LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
M.Sc. DEGREE EXAMINATION – STATISTICS
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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
- Discuss the statistical basis underlying the general use of 3-sigma limits on control charts.
- What is a control chart?
- Define rational subgroup concept.
- How is lack of control of a process determined by using control chart techniques?
- What is process capability ratio (PCR)?
- Why is the np chart not appropriate with variable sample size?
- Describe an attribute single sampling plan.
- Give an expression for AOQ for a single sampling plan.
- Write a short note on multivariate quality control.
- Define a) Specification limit. b) Natural tolerance limit.
Part B
Answer any five questions. 5 X 8 = 40
- What are the major statistical methods for quality improvement?
- 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.
- 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
- a) Calculate the control limits for the x and S control charts.
- b) Assume that all the points on both charts plot within the control limits. What
are the natural tolerance limits of the process?
- Write a detailed note on the moving average control chart.
- 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?
- Estimate process capability using and 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 |
- Find a single sampling plan for which p1 = 0.05, a = 0.05 p2 = 0.15 and b = 0.10.
- What are chain sampling and skip-lot sampling plans?
Part C
Answer any two questions. 2 X 20 = 40
- 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)
- a) Outline the procedure of constructing V-mask.
- b) What is Exponentially Weighted Moving Average control chart?. (15+5)
- 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)