LOYOLA  COLLEGE (AUTONOMOUS), CHENNAI-600 034.

M.Sc. DEGREE  EXAMINATION  – STATISTICS

FourTh SEMESTER  – APRIL 2003

ST  4801/ S  1016   indusTrial STATISTICS

16.04.2003

1.00 – 4.00                                                                                             Max: 100 Marks

PART – A                                       (10 ´ 2 = 20 Marks)

Answer ALL the questions.

 

1. Discuss the logic and statistical basis underlying the general use of 3s limits on control charts.
2. Mention the theoretical basis of p-chart and setup its control limits.
3. How is lack of control of a process determined using control chart techniques?
4. What is process capability ratio (PCR)?
5. Briefly explain the process -capability analysis.
6. What is Average run length (ARL)?
7. Explain an attribute single sampling plan.
8. What purpose does an OC curve serve?
9. Define AOQ and give an expression for AOQ for a single sampling plan.
10. Explain six-sigma quality.

 

PART – B                                          (5 ´ 8 = 40 Marks)

Answer any FIVE questions.

 

11. Define the terms : i) rational subgroups  ii) Specification limits

iii) natural tolerances iv) chance and assignable causes.

12. For the following case, state:
13. Which control charts(s) would be appropriate to use for ongoing

statistical process control;

1. Why you suggest the chart(s) given in a); ?
2. What assumptions are you making in suggesting the charts given in a)?

 

Case: A factory manufactures power sockets for use in the refining oil.  These

sockets look like those use by automobile mechanics, except that they are much

larger than and the surface in covered with block oxide instead of stainless steel

to indicate that they are specially designed for power tools.   The hexagonal

inside of  the socket is  prepared by an electrolytic method, and the resulting

diameter of the hexagon is very critical.

Rather than measure every possible diagonal in the socket, one diagonal is

selected at random. from each socket and recorded.  A sample of five

consecutively  produced sockets is taken each day, and the measures are made.

The process will be to collect data for a month, which consists of 22 observations,

and  develop trial  control limits.

 

 

 

 

 

 

 

 

 

 

 

13. A control chart indicates that the current process fraction non-conforming is

0.02. If 50 items are inspected each day, what is the probability of detecting a

shift  in the fraction  non-conforming to 0.04 on the first day after the shift?

By the end of the third day following the shift?

14. Write a detailed note on the moving average control chart.
15. Consider a modified control chart with center line at m= 0 and s =1.0. If n = 5, the tolerable fraction non-conforming is s = 0.00135 and the control limits

are at 3, sketch the OC curve for the chart.

16. Viscosity measurements on polymer are made every 10 minutes by an on-line viscometer. Eighteen observation are shown below.  The target viscosity for this process is m_o = 3200.

 

3169	3173	3162	3154	3139	3145	3160	3172	3175
3205	3203	3209	3208	3211	3214	3215	3209	3203

 

Construct a tabular cusum for this process using standardized values

of h = 8.01  and k = 0.25.

17. For the sampling plan N =120, n₁= n₂ =13, c₁ = 0 and c₂ =1, obtain Pa, ASN

(full inspection), AOQ (defective found replaced) and ATI when the submitted

lot has the fraction non-conforming at p = 0.18

18. What are acceptance and rejection lines of a sequential sampling plan for attributes? How are the OC and ASN values obtained for this plan?

 

PART – C                                       (2 ´ 20 = 40 Marks)

Answer any TWO questions.

 

19. a) Distinguish between c and u charts. Explain the situations where c and u

charts are applicable and how are the limits obtained for these charts.

1. b) Explain the procedure of obtaining the OC curve for a p-chart

with an illustration.                                                                                (10+10)

20. a) What are modified control charts? Explain the method of obtaining control

limits for modified control charts.

1. b) Write a detailed note on control charts based  on extreme values.          (12+8)

 

21. a) What purpose does a cumulative sum chart serve?
22. b) Outline the procedure of constructing V-                                      (5+15)

 

22. a) Explain with an illustration the methods of obtaining the probability of

acceptance   for a triple sampling plan.

1. What are continuous sampling plans and mention a few situations where these

plans are applied.                                                                                   (10 +10)

 

 

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