LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
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M.Sc. DEGREE EXAMINATION – STATISTICS
FOURTH SEMESTER – APRIL 2008
ST 4806 – STATISTICAL PROCESS CONTROL
Date : 21/04/2008 Dept. No. Max. : 100 Marks
Time : 9:00 – 12:00
SECTION – A
Answer ALL the questions 10×2 =20
- Discuss the statistical basis underlying the general use of 3 – sigma limits on control charts.
- What are chance and assignable causes of variation?
- Describe the rational subgroup concept
- Discuss the relationship between a control chart and statistical hypothesis testing.
- Why is the np chart not appropriate with variable sample size?
- What is process capability ratio (PCR) when only the lower specification is known ?.
- Define a) Specification limit. b) Natural tolerance limit.
- A Chain SP– I plan has n = 4 , c = 0 and i = 3 .Draw the OC curve for this plan.
- Explain sequential sampling plan.
- Write a note on modified control chart.
SECTION- B
Answer any FIVE questions 5 x 8= 40
11.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
is 1 – b. Find the following:
a). The probability that the out of control condition will be detected on the second sample
following the shift.
b). The expected number of subgroups analyzed before the shift is detected.
12.You consistently arrive at your office about one-half hour late than you would like. Develop
a cause and effect diagram that identifies and outlines the possible causes of this event.
13.Explain the method of constructing control limits for and R charts when the sample sizes
are different for various subgroups.
14.The manufacturer wishes to set up a control chart at the final inspection station for a gas
water heater. Defects in workmanship and visual quality features are checked in this
inspection. For the last 22 working days , 176 water heaters were inspected and a total of 924
nonconformities reported .
- a) What type of control chart would you recommend here and how would you use it?.
- b) Using four water heaters as the inspection unit ,calculate the center line and control
limits that are consistent with the past 22 days of inspection data.
15.Estimate process capability usingand R charts for the power supply voltage data . If
specifications are at 350 5 V, calculate PCR, PCRk and PCRkm. Interpret these capability
ratios.
| Sample # | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
| X1 | 6 | 10 | 7 | 8 | 9 | 12 | 16 | 7 | 9 | 15 |
| X2 | 9 | 4 | 8 | 9 | 10 | 11 | 10 | 5 | 7 | 16 |
| X3 | 10 | 6 | 10 | 6 | 7 | 10 | 8 | 10 | 8 | 10 |
| X4 | 15 | 11 | 5 | 13 | 13 | 10 | 9 | 4 | 12 | 13 |
16.Explain the V- Mask procedure with an illustration.
17.Describe Six- sigma quality .
18.Consider the single – sampling plan for which p1 = 0.01 , a = 0.05 , p2 = 0.10 and b = 0.10 .
Suppose that lots of N = 2000 are submitted. Draw the AOQ curve and find the AOQL.
SECTION- C
Answer any two questions 2 X 20 = 40
- 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) Find 0.900 and 0.100 probability limits for a c-chart when the process average is
equal to 16 non- conformities. (14+6)
- a)Suppose the process was in control with mean m0 and something happened today and mean
shifted to m0 + as , s is known. Using X – chart and – chart, find out which chart has a
greater chance of detecting the shift.
- b) Discuss Multivariate Quality Control (10+10)
- a)Explain the Tabular CUSUM for monitoring the process mean with an illustration.
- b) What is Exponentially Weighted Moving Average control chart ? (10+10)
- a) Describe AQL and LTPD concepts.
b).Write short notes on:-
- Skip – Lot sampling plan with an illustration
- Continuous sampling plans with an illustration ( 8 + 12 )