SCM 1.3
Information about the HILTI Guidelines for the
determination of quality capability statistics
SCM 1.3 Guideline for short-term capability study
SCM 1.3 Guideline for process capability study
Thorsten Ebert
July 2012
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SCM 1.3_Information Hilti Guideline Quality Capability Statistics | 07/2012
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Agenda
•
Why do we need (statistical) guidelines?
•
How do you describe technical processes?
•
What are process capability studies?
•
What are HILTI guidelines offering?
•
NOT: Any details of statistical distributions and analysis
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The prerequisite for an efficient quality control and
assurance is the understanding of technical processes,
i.e. answers to the following questions:
● Is the process meeting customer specifications?
 How much quality provides a process?
 How much non-conforming parts can be kept to a minimum?
● Process improvements possible or achieved?
 Are improvements needed in the process?
 Have you sustained these improvements, or has the process regressed to its
previous unimproved state?
● How will the process perform in the future?
 How capable is a process over a longer period of time?
 What conclusions can we make about the process?
 How can a process be as economically as possible?
 What statements can we trust
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The ISO / TR 10 017 defined statistical methods that may
be suitable for development, maintaining and improving a
quality management system:
Method by ISO / TR 10017
Content
Control charts
Graph of data derived from samples that are periodically drawn from a process and plotted in sequence.
Descriptive statistics
Descriptive statistics refers to procedures for summarizing and presenting quantitative data in a
manner that reveals the characteristics of the distribution of data.
Design of experiments (DoE)
Investigations carried out in a planned manner, and which rely on a statistical assessment of results to
reach conclusions at a stated level of confidence.
Hypothesis testing
Hypothesis testing is a statistical procedure to determine, with a prescribed level of risk, if a set of data
(typically from a sample) is compatible with a given hypothesis.
Measurement analysis
Evaluation of uncertainties of meas. systems under the range of conditions in which the system operates.
Process capability study /
analysis
Examination of the inherent variability and distribution of a process, in order to estimate its ability to produce
output that conforms to the range of variation permitted by specifications.
Regression analysis
Behaviour of a characteristic of interest (usually called the “response variable”) with potentially causal
factors (usually called “explanatory variables”).
Reliability analysis
Application of engineering and analytical methods to the assessment, prediction and assurance of problemfree performance over time of a product or system.
Sampling
Sampling is a systematic statistical methodology for obtaining information about some characteristic of a
population by studying a representative fraction (i.e. sample) of the population.
Simulation
Simulation is a collective term for procedures by which a (theoretical or empirical) system is represented
mathematically by a computer program for the solution of a problem.
Statistical tolerancing
Procedure based on certain statistical principles, used for establishing tolerances.
Time series analysis
Time series analysis is a family of methods for studying observations made sequentially over time.
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Overview of statistical characteristics
● Data size
● Minimum and maximum value
● Arithmetic mean
● Median
● Mode value
● Variance s2, Standard deviation s
● Range
● Quartile, Percentile
● Kurtosis
● Skewness
● Capability indicators Cm, Cmk, Pp, Ppk, Cp, Cpk
● Excess proportion
● Confidence interval for mean, variances, capability indicators and excess
proportions
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Why do we need guidelines, if we can apply
statistical methods?
● Definition of limits
● Description of a complex study
● Clear and complete definition of terms
● Integration of international statistical standards
● Description for handling of time-dependent distribution models
● Appropriate qualification linked to the various stages of qualification
● Handling of discrete features
● Indication of confidence intervals of the capability indices depending on
sample sizes
● Clarification on the use of statistical software
Various statistical procedures must be regulated so that these methods lead to
standardized and consistent decisions on the basis of data.
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Which sub-areas of statistics are important for a
process capability analysis?
