Six Sigma Quality: Capability and Control

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Six Sigma QualityCapability and Control
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Manufacturing Example
Source Cachon and Terwiesch (2009)
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The Concept of ConsistencyWho is the Better
Target Shooter?
Not just the mean is important, but also the
variance Need to look at the distribution
function
Source Cachon and Terwiesch (2009)
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Now let us do a simple exercise

1. With your right hand, write down the letter R.
   Do this 8 times in a row.
2. Start a new row.
3. With your left hand, write down 8 Rs.
4. Start a new row.
5. With your right hand, write down 4 Rs, and then
   switch to your left hand and write down 4 Rs.

Source Cachon and Terwiesch (2009)
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Two Types of Causes for Variation
Common Cause Variation (low level)
Common Cause Variation (high level)
Assignable Cause Variation

• Need to measure and reduce common cause
  variation
• Identify assignable cause variation as soon as
  possible

Source Cachon and Terwiesch (2009)
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The Statistical Meaning of Six Sigma
Process capability measure
Upper Specification Limit (USL)
Lower Specification Limit (LSL)
Process A (with st. dev sA)
x? Cp Pdefect ppm 1? 0.33 0.317 317,000 2? 0.67
0.0455 45,500 3? 1.00 0.0027 2,700 4? 1.33 0.00
01 63 5? 1.67 0.0000006 0,6 6? 2.00 2x10-9 0,00
3?
Process B (with st. dev sB)

• Estimate standard deviation using Excel
• Look at standard deviation relative to
  specification limits
• Dont confuse control limits with specification
  limits a process can be out of control, yet
  be capable or, a process can be in control, but
  be incapable

Source Cachon and Terwiesch (2009)
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Statistical Process Control
Capability Analysis
Conformance Analysis
Investigate for Assignable Cause
Eliminate Assignable Cause

• Capability analysis
• What is the currently "inherent" capability of
  my process when it is "in control"?
• Conformance analysis
• SPC charts identify when control has likely been
  lost and assignable cause variation has
  occurred
• Investigate for assignable cause
• Find Root Cause(s) of Potential Loss of
  Statistical Control
• Eliminate or replicate assignable cause
• Need Corrective Action To Move Forward

Source Cachon and Terwiesch (2009)
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How do you get to a Six Sigma Process? Step 1
Do Things Consistently (ISO 9000)
1. Management Responsibility 2. Quality System 3.
Contract review 4. Design control 5. Document
control 6. Purchasing / Supplier evaluation 7.
Handling of customer supplied material 8.
Products must be traceable 9. Process control 10.
Inspection and testing
11. Inspection, Measuring, Test Equipment 12.
Records of inspections and tests 13. Control of
nonconforming products 14. Corrective action 15.
Handling, storage, packaging, delivery 16.
Quality records 17. Internal quality audits 18.
Training 19. Servicing 20. Statistical techniques
Examples The design process shall be planned,
production processes shall be defined and
planned
Source Cachon and Terwiesch (2009)
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Step 2 Reduce Variability in the
ProcessTaguchi Even Small Deviations are
Quality Losses
Quality
Quality Loss
Loss C(x-T)2
Performance Metric, x
Good
Performance Metric
Bad
Maximum acceptable value
Minimum acceptable value
Target value
Target value

• It is not enough to look at Good vs Bad
  Outcomes
• Only looking at good vs bad wastes opportunities
  for learning especially as failures become rare
  (closer to six sigma) you need to learn from the
  near misses
• Catapult Land in the box opposed to perfect
  on target

Source Cachon and Terwiesch (2009)
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Step 3 Accommodate Residual Variability Through
Robust Design
Chewiness of BrownieF1(Bake Time) F2(Oven
Temperature)
F2
F1
Bake Time
Oven Temperature
25 min.
30 min.
350 F
375 F
Design A
Design B

• Double-checking (see Toshiba)
• Fool-proofing, Poka yoke (see Toyota)
• Process recipe (see Brownie)

Source Cachon and Terwiesch (2009)
Pictures from www.qmt.co.uk
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Source Cachon and Terwiesch (2009)
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Source Cachon and Terwiesch (2009)
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Why Having a Process is so ImportantTwo
Examples of Rare-Event Failures

• Case 1 Process does not matter in most cases
• Airport security
• Safety elements (e.g. seat-belts)

Bad outcome only happens Every 10 Mio units
1 problem every 10,000 units
99 correct

