Transcript Lesson 14 Statistical Process Control

Lesson 14
Statistical Process Control
Out of Control
UCL
purpose is to assure that
processes are performing in
an acceptable manner
Center
LCL
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sample number
14 - 1
Quality Assurance – An Evolutionary Process
Developing an effective quality assurance program is an evolutionary
process beginning with the quality assurance of incoming materials …
evolving to total quality management.
Inspection
Before/After
Production
Acceptance
Sampling
Least Progressive
Corrective
Action During
Production
Quality Built
Into The
Process
Process
Control
Continuous
Improvement
Most Progressive
14 - 2
Quality Control Concepts
The manufacturing manager of the Hiney Winery
is responsible for filling the Tiny Hiney wine
bottles with 16 oz of wine. If the wine bottles are
too full the Hiney Winery looses money and if
they are do not contain 16 ounces their
customers get upset.
The steps involved in filling the Heiney Wine
bottles is called a process. The process
involves people, machinery, bottles, corks, etc.
Do you think all Tiny Hiney’s will contain exactly
16 ounces of wine? Why or Why Not?
Tiny
Hiney Tiny
HineyTiny
Hiney Tiny
16 oz
Hiney
16 oz
16 oz
16 oz
14 - 3
Quality Control Concepts
Which sample has less variability?
16 oz.
16 oz.
Tiny
Hin
ey
14 - 4
Quality Control Concepts
We measure process variability based on a sample statistic (mean,
range, or proportion). The goal of statistical process control is to monitor
and reduce process variability.
Y
16 oz.
Time
All processes will vary over time!
14 - 5
What causes a process to vary?
People
Machines
Random or Natural Variation
(In Control)
Materials
Methods
Measurement
Special or Assignable Variation
(Out of Control)
Environment
Can you think of an example of
random and assignable variation for
each of the causes?
Can you think of a way to reduce it?
14 - 6
Quality Control Concepts
Random or Assignable Variation? Why?
16 oz.
16 oz.
Tiny
Hin
ey
14 - 7
Assignable Variation
Correctable problems
Not part of process
design
16 oz.
Due to machine wear,
unskilled workers, poor
material, etc.
Can only be detected in a process which has stable or constant
variation. The goal of process quality control is to identify assignable
causes of variation and eliminate them. Random variation is much
harder to identify; however, the goal remains to improve variability.
14 - 8
Monitoring Production (Inspection)
It is often impossible, impractical and cost prohibitive to inspect each
and every element of production therefore statistical methods based on
probability of failure are necessary to achieve a cost effective method of
assuring quality.
. Inspection of inputs/outputs … Acceptance Sampling
. Inspection during the transformation process … Process
Control
Inputs
Acceptance
Sampling
Transformation
Transformation
process
Process
Control
Outputs
Outputs
Acceptance
Sampling
14 - 9
Issues Involved In Inspection
. How much? How Often?
. Where (at what points) should inspection occur?
. Centralized or On-site inspection?
The traditional view of the amount of inspection was that there was an
optimum (cost) amount of inspection necessary to minimize risk of
passing a defective. This was predicated on the facts:
. As the amount of inspection increases the defectives that “get
through” will decrease (ie. The “cost of passing defectives go
down”)
. As the amount of inspection increases the cost of inspection
increases
The current view is that every effort involved in reducing the number of
defectives will reduce costs.
