LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

M.Sc. DEGREE EXAMINATION – STATISTICS

AC 50

FOURTH SEMESTER – APRIL 2007

ST 4806/ST 4803 – STATISTICAL PROCESS CONTROL

 

 

 

Date & Time: 18/04/2007 / 9:00 – 12:00          Dept. No.                                                          Max. : 100 Marks

 

 

Part A

Answer all the questions.                                                 10 X 2 = 20

 

1. Discuss the statistical basis underlying the general use of 3-sigma limits on control charts.
2. What is a control chart?
3. Define rational subgroup concept.
4. How is lack of control of a process determined by using control chart techniques?
5. What is process capability ratio (PCR)?
6. Why is the np chart not appropriate with variable sample size?
7. Describe an attribute single sampling plan.
8. Give an expression for AOQ for a single sampling plan.
9. Write a short note on multivariate quality control.
10. Define a) Specification limit. b) Natural tolerance limit.

Part B

Answer any five questions.                                                                 5 X 8 = 40

 

11. What are the major statistical methods for quality improvement?
12. A control chart with 3 sigma control limits monitors a normally distributed quality characteristic. Develop an expression for the probability that a point will plot outside the control limits when the process is really in control.
13. Samples of n = 6 items are taken from a manufacturing process at regular interval. A normally distributed quality characteristic is measured and x and S values are calculated for each sample. After 50 subgroups have been analyzed, we have

 

_i  = 1000 and       _i = 75

1. a) Calculate the control limits for the x and S control charts.
2. b) Assume that all the points on both charts plot within the control limits. What

are the natural tolerance limits of the process?

14. Write a detailed note on the moving average control chart.

 

 

 

15. In designing a fraction non-conforming chart with CL at p =0.20 and 3-sigma control limits, what is the simple size required to yield a positive LCL? What is the value of n necessary to give a probability of .50 of detecting a shift in the process to be 0.26?

 

16. Estimate process capability using and R charts for the power supply voltage data . If specifications are at 350 ± 5 V, calculate PCR, PCR_k and PCR_km. 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

17. Find a single sampling plan for which p₁ = 0.05, a = 0.05 p₂ = 0.15 and b = 0.10.
18. What are chain sampling and skip-lot sampling plans?

Part C

Answer any two questions.                                            2 X 20 = 40

 

19. a). Explain the procedure of obtaining the OC curve for a p-chart with an illustration.

b). Explain process capability analysis with an illustration.                                        (12+8 )

 

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

for modified control charts.

b). A control chart for non-conformities per unit uses 0.95 and 0.05 probability limits.The center line is at u = 1.4.Determine the control limits if the sample size n =10

(14+6)

21. a) Outline the procedure of constructing V-mask.
22. b) What is Exponentially Weighted Moving Average control chart?. (15+5)

 

22. a) Write a detailed note on six-sigma quality.

b). Explain with an illustration the method of obtaining the probability of acceptance

for a triple sampling plan.                                                                                        (10 + 10)

 

 

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