Loyola College B.Sc. Statistics April 2006 Statistical Process Control Question Paper PDF Download

             LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION – STATISTICS

AC 24

SIXTH SEMESTER – APRIL 2006

                                           ST 6602 – STATISTICAL PROCESS CONTROL

(Also equivalent to STA 602)

 

 

Date & Time : 24-04-2006/9.00-12.00         Dept. No.                                                       Max. : 100 Marks

 

 

Section A

 

Answer all questions                                                                         ( 10 ´ 2 = 20 )

 

  1. What are the chief aspects of quality?
  2. What are quality costs?
  3. What is the difference between conformity and non – conformity?
  4. Mention any two ways of detecting the stability of a process using control charts.
  5. What is the ARL for a process that is in – control? How is it interpreted?
  6. What are ‘Specification Limits’?
  7. Mention the difference between c – chart and u – chart.
  8. Mention the advantage of acceptance sampling plan procedures.
  9. What is the use of probability plots?
  10. Give the control limits for EWMA control chart.

 

Section B

Answer any five  questions                                                               ( 5 ´ 8 = 40 )

 

  1. Draw the phase diagram of quality improvement and explain it.
  1. What are 3 sigma limits? Explain the logic behind their usage in control charts.
  2. The number of nonconforming switches in samples of size 150 is shown below. Construct a fraction nonconforming control chart for these data. Does the process appear to be in control? If not, assume that assignable causes can be found for all points outside the control limits and calculate the revised control limits.

Sample number:1        2          3          4          5          6          7          8

Number of

Nonconforming

Switches          :8         1          3          0          2          4          0          1

 

Sample number:9        10        11        12        13        14        15

Number of

Nonconforming

Switches          :10       6          6          0          4          0          3

  1. A control chart is to be established on a process producing refrigerators. The inspection unit is one refrigerator and a control chart for nonconformities is to be used. As preliminary data, 16 nonconformities were counted in inspecting 30 refrigerators.
    • What are the 3 – sigma control limits?
    • What is the probability of Type I error for this control chart?
    • What is the probability of Type II error for this control chart?
    • Find the average run length if the number of defects is actually 2.
  2. Explain the different approaches in the construction of u – chart with variable sample size.
  3. Explain the procedure for constructing a cumulative sum control chart.
  4. What is meant by acceptance sampling? Mention its advantages.
  5. Derive an expression for ‘Average Outgoing Quality’ with reference to single sampling plan.

Section C

Answer any two  questions                                                               ( 2 ´ 20 = 40 )

 

  1. a.) Explain the role of designed experiments in quality improvement.

b.) The data below represent the results of inspecting all units of a personal computer produced for the last 10 days. Construct a standardized

fraction nonconforming control chart for these data. Does the process appear to be in control? If not, find the revised control limits.

Day:1     2     3     4     5     6     7     8     9     10

Units Inspected:80  110 90  75   130  120 70   125  105 95

Nonconforming

Units:4     7     5    8     6      6     4      5      8     7               (8+12)

  1. ) Explain the statistical basis of a p – chart and derive its control limits.

b.) Construct probability plot to verify whether the following data has been generated from a normal population.

15,10,18,20,22,14,16,17.                                                        (10+10)

 

  1. ) Derive the control limits for and R chart.

b.) Bath concentrations are measured hourly in a chemical process. The following data shows the concentration observed on the past 10 days each on a 4 hourly period.

Day                             Concentration

1                      160      186      190      206

2                      158      195      189      210

3                      150      179      185      216

4                      151      184      182      212

5                      153      175      181      211

6                      154      192      180      202

7                      158      186      183      205

8                      162      197      186      197

9                      169      205      185      188

10                    173      203      187      183

Analyze the data using the cumulative – sum control chart if the target mean concentration is 170.                                                                            ( 10 + 10 )

 

  1. a) What are rectifying inspection plans? Mention its advantages.

b)Consider a single sampling plan with n = 100 , c = 2. Find the OC function corresponding to the incoming lot fraction defective p = 0.05 , 0.10 , … , 0.30

( 10 + 10 )

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