14 - 10
Traditional View – How Much To Inspect
Cost
Total Cost
Cost of inspection (goes up as
amount increases)
Optimal
Amount of
Inspection
Cost of passing defectives
(goes down as amount
increases)
14 - 11
Issues Involved In Inspection
How much to inspect and how often the inspection is done depends
. On the item
.. Low cost, high volume items - little inspection
(e.g. paper clips, pencils, glassware, etc)
.. High cost, low volume items with a high cost of a
passing defective - more inspection (e.g. space shuttle)
. On the processes that produce the item
.. Reliability of the equipment
.. Reliability of the human element
.. The stability of the process … stable processes
(those that infrequently go “out of control”) require
less inspection than unstable processes
. On the lot (batch) size … large volumes of small lots will require
more inspection than small volumes of large lots
14 - 12
Issues Involved In Inspection
Where to inspect depends on
. Raw materials and purchased parts
. Finished products
. Before a costly operation (don’t add costs to defective items)
. Before a covering process such as painting or plating
. At points where there is a high variability in the output either
as a result of mechanical or human variability
. Before an irreversible process
14 - 13
Issues Involved In Inspection
Centralized or On-site Inspection decisions are important
. Centralized makes sense in retail environments, medical
environments, when specialized testing equipment is required
. On-site makes sense when quicker decisions are necessary to
ensure processes (mechanical/human) remain in control
Transformation Location 1
Transformation Location 2
Transformation Location 3
Corporate Headquarters
Transformation Location 4
14 - 14
Example Of Inspection – Service Business
Type of
business
Fast Food
Hotel/motel
Supermarket
Inspection
points
Cashier
Counter area
Eating area
Building
Kitchen
Parking lot
Accounting
Building
Main desk
Cashiers
Deliveries
Characteristics
Accuracy
Appearance, productivity
Cleanliness
Appearance
Health regulations
Safe, well lighted
Accuracy, timeliness
Appearance, safety
Waiting times
Accuracy, courtesy
Quality, quantity
14 - 15
Statistical Process Control
Statistical Process Control (SPC) is a methodology using statistical
calculations to ensure a process is producing products which conform
to quality standards (design based, manufacturing based, customer
based).
Major activities
. Monitor process variation
. Diagnose causes of variation
. Eliminate or reduce causes of variation
Designed to keep or bring a process into statistical control.
14 - 16
Statistical Process Control
Statistical Process Control involves statistical evaluation of a process
throughout the whole production cycle. The control process requires the
following steps:
. Define in sufficient detail the characteristics to be
controlled, what “in” and “out” of control means (ie. What
is the quality conformance standard?)
. Measure the characteristic (based on sample size data)
. Compare it to the standard
. Evaluate the results
. Take corrective action if necessary
. Evaluate the corrective action
14 - 17
Statistical Process Control Steps
Start
Produce Good
or Service
Take Sample
No
Special
Causes
Yes
Inspect Sample
Stop Process
Create/Update
Control Chart
Find Out Why
14 - 18
Process Variability
All processes possess exhibit a natural (random) variability which are
produced by a number of minor factors. If any one of these factors
could be identified and eliminated, the change to the natural variability
would be negligible.
An assignable variability is where a factor which contributes to the
variability of a process can be identified and quantified. Usually this
type of variation can be eliminated thus reducing the variability of the
process.
When the measurements exhibit random patterns the process is
considered to be in control. Non-random variation typically means that
a process is out of control.
14 - 19
Statistical Process Control
Process Variability can be measured and a probability distribution can
be calculated … it might look something like this
Which process
exhibits more
stability (less
variation)?
When the factors influencing process variability can be identified and
eliminated the probability distribution will exhibit less variability
14 - 20
The Normal Distribution and SPC
The Central Limit Theorem states that (for large samples) the sampling
distribution is approximately Normal regardless of the process
distribution; therefore, the Normal Distribution can be used to evaluate
measurement results and to determine whether or not a process is “in
control”.
Sampling
As the sample size increases,
distribution
the variation in the sampling
distribution decreases
Process
distribution
Mean
14 - 21
The Normal Distribution and SPC
Standard deviation


Mean
95.5%


99.7%
The standard deviation (a measure of variability) of the sampling
distribution is key to the statistical process control methods. 3
standard deviations (99.7% confidence) are typically used to establish
Control Limits (LCL, UCL) used to monitor process control.
14 - 22
Control Limits
In statistical process control, we are concerned with the sampling
distribution. Control Limits (LCL, UCL) are set using the standard
deviation of the sampling distribution.
Sampling
distribution
Process
distribution
Mean
LCL
UCL
Note: When control limits
are established some
probability still exists in
the tails.
14 - 23
In Control or Out of Control?
Sample measurements between the LCL and UCL usually indicate that
a process is in control. The probability of concluding a process is
out of control when it is actually is in control is called a Type I
error. The amount of probability (  ) left in the tail is referred to as the
probability of making a Type 1 error
/2
/2
In Control
Mean
Probability
of Type I error
LCL
UCL
Sample measurements beyond the LCL or UCL
suggest that a process is Out of Control
14 - 24
Process Control Chart
A Process Control Chart is a time series showing the sample statistics
and their relationship to the Lower Control Limit (LCL) and Upper
Control Limit (LCL). Once a control chart is established it can be used
to monitor a process for future samples. The Process Control Chart
may need to be re-evaluated if improvements are made.
