Transcript SPC: Statistical Process Control

spc
Statistical process control Key
Quality characteristic :Forecast Error for demand
BENEFITS of SPC
 Monitors and provides feedback for keeping processes in control.
 Triggers when a problem occurs
 Differentiates between problems that are correctable and those
that are due to chance.
Gives you better control of your process.
 Reduces need for inspection
 Provides valuable knowledge in the working of the process
Have you ever…
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Shot a rifle?
Played darts?
Played basketball?
Shot a round of golf?
What is the point
of these sports?
What makes
them hard?
Have you ever…
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Shot a rifle?
Played darts?
Shot a round of golf?
Played basketball?
Player A
Player B
Who is the better shot?
Discussion
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What do you measure in your process?
Why do those measures matter?
Are those measures consistently the same?
Why not?
Variability
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8
7
10
8
9
Deviation = distance between observations
and the mean (or average)
averages
Observations
Deviations
10
10 - 8.4 = 1.6
9
9 – 8.4 = 0.6
8
8 – 8.4 = -0.4
8
8 – 8.4 = -0.4
7
7 – 8.4 = -1.4
8.4
0.0
Player A
Player B
Variability
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Deviation = distance between observations
and the mean (or average)
averages
Observations
Deviations
7
7 – 6.6 = 0.4
7
7 – 6.6 = 0.4
7
7 – 6.6 = 0.4
6
6 – 6.6 = -0.6
6
6 – 6.6 = -0.6
6.6
0.0
7
6
7
7
6
Emmett
Jake
Variability
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8
7
10
8
9
Variance = average distance between
observations and the mean squared
Deviations
Squared Deviations
10 10 - 8.4 = 1.6
2.56
9 – 8.4 = 0.6
0.36
8 8 – 8.4 = -0.4
0.16
8 8 – 8.4 = -0.4
0.16
7 7 – 8.4 = -1.4
1.96
0.0
1.0
Observations
9
averages
Emmett
8.4
Jake
Variance
Variability
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Variance = average distance between
observations and the mean squared
Observations
7
7
7
6
6
averages
Deviations
Squared Deviations
Emmett
7
6
7
7
6
Jake
Variability
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Variance = average distance between
observations and the mean squared
Deviations
Squared Deviations
7
7 - 6.6 = 0.4
0.16
7
7 - 6.6 = 0.4
0.16
7
7 - 6.6 = 0.4
0.16
6 6 – 6.6 = -0.6
0.36
6 6 – 6.6 = -0.6
0.36
0.0
0.24
Observations
averages
6.6
Emmett
7
6
7
7
6
Jake
Variance
Variability
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Standard deviation = square root of variance
Emmett
Variance
Standard
Deviation
Emmett
1.0
1.0
Jake
0.24
0.4898979
Jake
But what good is a standard deviation
Variability
The world tends to be bellshaped
Even very rare
outcomes are
possible
(probability > 0)
Fewer
in the
“tails”
(lower)
Most outcomes
occur in the
middle
Fewer
in the
“tails”
(upper)
Even very rare
outcomes are
possible
(probability > 0)
Variability
Even outcomes that are equally likely (like
dice), when you add them up, become bell
shaped
Here is why:
Add up the dots on the dice
Probability
0.2
0.15
1 die
0.1
2 dice
0.05
3 dice
0
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
Sum of dots
“Normal” bell shaped curve
Add up about 30 of most things
and you start to be “normal”
Normal distributions are divide up
into 3 standard deviations on
each side of the mean
Once your that, you
know a lot about
what is going on
And that is what a standard deviation
is good for
Usual or unusual?
1. One observation falls
outside 3 standard
deviations?
2. One observation falls in
zone A?
3. 2 out of 3 observations fall in
one zone A?
4. 2 out of 3 observations fall in
one zone B or beyond?
5. 4 out of 5 observations fall in
one zone B or beyond?
6. 8 consecutive points above
the mean, rising, or falling?
X
XX
X 34 56
X1X XX2
X
78
Causes of Variability
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Common Causes:
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Random variation (usual)
 No pattern
 Inherent in process
 adjusting the process increases its variation
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Special Causes
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Non-random variation (unusual)
May exhibit a pattern
Assignable, explainable, controllable
adjusting the process decreases its variation
SPC uses samples to identify that special causes have occurred
Limits
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Process and Control limits:
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Statistical
Process limits are used for individual items
Control limits are used with averages
Limits = μ ± 3σ
Define usual (common causes) & unusual (special causes)
Specification limits:
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Engineered
 Limits = target ± tolerance
 Define acceptable & unacceptable
Process vs. control limits
Distribution of averages
Control limits
Specification limits
Variance of averages < variance of individual items
Distribution of individuals
Process limits
Usual v. Unusual,
Acceptable v. Defective
A
B
C
μ
Target
D
E
More about limits
Good quality:
defects are rare
(Cpk>1)
μ
target
Poor quality: defects are
common (Cpk<1)
μ
target
Cpk measures “Process Capability”
If process limits and control limits are at the same location, Cpk = 1. Cpk ≥ 2 is exceptional.