• Case 2 Process has built-in rework loops
• Double-checking

99
Good
99
99
1
Bad
1
1
Bad outcome only happens with probability
(1-0.99)3
Learning should be driven by process deviations,
not by defects
Source Cachon and Terwiesch (2009)
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Capability Definition

• The ability of a product, process, person or
  organization to perform its specified purpose
  based on tested, qualified or historical
  performance, to achieve measurable results that
  satisfy established requirements or
  specifications.
• http//www.isixsigma.com/dictionary/Capability-592
  .htm

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Capability Study

• Steps
• Determine process requirements.
• Collect baseline data on process output when
  process is not exhibiting unusual behavior
  calculate process mean and standard deviation.
• Compare specs to process mean 3 standard
  deviations.
• If specs are outside 3 s, process is capable

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Capability Study Step 1

• Determine customer specifications (Voice of the
  customer).
• Check to make sure customer specs are
  appropriate.
• Usually customers wont change these but
  sometimes they do overspecify and more realistic
  specs can be established.

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Capability Study Step 2

• Collect data on process output. Calculate mean
  and standard deviation. 3s points are called
  natural tolerances (or sometimes Voice of the
  Process).
• All processes have variation in their output!

3 ?
- 3 ?
process variation
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Capability Study Step 3

• Compare specifications to the inherent variation
  of the process. Tolerances
• If specs are outside at least 3 standard
  deviations, the process is capable.

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Capability Study Step 4

• If specs are within 3-sigma, process is not
  capable of consistently producing within customer
  requirements.

specifications
3 ?
- 3 ?
process variation
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Capability Study

• When a process is not capable,
• we have to inspect to find the output that does
• not meet the requirements, which adds cost.
• If we need to rework or scrap bad output,
• that adds even more cost!

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Capability Study

• The producer wants specs to be far away from the
  natural variation of the process.
• But customers wont just change their specs.

specifications
3 ?
- 3 ?
process variation
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Teasing Out Non-Random Variation

• So we have to tease out the non-random
  variation
• from what, at first, appears to be totally random
  variation.

specifications
3 ?
- 3 ?
process variation
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CP

• Compares the natural tolerance of the process
  (its natural variation) to the specs.
• A CP of 1 denotes a capable process but to
  allow for drift, 1.33 is often used as the
  acceptable minimum.
• Disadvantage CP doesnt account for process
  centering

Remember This is the overall process
(population ) s, not the sample s (in other
words, 3s is not the same as used for UCL and LCL
in control charts.
Upper spec Lower spec 6s
CP
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CPK

• Compares the natural tolerance of the process
  (its natural variation) to the specs.
• A CPK of 1 is required and 1.33 is preferred..

Zmin 3
CPK
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CPK Getting Zs

• Think about whats happening here.
• Were looking at the difference between the grand
  mean and the upper and lower specs.
• In a centered 6-sigma process, wed expect these
  both to be 6!

Upper specification - X s
ZU
X - Lower specification s
ZL
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CPK

• Compares the natural tolerance of the process
  (its natural variation) to the specs.
• Think about whats happening here
• When a process isnt centered around the mean,
  one Z will be smaller than the other. If that Z
  divided by 3 is at least 1 (preferably 1.33),
  then the process is capable.

Zmin 3
CPK
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Cpk The Comparison Method

• Basically, CP and CPK are computing a single
  value to determine whether a process is capable.
• We can do this visually, assessing whether the
  process specs are outside at least 3 sigma on
  each side.

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What do you get if you combine a run chart
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with the Normal Curve?
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Statistical Process Control (SPC)!
Upper Control Limit 3 SE
Center Line Mean
Center Line Mean
Lower Control Limit -3 SE
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Control

• Basically were comparing the information about
  the output of a process in real time with
  historical information about the process output
  and asking the question Do we have any
  evidence that would make us believe the process
  has changed?

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Control

• A process is in control when it exhibits only
  random variation (more on this )
• When a process is capable and in control, the
  process is producing output that meets customer
  specifications.

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SPC Means and Ranges

• Distributions of measured data can change two
  ways
• The mean can shift The variation can
  change

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Control

• There are a number of types of control charts.
• What type of control chart should be used depends
  on
• The type of data.
• The size of the sample.
• With variable data the key is sample size.
• With attribute data, we must determine
• Whether were counting defectives (whether a unit
  of output is good or bad within a sample of
  units) or
• Defects (number of occurrences of a flaw on a
  single unit) and
• Whether the sample size or unit is constant.