Y
UCL
Center
LCL
Time
14 - 25
Using A Process Control Chart
Measurements outside the control limits may indicate abnormal
variation usually due to assignable sources
UCL
Center
LCL
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Sample number
We expect to see normal or random variation due to chance for
measurements within the control limits
14 - 26
Using A Process Control Chart
We expect to see normal or random variation patterns within the
control limits; however, this does not guarantee a process is in control.
Consider the following example. What should a quality control manager
do in this situation?
UCL
Center
LCL
0
1
2
3
4
5
6
7
8
9
10 11 12 13 14 15
Sample number
14 - 27
In Control or Out of Control
A process is deemed to be in control if the following two conditions are met.
1. Sample statistics are between the control limits
Control Charts are used to test this condition
2. There are no non-random patterns present
Pattern analysis rules are used to test this condition
Otherwise, the process is deemed to be out of control.
14 - 28
Control Charts
Four commonly used control charts
. Control charts for variables (measured or continuous)
. Range chart - monitor variation (dispersion)
. Mean charts - monitor central tendency
. Control charts for attributes (counted or discrete)
.. p-chart - used to monitor the proportion of defectives
generated by a process
.. c-chart – used to monitor the number of defects per unit (e.g.
automobiles, hotel rooms, typed pages, rolls of carpet)
14 - 29
Pattern Analysis
Run Charts – Check For Randomness
Used in conjunction with control charts to test for randomness of observational data.
The presence of patterns in the data or trends indicates that non-random
(assignable) variation is present.
A run is a sequence of observations with a certain characteristic.
Two useful run tests:
. Runs above and below the centerline
data translated into A (above) and B (below)
. Runs up and down
data translated into U (up) and D (down)
14 - 30
Counting A/B Runs
Counting Above/Below Runs
B
1
A
2
A
2
B
3
A
4
(7 runs)
B
5
B
5
B
5
A
6
A
6
B
7
If a value is equal to the centerline, the A/B rating
is different from the last A/B rating.
14 - 31
Counting U/D Runs
Counting Up/Down Runs
U
1
Note: the first
value does not
receive a
notation
U
1
D
2
(8 runs)
U
3
D
4
U
5
D
6
U
7
U
7
D
8
If two values are equal, the U/D rating is
different from the last U/D rating.
14 - 32
Expected Number of Runs
Once the runs are counted they must be compared to the expected number of runs in
a completely random series. The expected number of runs and the standard
deviation of the expected number of runs are computed by the following formula:
E(r) a/ b
N
=
+1
2
a / b =
N -1
4
2N -1
16N - 29
E(r) u/d =
 u/d =
3
90
N = number of observations
14 - 33
Compare Observed Runs to Expected Runs
Next, we compare the observed number of runs to the expected number
of runs by calculating the following Standard Normal Z-statistic:
Za / b 
Z u/d =
r - E(r) a / b
a / b
r - E(r) u/d
 u/d
r = observed number of runs
14 - 34
Run Test - In or Out of Control
For a degree of confidence of 99.7% (3 standard deviations), we compare the
comparison to -3 standard deviations and + 3 standard deviations.
. If either the Zab or Zud is
.. < lower limit then we have too few runs (Out of Control)
.. Between the lower limit and upper limit then we have an acceptable number
of runs (In Control)
.. > upper limit then we have too many runs (Out of Conrtrol)
Too Few Runs
Acceptable number
Runs
-3.00
Too Many Runs
3.00
14 - 35
Statistical Process Control
Control Charts
Quantitative
Variable Charts
Range Chart
MeanCharts
Chart
Mean
Qualitative
Attribute Charts
P Charts
C Charts
14 - 36
14 - 37
Statistical Process Control Menu
14 - 38
Goodman Tire & Rubber Company
The Goodman Tire & Rubber Company periodically tests its tires for tread wear under
simulated road conditions. To monitor the manufacturing process 3 radial tires are
chosen from each shift of production operation. The operations manager recently
attended a statistical process control (SPC) seminar and decided to adopt SPC to
control and study tread wear.
The manager believes the production process is under control and
to establish control limits and monitor the process he took 3
randomly selected radial tires from 20 consecutive shifts. They were
tested for tread wear and recorded in the table on the next slide.
Tread wear is recorded in millimeters which is a measured variable;
therefore, a range and mean chart should be developed.
Let’s take a look at the steps the manager must use to establish and
analyze the control chart.
