LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034

B.Sc. DEGREE EXAMINATION –STATISTICS

AC 24

SIXTH SEMESTER – APRIL 2007

ST 6602 – STATISTICAL PROCESS CONTROL

Date & Time: 20/04/2007 / 9:00 – 12:00 Dept. No. Max. : 100 Marks

PART-A

Answer all the questions: 10×2=20

Mention any 4 advantages of a control chart.
Write the 3-σ control limits for a c-chart with the process average equal to 4 defects.
The control limits for a p-chart are given below

UCL=.161,CL=.08,LCL=0,n=100

Find the equivalent control limits for an np chart.

Write the need for an EWMA control chart.
Define consumers risk,producers risk.
Mention any 4 advantages of acceptance sampling.
Write the expression for AOQ of a double sampling plan.
Write the control limits for an s-chart when σ is given.
Explain the term process capability.
What are the uses of a stem and leaf plot?

PART-B

Answer any 5 questions: 5×8=40

The number of defective switches in samples of size 150 are shown below. Construct a fraction defective chart for these data.

Sample number number of defective

switches

1 8

2 1

3 3

4 0

5 2

6 4

7 0

8 1

9 10

10 6

11 6

12 0

Explain the oc curve of a control chart in detail.

Explain the theory behind the construction of control limits for and S charts.
Explain the double sampling plan in detail.
Draw box-whisker plots for the following data on two variables and compare.

Sample no: 1 2 3 4 5 6 7 8 9 10 11 12

x₁ : 6 10 7 8 9 12 16 7 9 15 8 6

x₂ : 15 11 5 13 13 10 9 4 12 13 16 11

Explain the CUSUM chart in detail.
Explain the methods of measuring process capability in detail.
A p-chart is used with UCl=.19,CL=.1,LCL=.01 to control a process
- If 3-σ limits are used , find n .
- Obtain the α-risk.
- Obtain the β-risk if p has shifted to p=.2

PART-C

Answer any 2 questions: 2 x 20=40

19.a) A paper mill uses a control chart to monitor the defects in finished rolls of a

paper. Use these data to set up chart for defects per roll of paper. Does the

process appear to be in control?

Day Number of Rolls Total number of defects

1 18 12

2 18 14

3 24 20

4 22 18

5 22 15

6 22 12

7 20 11

8 20 15

9 20 12

10 20 10

b) Explain the need for

i)Pareto diagram

ii)Cause and effect diagram

iii)Defect concentration diagram in statistical process control .

a)The data shown below represents from nominal diameter value for holes drilled

in aerospace manufacturing.

Sample no x1 x2 x3 x4 x5

1 -30 50 -20 10 30

2 0 50 -60 -20 30

3 -50 10 20 30 20

4 -10 -10 30 -20 50

5 20 -40 50 20 10

6 0 0 40 -40 20

7 0 0 20 -20 10

8 70 -30 30 -10 0

9 0 0 20 -20 10

10 10 20 30 10 50

Set up & R charts. Is the process in control?

b)A normally distributed quality characteristic is controlled through use of an

and R charts.

char R-chart

UCL=626 UCL=18.795

CL=620 CL=8.236

LCL=614 LCL=0

i) If specifications are 610±15 what percentage of defective items is produced?
ii) What is the probability of detecting a shift in the process mean to be 610 on

the first sample? (σ remains constant).

iii) What is the probability of type I error?

iv) If S chart were to be used for the R chart what would be the approximate

parameters of the S chart? (4x 2.5)

a) Draw EWMA control chart for the following data on the sample mean with λ = .2 ,σ = 2.

Sample number x

b)Also obtain the tabular CUSUM values with Δ=.5σ ,α=.005

a) Draw the oc curve for a single sampling plan with n=100,c=2,N=1000

b) Obtain the single sampling plan for which

P= .01, α = .05, P= .06, β= .10

c) Obtain the expressions for AOQ and ATI. (10+10)

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