Process capability
Good quality: defects are rare (Cpk>1)
Poor quality: defects are common (Cpk<1)
=
USL – x
=
3σ
24 – 20
= .667
3(2)
=
x - LSL
=
3σ
20 – 15
= .833
3(2)
Cpk = min
=
=
3σ = (UPL – x, or x – LPL)
14
15
20
24
26
Going out of control
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When an observation is unusual, what can we conclude?
The mean
has changed
X
μ1
μ2
Going out of control
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When an observation is unusual, what can we conclude?
σ1
The standard deviation
has changed
σ2
X
The SPC implementation process
• Identify what characteristics to be controlled
• Establish Control limits
• Find how to control the process
• Learn how to measure improvement of a process
• Learn how to detect shift and how to set alerts that take action.
• Learn about the two types of causes that affect your variation.
Setting up control charts:
Calculating the limits
1.
2.
3.
4.
5.
6.
7.
8.
Sample n items (often 4 or 5)
Find the mean of the sample x-bar
Find the range of the sample R
Plot x bar on the x bar chart
Plot the R on an R chart
Repeat steps 1-5 thirty times
Average the x bars to create (x-bar-bar)
Average the R’s to create (R-bar)
Setting up control charts:
Calculating the limits
9.
10.
Find A2 on table (A2 times R estimates 3σ)
Use formula to find limits for x-bar chart:
X  A2 R
11.
Use formulas to find limits for R chart:
LCL  D3 R
UCL  D4 R
Let’s try a small problem
smpl 1
smpl 2
smpl 3
smpl 4
smpl 5
smpl 6
observation 1
7
11
6
7
10
10
observation 2
7
8
10
8
5
5
observation 3
8
10
12
7
6
8
x-bar
R
X-bar chart
UCL
Centerline
LCL
R chart
Let’s try a small problem
smpl 1
smpl 2
smpl 3
smpl 4
smpl 5
smpl 6
observation 1
7
11
6
7
10
10
observation 2
7
8
10
8
5
5
observation 3
8
10
12
7
6
8
X-bar
7.3333
9.6667
9.3333
7.3333
7
7.6667
R
1
3
6
1
5
5
X-bar chart
8.0556
3.5
R chart
11.6361
9.0125
Centerline
8.0556
3.5
LCL
4.4751
0
UCL
Avg.
R chart
10
9
8
7
6
5
4
3
2
1
0
9.0125
3.5
0
1
2
3
4
5
6
X-bar chart
11.6361
8.0556
4.4751
AP Uploads Quality control
Interpreting charts
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Observations outside control limits indicate the process
is probably “out-of-control”
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Significant patterns in the observations indicate the
process is probably “out-of-control”
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Random causes will on rare occasions indicate the
process is probably “out-of-control” when it actually is not
Interpreting charts
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In the excel spreadsheet, look for these shifts:
A
B
C
Show real time examples of charts here
D
Lots of other charts exist
P chart
C charts
U charts
Cusum & EWMA
For yes-no questions
like “is it defective?”
(binomial data)
For counting number
defects where most
items have ≥1 defects
(eg. custom built
houses)
Average count per
unit (similar to C
chart)
Advanced charts
p 3
p(1  p)
n
c 3 c
u
u 3
n
“V” shaped or Curved
control limits (calculate
them by hiring a
statistician)
SPC Station
SPC as a triggering tool
Selecting rational samples
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Chosen so that variation within the sample is considered to be from
common causes
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Special causes should only occur between samples
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Special causes to avoid in sampling
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passage of time
workers
shifts
machines
Locations
Chart advice
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Larger samples are more accurate
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Sample costs money, but so does being out-of-control
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Don’t convert measurement data to “yes/no” binomial data (X’s to P’s)
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Not all out-of control points are bad
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Don’t combine data (or mix product)
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Have out-of-control procedures (what do I do now?)
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Actual production volume matters (Average Run Length)
Statistical Process Control (S.P.C.)
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This is a control system which uses statistical techniques for
knowing, all the time, changes in the process.
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It is an effective method in preventing defects and helps
continuous quality improvement.
What does S.P.C. mean?