First of all, he notes
sample size = 3
process variability is not known
14 - 39
Sample
Tire 1
Tire 2
Tire 3
Range
1
3.1
4.2
2.8
1.4
2
2.6
1.8
3.5
1.7
3
2.5
3.0
3.4
0.9
4
1.7
2.5
2.1
0.8
5
3.8
2.9
3.5
0.9
6
4.1
4.2
3.6
0.6
7
2.1
1.7
2.9
1.2
8
3.2
2.6
2.8
0.6
9
4.1
3.4
3.3
0.8
10
2.9
1.7
3.0
1.3
11
2.6
3.1
4.0
1.4
12
2.3
1.9
2.5
0.6
13
1.7
2.4
3.2
1.5
14
4.3
3.5
1.7
2.6
15
1.8
2.5
2.9
1.1
16
3.0
4.2
3.1
1.2
17
2.8
3.6
3.2
0.8
18
4.0
2.9
3.1
1.1
19
1.8
2.9
2.8
1.1
20
2.2
3.4
2.6
1.2
Mean
3.3666666
7
2.6333333
3
2.9666666
7
The first step: calculate the range for
each sample.
The next step: calculate the mean for
each sample.
2.1
3.4
3.9666666
7
2.2333333
3
Then: calculate the grand (average)
range for all samples.
Grand
Range
1.14
2.8666666
7
3.6
2.5333333
3
3.2333333
3
Then: calculate the grand (average)
mean for all samples.
Grand
Average
2.9166666
7
2.2333333
3
2.4333333
3
3.1666666
7
2.4
14 - 40
3-Sigma Control Chart Table
Sample Size
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
A2
1.880
1.023
0.729
0.577
0.483
0.419
0.373
0.337
0.308
0.285
0.266
0.249
0.235
0.223
0.212
0.203
0.194
0.187
0.180
0.173
0.167
0.162
0.157
0.153
D3
0
0
0
0
0
0.076
0.136
0.184
0.223
0.256
0.283
0.307
0.328
0.347
0.363
0.378
0.391
0.403
0.415
0.425
0.434
0.443
0.451
0.459
D4
3.267
2.574
2.282
2.114
2.004
1.924
1.864
1.816
1.777
1.744
1.717
1.693
1.672
1.653
1.637
1.622
1.608
1.597
1.585
1.575
1.566
1.557
1.548
1.541
d2
1.128
1.693
2.059
2.326
2.534
2.704
2.847
2.970
3.078
3.173
3.258
3.336
3.407
3.472
3.532
3.588
3.640
3.689
3.735
3.778
3.819
3.858
3.895
3.931
d3
0.853
0.888
0.880
0.864
0.848
0.833
0.820
0.808
0.797
0.787
0.778
0.770
0.763
0.756
0.750
0.744
0.739
0.734
0.729
0.724
0.720
0.716
0.712
0.708
Next we must determine the center line,
upper and lower control limits for the
range and mean chart which are calculated
by very simple formula.
There is only one formula for the range
chart.
However; there are two formulae for the
mean chart. The one chosen is dependent
up on whether the variability (standard
deviation) of the process is
. known
. unknown
The 3-simga control chart table is used to
calculate these formulae.
14 - 41
Range Chart (R Chart)
The Range Chart measures the variability of a sample measurements in a process.
The range chart must be interpreted first because the process variability must be
in control before we can monitor whether a process is in or out of control.
The Range Chart Centerline, UCL and LCL are calculated by the following formula.
Centerline  grand range  R
LCL  R * D3
UCL  R * D4
The Goodman Tire & Rubber Company
range chart calculations are:
Centerline  1.14
LCL  1.14* 0
UCL  1.14* 2.574
3s Control Chart Settings
UCL
2.9344
Centerline
1.1400
LCL
0.0000
14 - 42
Range Chart (R Chart)
Range
Control Chart
1.4
1.7
3.5
0.9
0.8
3
UCL, 2.9344
0.9
0.6
2.5
1.2
0.6
2
0.8
1.3
1.5
1.4
0.6
Centerline, 1.1400
1
1.5
2.6
0.5
1.1
1.2
LCL, 0.0000
0
0
10
20
30
40
50
60
70
0.8
1.1
1.1
1.2
Range
The sample range values are now plotted on the range control chart
14 - 43
Mean Chart ( X Chart) - Known Variation
The Mean Chart measures the average of sample measurements in a process. When
the variation of the process is known the 3-sigma table is not used.