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Two Types of Data

• Counted data (Attribute Data)
• Nominal data.
• Need just one chart, because mean and standard
  deviation are related.
• Measured data (Variables Data)
• Ratio and Interval data.
• Need two charts, because mean and standard
  deviation are independent.

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Control

• The most commonly used charts for attributes are
  the p and Np charts the most commonly used
  charts for variables are the X-bar and R charts.

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p Chart

• Where is the observed value of the average
  fraction defective

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p Chart
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X-bar and R Charts
chart
R chart
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X-bar and R Charts
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X-bar and R Charts
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X-bar and R Charts
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X-bar and R Charts Xootr
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SPC Summary

• SPC is a tool for
• Achieving process stability
• Improving capability by reducing variability
• Variability can be due to
• Chance causes (relatively small)
• Assignable causes (generally large compared to
  background noise)

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Determining Sample Size Attributes

• For attributes (data you count)
• Want to collect a large enough sample that you
  find, on average, two of the attribute youre
  looking for.
• For example, in a p-chart if you have a baseline
  percent defective of 10, what should sample size
  be?
• There would be one defect every 10 units, on
  average,
• so youd need a sample of size 20.

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Determining Sample Size Variables

• For variables (data you measure) Sample size
  is typically 4 or 5 because measured data is
  continuous and is therefore more powerful for
  finding changes.

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Sample Size Variables Data

• This curve shows the probability of detecting a
  shift in the mean.
• For example, a single sample of size 5 has about
  a 60 chance of detecting a 1.5 sigma shift.

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When to Sample

• Frequency depends on two factors
• How often a process is likely to change.
• How much the sampling process costs.

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Control Chart Interpretation

• In Control Random within statistical pattern

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Typical Out-of-Control Patterns

• Point outside control limits
• Sudden shift in process average
• Cycles
• Trends
• Hugging the center line
• Hugging the control limits
• Instability

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Points Outside Limits
One sample mean above UCL investigate for
assignable cause.
UCL 3?
Center Line
LCL -3?
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Two in a Row between 2 and 3 SD
Two consecutive sample means between 2 and 3
? investigate for assignable cause.
Two consecutive sample means between -2 and -3
?. Investigate for assignable cause.
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Two out of Three between 2 and 3 SD
Two out of 3 sample means between 2 and 3 ?
investigate for assignable cause.
Two out of 3 sample means between -2 and -3 ?.
Investigate for assignable cause.
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Four out of Five between 1 and 3 SD
Four out of five sample means between 1 and 3
? investigate for assignable cause.
UCL 3?
Center Line
Four out of five sample means between -1 and -3
?. Investigate for assignable cause.
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Five in a Row Above or Below CL
Run of five sample means above Center Line
investigate for assignable cause.
UCL 3?
Center Line
Run of five sample means below Center
Line investigate for assignable cause.
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Trends
6 in a row steadily increasing or decreasing
investigate for assignable cause.
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Trends
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Eight in a Row between 2 and 3 SD
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Cycles
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Fourteen in a Row Alternating Up and Down
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Fifteen in a Row within 1 SD
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In or Out of Control?
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In or Out of Control?
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SPC Summary

• SPC is not particularly complex to use once you
  get familiar with it.
• SPC does not stop the production of defects (but
  it does minimize them!).
• SPC does not measure the quality of a worker.
• SPC tests whether the system is operating as
  intended.
• SPC lies at the core of continuous improvement.

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SPC Mechanics
Data Type Chart Average Center Line Lower Control Limit _at_ 3s Upper Control Limit_at_ 3s
Attribute (counted) p Average percentage of attribute
Variable (measured) Average measure of a variable in a sample
Variable (measured) R Average sample range
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SPC Mechanics
Sample Size n X-bar Charts X-bar Charts X-bar Charts R Charts R Charts
Sample Size n A2 A3 d2 D3 D4
2 1.880 2.659 1.128 0 3.267
3 1.023 1.954 1.693 0 2.574
4 0.729 1.628 2.059 0 2.282
5 0.577 1.427 2.326 0 2.114
6 0.483 1.287 2.534 0 2.004
7 0.419 1.182 2.704 0.076 1.924
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SPC Mechanics

• Use d2
• To calculate the average sample range (R-bar)
  R-bar s d2
• For a particular sample size
• When
• The process (population) standard deviation s is
  known
• But the baseline data was not collected in
  samples
• To calculate population standard deviation from
  the average sample range, Solving for s s
  R-bar/d2