Six Sigma Quality: Capability and Control - PowerPoint PPT Presentation

1 / 66
About This Presentation
Title:

Six Sigma Quality: Capability and Control

Description:

Six Sigma Quality: Capability and Control * * * * * * * * * * * * SPC Mechanics Sample Size = n X-bar Charts R Charts A2 A3 d2 D3 D4 2 1.880 2.659 1.128 0 3.267 3 1 ... – PowerPoint PPT presentation

Number of Views:586
Avg rating:3.0/5.0
Slides: 67
Provided by: SMG5
Category:

less

Transcript and Presenter's Notes

Title: Six Sigma Quality: Capability and Control


1
Six Sigma QualityCapability and Control
2
Manufacturing Example
Source Cachon and Terwiesch (2009)
3
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)
4
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)
5
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)
6
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)
7
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)
8
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)
9
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)
10
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
11
Source Cachon and Terwiesch (2009)
12
Source Cachon and Terwiesch (2009)
13
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)
14
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

15
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

16
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.

17
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
18
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.

19
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
20
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!

21
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
22
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
23
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
24
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
25
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
26
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
27
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.

28
What do you get if you combine a run chart
29
with the Normal Curve?
30
Statistical Process Control (SPC)!
Upper Control Limit 3 SE
Center Line Mean
Center Line Mean
Lower Control Limit -3 SE
31
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?

32
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.

33
SPC Means and Ranges
  • Distributions of measured data can change two
    ways
  • The mean can shift The variation can
    change

34
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.

35
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.

36
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.

37
p Chart
  • Where is the observed value of the average
    fraction defective

38
p Chart
39
X-bar and R Charts
chart
R chart
40
X-bar and R Charts
41
X-bar and R Charts
42
X-bar and R Charts
43
X-bar and R Charts Xootr
44
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)

45
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.

46
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.

47
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.

48
When to Sample
  • Frequency depends on two factors
  • How often a process is likely to change.
  • How much the sampling process costs.

49
Control Chart Interpretation
  • In Control Random within statistical pattern

50
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

51
Points Outside Limits
One sample mean above UCL investigate for
assignable cause.
UCL 3?
Center Line
LCL -3?
52
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.
53
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.
54
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.
55
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.
56
Trends
6 in a row steadily increasing or decreasing
investigate for assignable cause.
57
Trends
58
Eight in a Row between 2 and 3 SD
59
Cycles
60
Fourteen in a Row Alternating Up and Down
61
Fifteen in a Row within 1 SD
62
In or Out of Control?
63
In or Out of Control?
64
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.

65
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
66
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
67
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
Write a Comment
User Comments (0)
About PowerShow.com