The Mean Chart Centerline, UCL and LCL (3 sigma limits) are calculated by the
following when the variation of the process is known.
Centerline  grand average X
LCL  X  3
UCL  X  3

n

n
where : n  samplesize
  processst andarddeviat ion
14 - 44
Mean Chart ( X Chart) - Unknown Variation
The Mean Chart measures the average of sample measurements in a process. When
the variation of the process is unknown the 3-sigma table is used.
The Mean Chart Centerline, UCL and LCL are calculated by the following formula when
the variation of the process is unknown.
Centerline grand average X
LCL  X  A2 R
UCL  X  A2 R
The Goodman Tire & Rubber Company mean chart
calculations are:
Centerline  2.9167
LCL  2.9167 1.14*1.023
UCL  2.9167 1.14*1.023
3s Control Chart Settings
UCL
4.0829
Centerline
2.9167
LCL
1.7504
14 - 45
Mean Chart ( X Chart) - Unknown Variation
Mean
3.3666666
7
2.6333333
3
2.9666666
7
Control Chart
4.5
UCL, 4.0829
4
3.5
2.1
3.4
3
3.9666666
7
2.5
2.2333333
3
2
2.8666666
7
1.5
3.6
2.5333333
3
Centerline, 2.9167
LCL, 1.7504
1
0.5
3.2333333
3
0
2.2333333
3
2.4333333
3
3.1666666
7
2.4
0
10
20
30
40
50
60
70
Mean Unknown Variation
The sample mean values are now plotted on the mean control chart
14 - 46
1. Choose the RM (Range &
Mean) menu option
14 - 47
4. Return
3. Select
Known or
Unknown
Range & Mean Chart Worksheet
2. Enter
Data
14 - 48
5. Enter problem name
then click OK
14 - 49
6. Choose the CC (Control
Chart) menu item
14 - 50
7. Choose the Range control chart
Notice the range control chart shows the sample ranges
Pattern Analysis for AB and UD indicate the patterns are
random (YES)
Therefore; the range chart indicates the variation of the
process is in control
14 - 51
8. Choose the Mean Unknown Variation control chart
Notice the mean control chart shows the sample averages
Pattern Analysis for AB and UD indicate the patterns are
random (YES)
Therefore; the mean chart indicates the average of the
process is in control
14 - 52
Summary - Range & Mean Control Charts
Both charts are necessary to effectively monitor a process.
The mean charts detect when a process mean is shifting
The range charts detect when the process variability is changing.
The range chart must be interpreted first. If the variability is not constant, the
process is not in control.
14 - 53
Summary - Range & Mean Control Charts
(process mean is
shifting upward)
Sampling
Distribution
UCL
Detects shift in
process mean
x-Chart
LCL
UCL
Does not
detect shift
R-chart
LCL
14 - 54
Mean & Range Control Charts
Sampling
Distribution
(process variability is increasing)
UCL
Does not
reveal increase
x-Chart
LCL
UCL
R-chart
Reveals increase
LCL
14 - 55
Statistical Process Control
Control Charts
Quantitative
Variable Charts
Range Chart
Mean Chart
Qualitative
Attribute Charts
P Chart
C Chart
14 - 56
P-Chart (Proportion Chart)
The P-Chart measures the proportions in a process.
The Proportion Chart Centerline, UCL and LCL are calculated by the following formula.

Centerline = p




p(1p)
p(1p)
 -3
 +3
LCL = p
UCL = p
n
n
total number defective
=
p
n *(number of samples)
n = sample size
14 - 57
Mail Sorting
Sample
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Sample
Size
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
Defective
14
10
12
13
9
11
10
12
13
10
8
12
9
10
11
10
8
12
10
16
Automated mail sorting machines are used to sort mail
by zip codes. These machines scan the zip codes and
divert each letter to its proper carrier zone.
Even when a machine is properly operating some mail is
improperly diverted (a defective).
Check the sorting machine here to see if it is in control.
14 - 58
Mail Sorting
Sample
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Sample
Size
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
100
Proportion
Defective Defective
14
0.14
10
0.10
12
0.12
13
0.13
9
0.09
11
0.11
10
0.10
12
0.12
13
0.13
10
0.10
8
0.08
12
0.12
9
0.09
10
0.10
11
0.11
10
0.10
8
0.08
12
0.12
10
0.10
16
0.16
Calculate the actual proportion defective per
sample by dividing the observed defective by
the sample size.
