer any five  questions                                                               ( 5 x 8 = 40 )

 

1. What are chance causes and assignable causes for variation? Explain their role in the process control.
2. What are the different types of ‘Quality costs’? Explain them with examples.
3. A fraction nonconforming control chart with central line 0.10, UCL = 0.19 and LCL = 0.01 is used to control a process.

• If 3 – sigma limits are used, find the sample size for the control chart.
• Find the probability of Type I error.

1. Explain the statistical basis of a c – chart.
2. What are control limits, specification limits and natural tolerance limits?
3. Compare the advantages and disadvantages of variable control charts over attribute control charts.
4. Samples of n = 6 items are taken from a manufacturing process at regular intervals. A normally distributed quality characteristic is measured and  and S values are calculated for each sample. The sum of  and S values after 50 subgroups have been analyzed are found to be 1000 and 75 respectively.

• Compute the control limits for the and S charts.
• If the specification limits are 15 and 23 respectively, comment about the ability of the process to produce items conforming to specifications.
• Find the ARL for the above process when the process mean shifts to 21.

1. Derive the control limits for EWMA control chart.

Section C

Answer any two  questions                                                               ( 2 x 20 = 40 )

 

1. a.) Explain the procedure of constructing ‘Stem and Leaf’ plot and ‘Cause and Effect’ diagram.

b.) The time to failure in hours of an electronic component subjected to an accelerated life test is shown below. Construct a Box plot for these data and interpret it.

127, 125,125,124,151,156,137,140,133,128,122,130,118,137.                (14+6)

 

1.  a.) An automobile manufacturer wishes to control the number of nonconformities in a subassembly area producing manual transmissions. The inspection unit is defined as four transmissions and data from 16 samples(each of size 4) are shown below:

Sample Number:1       2          3          4          5          6          7          8

Number of

Nonconformities:1      3          2          1          0          2          1          5

 

Sample Number:9       10        11        12        13        14        15        16

Number of

Nonconformities:2      1          0          2          1          1          2          5

• Set up a control chart for nonconformities per unit.
• Suppose the inspection unit is redefined as 8 transmissions. Design an appropriate control chart for monitoring future production.

b.) Explain the statistical basis for a  p – chart and derive its control limits.

(12 + 8)

1. a.) A high voltage power supply should have a nominal output voltage of            350 Volts. A sample of 4 units are selected each day and tested for process control purposes. The data shown below give the difference between the observed reading on each unit and the nominal voltage times ten i.e.,

x_i = ( observed voltage on unit i – 350) x 10

 

S.No	1	2	3	4	5	6	7	8	9	10	11	12
X1	6	10	7	8	9	12	16	7	9	15	8	6
X2	9	4	8	9	10	11	10	5	7	16	12	13
X3	10	6	10	6	7	10	8	10	8	10	14	9
X4	15	11	5	13	13	10	9	4	12	13	16	11

 

• Set up and R charts on this process. Is the process in statistical control?
• If specifications are at 350 ± 5 Volts, comment on the process capability.

b.)Explain the procedure of V – mask in determining the control limits of a

CUSUM chart.                                                                                   ( 14 + 6 )

1. a) Consider the following two single sampling plans

SSP 1 : n = 100 , c = 1

SSP 2 : n = 200 , c = 2

Find the OC function for the above plans corresponding to the incoming lot fraction defective p = 0.05 , 0.10 , … , 0.30. Which plan is better? Justify.

1. b) What is meant by ‘Average Run Length’ ? Derive an expression for the same. ( 14 + 6 )

 

 

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