5
HOW SPC WORKS
BASIC SPC TOOLS
• SPC is a powerful collection of problem-solving tools useful in
achieving process stability and improving capability through the
reduction of variability. SPC can be applied to any process. Its seven
major tools, known as “the magnificent seven” are
• SPC builds an environment in which all
individuals in an organization seek continuous
improvement in quality and productivity.
• This environment is best developed when the
management becomes involved in the process
•A certain amount of inherent or natural variability always exists in a
production process regardless of how well designed or carefully
maintained it is.
•This variability is known as natural variability or ‘background noise’.
•It is the cumulative effect of many small essentially unavoidable causes.
Also known as ‘stable system of chance causes’.
•A process is operating with only chance causes of variation present is
said to be in statistical control. It is the rock bottom variation which s
always there and can be reduced by changing the process.
• Other types of variability may occasionally be present in the
output of the process.
• Following are the sources of variability:
• Improperly adjusted or controlled machines
• Operator errors
• Defective raw material
• Such variability is known as ‘assignable causes’ and are large
as compared to background noise
• A process that is operating in the presence of assignable
causes is said to be out of control.
• NO PROCESS IS STABLE FOREVER
• The major objective of SPC is to quickly detect the causes of
the process shift so the investigation of the process and
corrective action may be taken before any nonconforming
units are made.
• A graphical display of quality
characteristics that has been
measured or computed from a
sample versus the sample
number or time
• A control chart contains
– A center line
• Represents the average value
of the quality characteristics
according to the in control
state
– An upper control limit
– A lower control limit
• All sample points fall between
these points if the process is in
control
– No action is necessary
A point that plots outside the control limits is
evidence that the process is out of control
– Investigation and corrective action are required to find and
eliminate assignable cause(s)
• If the process is in control, all the plotted points
should have an essentially random pattern. If they
behave in a systematic or non random manner then
this could be an indication that the process is out of
control.
• There is a close connection between control charts
and hypothesis testing- point falling within the
control limit.
• A point plotting within the control limit is
equivalent to failing to reject the hypothesis of
statistical control, and a point plotting outside
the control limits is equivalent to rejecting the
hypothesis of statistical control.
Photolithography Example
• Important quality
characteristic in hard
bake is resist flow width
• Process is monitored by
average flow width
– Sample of 5 wafers
– Process mean is 1.5
microns
– Process standard deviation
is 0.15 microns
• Note that all plotted
points fall inside the
control limits
– Process is considered to
be in statistical control
Shewhart Control Chart Model
• Root cause for assignable causes should be identified
and eliminated. Cosmetic solutions will lead to only
short term corrections.
• A very important part of the corrective action process
associated with control chart is OCAP( out of control
action plan ).
• It’s a flow chart consists of checkpoints, which are
potential assignable causes, and terminators, which
are actions taken to resolve the out of control
condition.
Sample size and the sampling
frequency
• The greater the sample size is the greater the
probability of detecting the small shifts in the process.
• Small samples at short intervals or large samples at
large intervals. Current practice in the industry is to
take small samples at short intervals.
• Another way regarding sampling frequency and
sample size is through ARL ( average run length)
• ARL = 1/p, where p is the probability that any point
exceeds the control limit
• e.g with 3 sigma limits, p = 0.0027 is the probability
that a single point fall outside the control limits.
• ARL = 1/ 0.0027 = 370,which means an out of
control signal will be generated after 370 samples on
average, even is the process is in control
Analysis of Patterns in Control Limits
• Even if all the points fall within limits, the
points may not indicate statistical control if
they do no follow the random pattern.
• In a non- random pattern, if the points have an
increasing trend over a number of samples, we
would call this run up, on the other hand run
down.
The WECO Rules
•
•
To identify the non random patterns of the control
chart, The Western Electric Handbook suggests a
set of decision rules.
The process is out of control if :
1.
2.
3.
4.
One point plots outside the 3-sigma control limit.
2 out of three consecutive points plot beyond the 2- sigma
warning limits
Four out of five consecutive points plot at a distance of one
sigma or beyond from the center line
Eight consecutive points plot on one side of the center line
4-4 THE REST OF THE “MAGNIFICENT SEVEN”
1.
2.
3.
4.
5.
6.
7.
Histogram or stem-and-leaf plot
Check sheet
Pareto chart
Cause-and-effect diagram
Defect concentration diagram
Scatter diagram
Control chart
Check sheet
• Check sheet can be very useful in
collecting either the historical or current
data in the early stages of production.
• The time oriented summary of data is
helpful in looking for trends or other
meaningful patterns.
Procedure
• Decide what event or problem will be observed. Develop
operational definitions.
• Decide when data will be collected and for how long.
• Design the form. Set it up so that data can be recorded
simply by making check marks or Xs or similar symbols
and so that data do not have to be recopied for analysis.
• Label all spaces on the form.
• Test the check sheet for a short trial period to be sure it
collects the appropriate data and is easy to use.
• Each time the targeted event or problem occurs, record
data on the check sheet.
Pareto chart
• It id simply the frequency distribution of attribute
data arranged by category.
• Most useful of the ‘magnificent seven’.
• It identify the most frequent defects, but not the
most important.
• To identify the most important there are two
methods which can be used:
– Use the weighting scheme to modify the frequency
counts.
– Accompany the frequency Pareto chart analysis with
the cost or exposure Pareto chart.
Pareto Chart
Cause-and-Effect Diagram
• Once a defect, error, or problem has been
identified, potential causes of this
undesirable effect has to be analyzed.
• It is a formal tool to unlayer such causes.
Cause-and-effect diagrams
• Cause-and-effect diagrams are also called:
– Ishikawa diagrams (Dr. Kaoru Ishikawa, 1943)
– fishbone diagrams
• Cause-and -effect diagrams do not have a
statistical basis, but are excellent aids for
problem solving and trouble-shooting
• Cause-and-effect diagrams can
– reveal important relationships among various
variables and possible causes
– provide additional insight into process behavior
Cause-and-Effect Diagram
Defect Concentration Diagram
Scatter Diagram