LOYOLA COLLEGE (AUTONOMOUS), CHENNAI – 600 034
B.Sc. DEGREE EXAMINATION –STATISTICS

SIXTH SEMESTER – APRIL 2007
ST 6602 – STATISTICAL PROCESS CONTROL
Date & Time: 20/04/2007 / 9:00 – 12:00 Dept. No. Max. : 100 Marks
PARTA
Answer all the questions: 10×2=20
 Mention any 4 advantages of a control chart.
 Write the 3σ control limits for a cchart with the process average equal to 4 defects.
 The control limits for a pchart 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 schart when σ is given.
 Explain the term process capability.
 What are the uses of a stem and leaf plot?
PARTB
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 boxwhisker plots for the following data on two variables and compare.
Sample no: 1 2 3 4 5 6 7 8 9 10 11 12
x_{1} : 6 10 7 8 9 12 16 7 9 15 8 6
x_{2} : 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 pchart is used with UCl=.19,CL=.1,LCL=.01 to control a process
 If 3σ limits are used , find n .
 Obtain the αrisk.
 Obtain the βrisk if p has shifted to p=.2
PARTC
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 Rchart
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
 45
 55
 37
 64
 95
 08
 5
 87
 25
 46
 39
 69
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)