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
Answer ALL the questions .
PART

A (10

2 = 20 Marks)
01.
Discuss the logic and statistical basis underlying the general use of 3

limits on control charts.
02.
Mention the theoretical basis of p
 chart and setup its control limits.
03.
How is lack of control of a process determined using control chart techniques?
04.
What is process capability ratio (PCR)?
05.
Briefly explain the process
 capability analysis.
06.
What is Average run length (ARL)?
07.
Explain an attribute single sampling plan.
08.
What purpose does an OC curve serve?
09.
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: a) Which control charts(s) would be appropriate to use for ongoing
statistical process control; b) Why you suggest the chart(s) given in a); ? c) 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.
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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

= 0 and

=1.0. If n = 5, the tolerable fraction non
 conforming is

= 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
 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, n
1
= n
2
=13, c
1
= 0 and c
2
=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?
Answer any TWO questions .
PART

C (2

20 = 40 Marks)
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.
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.
b) Write a detailed note on control charts based on extreme values. (12+8)
21. a) What purpose does a cumulative sum chart serve?
b) Outline the procedure of constructing V
 mask. (5+15)
22.
a) Explain with an illustration the methods of obtaining the probability of
acceptance for a triple sampling plan. b) What are continuous sampling plans and mention a few situations where these
plans are applied. (10 +10)
* * * * *
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