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Statistical:
Statistics are tools used to make predictions on
performance.
There are a number of simple methods for analysing data
and, if applied correctly, can lead to predictions with a high
degree of accuracy.
What does S.P.C. mean?
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Process:
The process involves people, machines, materials, methods,
management and environment working together to produce
an output, such as an end product.
What does S.P.C. mean?
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Control:
Controlling a process is guiding it and comparing actual
performance against a target.
Then identifying when and what corrective action is
necessary to achieve the target.
S.P.C.
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Statistics aid in making decisions about a process based
on sample data and the results predict the process as a
whole.
People
Machines
Material
Output
Management
Methods
Environment
The Aim of S.P.C.
- Prevention Strategy
Prevention Benefits:
 Improved design and process capability.
 Improved manufacturing quality.
 Improved organisation.
 Continuous Improvement.
S.P.C. as a Prevention Tool
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The S.P.C. has to be looked at as a stage towards completely preventing
defects.
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With stable processes, the cost of inspection and defects are significantly
reduced.
The Benefits of S.P.C.
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Assesses the design intent.
Achieves a lower cost by providing an early warning system.
Monitors performance, preventing defects.
Provides a common language for discussing process performance.
Process Variations
Process Element
Variable Examples
Machine………………………….Speed, operating
temperature, feed rate
Tools………………………………..Shape, wear rate
Fixtures…………………………..Dimensional accuracy
Materials…………………………Composition, dimensions
Operator…………………………Choice of set-up, fatigue
Maintenance…………………Lubrication, calibration
Environment…………………Humidity, temperature
Process Variations
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No industrial process or machine is able to produce consecutive items
which are identical in appearance, length, weight, thickness etc.
The differences may be large or very small, but they are always there.
The differences are known as ‘variation’. This is the reason why
‘tolerances’ are used.
Stability
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Common causes are the many sources of variation that are always present.
A process operates within ‘normal variation’ when each element varies in a random
manner, within expected limits, such that the variation cannot be blamed on one
element.
When a process is operating with common causes of variation it is said to be stable.
Process Control
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The process can only be termed ‘under control’ if it gives
predictable results.
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Its variability is stable over a long period of time.
Process Control Charts
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Graphs and charts have to be chosen for their simplicity, usefulness
and visibility.
They are simple and effective tools based on process stability
monitoring.
They give evidence of whether a process is operating in a state of
control and signal the presence of any variation.
Data Interpretation
Consider these 50 measurements
Bore Diameter 36.32 ±0.05mm (36.27 - 36.37mm)
1
2
3
4
5
6
7
8
9
10
36.36
36.34
36.34
36.33
36.35
36.33
36.33
36.34
36.35
36.35
11
12
13
14
15
16
17
18
19
20
36.37
36.35
36.32
36.35
36.34
36.34
36.35
36.33
36.32
36.35
21
22
23
24
25
26
27
28
29
30
36.34
36.37
36.34
36.35
36.34
36.35
36.36
36.33
36.36
36.38
31
32
33
34
35
36
37
38
39
40
36.35
36.35
36.36
36.37
36.34
36.36
36.38
36.34
36.35
36.35
41
42
43
44
45
46
47
48
49
50
36.36
36.37
36.37
36.35
36.37
36.36
36.35
36.34
36.35
36.34
Data Interpretation
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As a set of numbers it is difficult to see any pattern.
Within the table, numbers 30 and 37 were outside the
tolerance – but were they easy to spot?
A way of obtaining a pattern is to group the measurements
according to size.
Data Interpretation – Tally Chart
36.39
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36.38
36.37
36.36
36.35
36.34
36.33
36.32
36.31
36.30
36.29
36.28
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The tally chart groups the
measurements together by size as
shown.
The two parts that were out of
tolerance are now easier to detect
(36.38mm).
Tally Chart - Frequency
36.39
36.38
2
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The tally chart shows patterns and we
can obtain the RANGE - 36.32mm to
36.38mm.
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The most FREQUENTLY
OCCURRING size is 36.35mm.
6
36.37
36.36
7
36.35
16
36.34
12
36.33
36.32
36.31
36.30
36.29
36.28
5
2
Tally Chart - Information
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The tally chart gives us further information:
The number of bores at each size;
The number of bores at the most common size;
The number of bores above and below the most common size (36.35mm)
number above 36.35mm is 7+6+2=15
number below 36.35mm is 12+5+2=19
Histogram
We can redraw the frequency chart as a bar chart known as a histogram:
16
14
12
10
8
6
4
2
0
36.31
36.32
36.33
36.34
36.35
36.36
36.37
36.38
36.39