ST 4801 – INDUSTRIAL STATISTICS

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

SECTION A

Answer all the questions 10 x 2 = 20

Define rational subgroup concept.
What are chance and assignable causes of variation?
What information is provided by the OC curve of a control chart?
Write down the expression for process capability ratio (PCR) when only the lower specification is known.
Why is the np chart not appropriate with variable sample size?
What is an Average Run Length (ARL)?
Explain an attribute single sampling plan.
Give an expression for AOQ for a single sampling plan.
What is a control chart?
Write a short note an multivariate quality control chart

SECTION B

Answer any five questions 5 x 8= 40

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.

A control chart for the fraction non-conforming is to be established using a CL of p = 0.10. What sample size is required if we wish to detect a shift in the process fraction non-conforming to 0.20 with probability 0.50?
Explain the method of constructing control limits for and R charts when the sample sizes are constant.
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 0.26?
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

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 is chain sampling and skip-lot sampling plans?
Write short notes on V-mask procedure.

SECTION 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.

20 a) What are acceptance and rejection lines of a sequential sampling plan for

attributes?. How are the OC and ASN values obtained for this plan

b). A control chart for non-conformities per unit uses 0.95 and 0.05 probability limits.

The center line is at u = 2.4.Determine the control limits if the sample size n =15

(10+10)

21 a) Write a detailed note on the moving average control chart.

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

for modified control charts. (8+12)

22 a) Explain with an illustration the method of obtaining the probability of acceptance

for a double sampling plan.

b) What are continuous sampling plans and mention a few situations where these plans

are applied. (12+8)