LOYOLA COLLEGE (AUTONOMOUS), CHENNAI –600 034
B.Sc., DEGREE EXAMINATION – STATISTICS
SIXTH SEMESTER – APRIL 2004
ST 6602/STA 602 – STATISTICAL PROCESS CONTROL
07.04.2004 Max:100 marks
1.00 – 4.00
SECTION – A
Answer ALL the questions (10 ´ 2 = 20 marks)
- Explain Statistical Process Control.
- What are control limits?
- Describe Total Quality Management (TQM).
- Define ‘Chance’ and ‘Assignable’ causes of variation.
- Discuss rational subgroup concept.
- What information is provided by the operating characteristic curve of a control chart?
- Define Process Capability Ratio (PCR).
- Define Average Run Length Concept.
- Why is np-chart not appropriate with variable sample size?
- Explain Demerit Scheme.
SECTION – B
Answer any FIVE questions (5 ´ 8 = 40 marks)
- What is quality? What are different dimensions of quality?
- A quality characteristic is monitored by a control chart designed so that the probability that a certain out-of-control condition will be detected on the first sample following the shift to that state is 1 -b.
Find the following:
- The expected number of subgroups analyzed before the shift is detected.
- The probability that the shift is not detected on m -th subsequent sample.
- Samples of n = 8 items each are taken from a manufacturing process at regular intervals. A quality characteristic is measured and and R values are calculated for each sample. After 50 samples, we have
Assume that the quality characteristic is normally distributed. Compute control limits for
the and R control charts.
- Statistical monitoring of a quality characteristic uses both an and S charts. The charts are to be based on the standard values m = 200 and s = 10, with n = 4. Find 3 – sigma control limits for the S-chart and – chart.
- Distinguish between c and u charts.
- In designing a fraction non-conforming chart with center line at p = 0.20 and 3 – sigma control limits, what is the sample size required to yield a positive LCL?
- Define the terms i) Specification Limits and ii) Natural Tolerances with an illustration.
- How is lack of control of a process determined using control chart technique?
SECTION – C
Answer any TWO questions (2 ´ 20 = 40 marks)
- a) Explain ‘Stem – amd – Leaf plot’ with an illustration.
- b) A normally distributed quality characteristic is monitored by a control chart with L –
sigma control limits. Develop a general expression for the probability that a point will
plot outside the control limits when the process is really in control. (10+10)
- Suppose each automobile produced on an assembly between 9 a.m. and 10 a.m. is examined for paint blemishes on the left front door, with the results given in the following Table. These blemishes may not be easily seen with the naked eye, but a trained inspector with a special light source and magnifying glasses can spot them.
| Automobile No. | 1 2 3 4 5 6 7 8 9 10
0.84 0.62 0.84 1.08 0.62 0.84 1.08 0.84 1.08 0.62
3 2 4 5 4 2 12 6 7 4 |
| Surface Area in Sq.Mt. | |
| No. of Blemishes |
For the above case, state:
- Which control chart (s) would be appropriate to use for ongoing SPC?
- Why do you suggest the chart (s) in a) ?
- What assumptions are you making in suggesting the chart (s) in a) ? (8+6+6)
- a) Mention the theoretical base of p-chart and set up its control limits:
- Explain the procedure of obtaining the OC curve for a p-chart with an illustration.
(8+12)
- Write short notes on:-
- Six – Sigma quality
- Single Sampling Plan. (10+10)
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