The average proportion is
ˆ  .1100
p
3 Control Chart Settings
UCL
0.2039
Centerline
0.1100
LCL
0.0161
The sample proportion values are now
plotted on the proportion control chart
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P-chart Worksheet
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Choose the Proportion control chart
Notice the proportion control chart shows the sample proportions
Pattern Analysis for AB and UD indicate the patterns are random
(YES)
Therefore; the proportion chart indicates the process is in control
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Types of Control Charts
Control Charts
Quantitative
Variable Charts
Range Charts
Mean Charts
Qualitative
Attribute Charts
P Charts
C Charts
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C-Chart (Defects Per Unit)
The C-Chart is used to monitor the number of defects per unit (e.g. automobiles, hotel
rooms, typed pages, rolls of carpet).
The C Chart Centerline, UCL and LCL are calculated by the following formula.
UCL = c + 3 c
LCL = c - 3 c where
c = process average number of defects per unit
In the event c is unknown, it can be estimated by sampling and
computing the average defects observed. In this case the average can
. Also, note that since the formula is
be substituted in the formula for c
an approximation the LCL can be negative. In these cases the LCL is
set to 0.
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Coiled Wire
Sample
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
Number
Defects
3
2
4
5
1
2
4
1
2
1
3
4
2
4
2
1
3
1
Example 5: Rolls of coiled wire are monitored using a cchart. Eighteen rolls of wire have been examined and
the number of defects per roll has been recorded in the
data provided here. Is the process in control? Use 3
standard deviations for the control limits.
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Coiled Wire
Number
Defects
3
2
4
5
1
2
4
1
2
1
3
4
2
4
2
1
3
1
The average number of defects per roll of coiled wire is

c  2 .5
3Control Chart Settings
UCL
7.2434
Centerline
2.5000
LCL
0.0000
The sample number defects values are now plotted on the defects
per unit control chart
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C-chart Worksheet
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Choose the Defects per unit (C) control chart
Notice the unit defective control chart shows the sample proportions.
Pattern Analysis for AB and UD indicate the patterns are random
(YES)
Therefore; the C chart indicates the process is in control
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Process Variability
Process variability can significantly impact quality. Some commonly used terms refer to
the variability of a process output.
. Tolerances - specifications for the range of acceptable values
established by engineering or customer specifications
. Control limits - statistical limits that reflect the extent to which
sample statistics such as means and ranges can vary due to
randomness
. Process variability - reflects the natural or inherent (e.g.random
variability in a process. It is measured in terms of the process standard
deviation.
. Process capability - the inherent variability of process output
relative to the variation allowed by the design specification.
3-sigma control is when the process performs within 3 standard deviations of the
mean.
6-sigma control is when the process performs within 6 standard deviations of the
mean.
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Three Sigma and Six Sigma Quality
Product Upper
specification
Product Lower
specification
1.35 ppt
1.35 ppt
1.7 ppm
1.7 ppm
Process Mean
+/- 3 Sigma
+/- 6 Sigma
ppt – parts per thousand
ppm – parts per million
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Process Capability
Lower
Specification
Upper
Specification
Process variability matches specifications
Lower
Specification
Upper
Specification
Process variability well within specifications
Lower
Specification
Upper
Specification
Process variability exceeds specifications
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Process Capability - Example
Example 7: A manager has the option of using any one of the following three machines
for a job. The machines and their standard deviations are listed below. Determine
which machines are capable of doing the job if the specifications are 1.00mm to
1.60mm.
Machine
A
B
C
Std Dev
(mm)
0.10
0.08
0.13
1.00mm - Lower
specification
1.60 - Upper
specification
.60mm - tolerance width
The specifications indicate that the tolerance
width is .6mm. (e.g. 1.60 – 1.00)
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Process Capability - Example
Process capability for 3-sigma control is deemed to be within 3 standard deviations of
the mean. Therefore for this example the process capability is 6 * (standard deviation)
shown in the table below.
Machine
A
B
C
Std Dev Machine
(mm)
Capability
0.10
0.60
0.08
0.48
0.13
0.78
Therefore, Machine A & B are capable of meeting the specifications, Machine C
is not.
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Homework
Read and understand all material in the chapter.
Discussion and Review Questions
Recreate and understand all classroom examples
Exercises on chapter web page
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