1. Statical Process Control
X,S and Shewhart control chart for
individual measurments
Prepared by : Harsh B Joshi
(M.Tech Production Engineering, 2nd Semester)
Parul Institute of Engineering, Limda
2. • Introduction
• Why Control Charts?
• X bar and S bar control charts
• Example
• Shewhart Control chart
CONTENTS
3. Two types of process data:
Variable:
Continuous data. Things we can measure. Example includes length,
weight, time, temperature, diameter, etc.
X bar and R Chart, X bar and sigma chart, chart for the individual
units
Attribute:
Non continuous data. Things we count. Examples include number
or percent defective items in a lot, number of defects per item etc.
p chart, np chart, c chart, u chart, U chart
Introduction
8. Let be the measurements on ith sample (i=1,2,…,k). The
mean , and standard deviation for ith sample are given by
Then the mean of sample means, and the mean of sample standard
deviations are given by,
, 1,2, ,ijx j n
ix is
1
1 j n
i ij
j
x x
n
2
1
j n
ij i
i
j
x x
s
n
x s
1
1 i k
i
i
x x
k
1
1 i k
i
i
s s
k
9. • Let us now decide the control limits for .ix
When the mean and standard deviation of the population from which
samples are taken are given,
iE x
3
+3 Vari i
A
E x x A
n
3
3 Var
A
i iE x x A
n
CL =
UCL=
LCL =
10. • When the mean and standard deviation are not known.
CL =
UCL= LCL=
x
1
2
1
2
2
2
3
3
A
A
x s x A s
c n
x R x A R
d n
1
2
1
2
2
2
3
3
A
A
x s x A s
c n
x R x A R
d n
11. Let us now decide the control limits for .is
• When the standard deviation of the population from
which samples are taken is known.
2iE s c
2
2 3 2 3 2+3 Var 3 3i i
B
E s s c c c c B
1
2 3 2 3 13 Var 3 3i i
B
E s s c c c c B
CL =
UCL =
LCL =
12. • When the standard deviation of the population is not
known.
iE s s
4
3 3
4
2 2
3
+3 Var 3 1i i
B
c c
E s s s s s B s
c c
3
3 3
3
2 2
3
3 Var 3 1
B
i i
c c
E s s s s s B s
c c
CL =
UCL =
LCL =
18. • MR2i = |xi – xi-1| or MR3i = |xi – xi-2|
• Computation of the Moving Range:
Moving Range Control Chart
Shewhart control charts uses generally the Moving Range method
for individual measurements.
19. We know that,
Where,
CL x x
1
1
n
x in
i
x x
Control Chart For Individual Measurements
20. • x chart upper and lower limits:
2
UCL 3 3
3
x x x
MR
x
d
2
3
MR
LCL x
d