Statistical Process Control
(SPC)
What is Quality?


Fitness for use
Conformance to the standard
Quality Improvement
Quality improvement processes that involve
statistical method;
1.
2.
3.
Incoming Quality Control
Statistical Process Control
Outgoing Quality Control
Incoming & Outgoing QC
Acceptance Sampling


Lot by lot sampling plan for attributes
Acceptance sampling by variables
Lot by Lot Sampling Plan For
Attributes
Types Of Sampling Plan
 Single Sampling Plan
 Double Sampling Plan
 Multiple Sampling Plan
 Sequential Sampling Plan
MIL STD 105E (ISO 2859)
Acceptance Sampling By Variables
Types Of Sampling Plan
 Plan that control the lot/process fraction
defective/nonconforming.
 Plan that control the lot/process parameter
MIL STD 414 Tables
Statistical Pocess Control
Chance and Assingable Cause Of Quality
Statistical basis for control chart
 Basic Principles
 Choice Of Control Limit
 Sample Size & Sampling Frequency
 Subgroups
 Analysis Of Patterns On Control Charts
x
Control Charts For Variables
(Univariate)
x and R charts
x and s charts
x and R charts





Statistical basis of the charts
Development and use of the charts
Interpretation of the charts
The operating characteristics function
Average Run Length (ARL) for the mean chart
x and s charts

Constuction & Operation of the charts

Control charts with variable sample size
Control Charts For The Attributes
Control Charts for the fraction non-conforming
 Development & Operation
 Variable sample size
 OC and ARL
Control Charts for non-conformities
 Procedure with constant sample size
 Procedure with variable sample size
 OC and ARL
Process Capability Analysis



Using histogram
Using probality plots
Process Capability Ratio (PCR)





Cp
PCR for an of center process
Normality and PCR
Confidence Interval & Test on PCR
PCR using control charts
Chance and Assingable Cause Of
Quality

2 types of variation
1.
2.

Natural variability (chance)
Assignable causes
Process with assignable causes is said to be
out of control.
Basic Principles

Control charts consist of



Center line
Upper control limit
Lower control limit
These limits is chosen so that when the process is in control,
almost all the sample points will fall within the control limits.
Choice Of Control Limit
2 types of control limits

Three-sigma limits.


The distance between CL and the UCL/LCL is 3 sigma.
The 0.001 probability limits chart (use 3.09 sigma).

The distance between CL and the UCL/LCL is 3.09 sigma.
Note:3-sigma limits popular in US.
0.001 prob. limits popular in UK & Western Europe.
Sample Size & Sampling Frequency

Larger samples easier to detect.


Use large sample if the shift of interest is small
and small sample if the shift of interest is large.
Frequent sampling is better.
Current practice favour small but more
frequent samples.
Analysis Of Patterns On Control
Charts
Process out of control if
1. One or more points fall outside the control
limits.
2. Points exhibit some non-random pattern.
3. Exhibit a cyclic behaviour.
Pattern recognition
Process is out of control if
 One point plots outside the control limit.
 Two out of three consecutive points plot beyond the
two sigma warning limits.
 Four out of five consecutive points plot at a distance
of the one sigma or beyond from the center line.
 Eight consecutive points plot on one side of the
center line.
x
Control Charts For Variables
(Univariate)
x and R charts
x and s charts
Control Charts For Attributes
•Control Chart For Fraction Nonconforming
•Control Chart For Nonconformities
x charts
UCL  x  A 2 R
CL  x
LCL  x  A 2 R
R charts
UCL  D 4 R
CL  R
LCL  D 3 R
S charts
S
UCL  S  3
1  c 24
c4
CL  S
S
LCL  S  3
1  c 24
c4
Fraction Nonconfor min g Chart
(p charts )  std given
p(1  p )
UCL  p  3
n
CL  p
p(1  p)
LCL  p  3
n
Fraction Nonconfor min g Chart
(p charts )  (no std given )
p (1  p )
UCL  p  3
n
CL  p
p (1  p )
LCL  p  3
n
Nonconform ities Control Chart
(c charts )  (std given )
UCL  c  3 c
CL  c
LCL  c  3 c
Nonconform ities Control Chart
(c charts )  (no std given )
UCL  c  3 c
CL  c
LCL  c  3 c
Process Capability
Calculated using
1.
Process capability ratio (PCR), Cp.
2.
Probability ;
P( x  LSL)  P( x  USL) 
LSL  x
USL  x
P( z 
)  P( z 
)
ˆ
ˆ
*need to know process std deviation
Process standard deviation
Process standard deviation is calculated by
R
ˆ 
d2
*use to estimate process capability
Process Capability Ratio (PCR), Cp
Cp 
USL  LSL
6
And is estimated by
Ĉ p 
USL  LSL
6ˆ
Interpretation
What does it mean if
 Cp < 1
 Cp = 1
 Cp > 1