•
•
Descriptive statistics
Analytical statistics
 often analyses of population
 investigation of a sample out of a
population
Organizing data / features
Plots of data / features
•
•
•
Calculation of population characteristics
Design of a mathematical model out of samples
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Confidence intervals
Hypothesis testing
Correlation analysis
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During a process capability study different
distribution models must be considerd
unimodal
polymodal
symmetrical
nonsymmetrical
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The Quantile method is universally applicable
for the calculation of capability indices
U
L
a


L
U
XL
XU
Lower
Process capability index
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= upper specification limit
= lower specification limit
= specified tolerance U - L
= process location
= process spread
= XU - XL
= L + U
(= 99.73% of the distribution)
= lower process variation
= upper process variation
= lower variation range limit X0,135%
= upper variation range limit X99,655%
Upper
Prozessfähigkeitsindex
Minimum process capability index
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The consideration of the process location μ
leads to minimum (critical) capability indices
The capability indices Pp / Cp describe
the potential capacity of a process to
produce a specific characteristic within
the prescribed limits. For this purpose,
the process spread is compared with the
tolerance T = U - L for the characteristic
The minimum (critical) capability indices
Ppk / Cpk assess the quality capability of a
process based on a comparison of the
process spread with the tolerance range
at the same time as taking the process
location into account
Lower
Process capability index
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U
L
a


L
U
XL
XU
= upper specification limit
= lower specification limit
= specified tolerance U - L
= process location
= process spread
= XU - XL
= L + U
(= 99.73% of the distribution)
= lower process variation
= upper process variation
= lower variation range limit
= X0,135%
= upper variation range limit
= X99,655%
Upper
Prozessfähigkeitsindex
Minimum process capability index
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Process indicators are linked by the statistical
model with excess proportion
Cmk
Ppk
Cpk
1-sided upper excess
proportion
2-sided upper excess
proportion
Prozess
spread
(%)
ppm
(%)
ppm
(%)
1,00
0,1350000
1350
0,2700000
2700
99,7300000
1,33
0,0031686
31,686
0,0063372
63,372
99,9936628
1,67
0,0000287
0,287
0,0000574
0,574
99,9999426
2,00
0,0000001
0,001
0,0000002
0,002
99,9999998
In general, the larger the value of each process indicator, the better the
performance to meet the requirements of the process is classified.
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The limit values ​for process capabilities are
dependent on the HILTI feature classification:
Capability index
H- and N-feature
K-feature
Cm (LIMIT)
 1.67
 2.00
Cmk (LIMIT)
 1.33
 1.67
Pp (LIMIT) / Cp (LIMIT)
 1.33
 1.67
Ppk (LIMIT) / Cpk (LIMIT)
 1.00
 1.33
Limit = minimum value for different features and qualification phases
2,4
2,00
2,0
1,67
1,67
1,67
1,6
1,33
1,33
1,33
H- and N-feature
K-feature
1,2
1,00
0,8
Cm
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Pp or Cp
Ppk or Cpk
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The guideline process capabilities considers 8
different time-dependent distribution models
Location is constant
Location is not constant
Variation is constant
A
C
Variation is not constant
B
D
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Instantaneous distributions build up the
resulting distribution
Time-dependent distribution model  the choice arises from the process study
Characteristic
Change of location
over time
Change of variation
over time
Instantaneous
distribution
Resulting
distribution
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A1
A2
B
C1
C2
C3
C4
D
none
none
none
random
random
systematic
systematic &
random
systematic &
random
none
none
random
none
none
none
none
systematic &
random
Normally
distributed
unimodal, not
normally
distributed
Normally
distributed
Normally
distributed
Normally
distributed
any shape
any shape
any shape
Normally
distributed
unimodal,
unimodal,
not normally not normally
distributed
distributed
Normally
distributed
unimodal,
not normally
distributed
any shape
any shape
any shape
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Different qualification phases require different
measures
Process study before series production
Measuring system analysis
Short-term
process analysis
↓
Start of
series
product.
Process study during series production
Preliminary process analysis
↓
Long-term process analysis
Gage R&R study
Short-term
capability study
Process performance study
Process capability study
Minimum quantity 50 pieces
or as appropriate to the
process
Minimum
quantity 50
pieces or as
appropriate to
the process
Minimum quantity 100 pieces
or as appropriate to the
process. To keep the requisite
control chart, a minimum of
20 individual random samples
are necessary
An appropriate period under normal series
conditions, during which it can be assured that
all influential factors can take effect. (standard
value: 20 production days); total random sample
size ≥ 125
Cg / Cgk,
Gage R&R
Cm / Cmk
Pp / Ppk
Cp / Cpk
Indicator for the
measurement quality before
commencement of data
acquisition
Indicator of a
process under
short-term, ideal
conditions
Indicator of a process under
real-life conditions (influence
of 5M factors), which has not
yet been proven to be in a
state of statistical control
Indicator of a process under series production
conditions (full influence of 5M factors), which
has previously been proven to be in a state of
statistical control
↓
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Capability studies need to be aligned with PPM
and SCM tasks
PPM-3.2 TTM
G1
G2
G3
G4
Prototype/Sample parts
G5
Pre-series parts
PQA
Product
quality
assessment
QEST
Quality of
development in
complete system
QEST
Quality of
development in
complete system
QN
Quality of 0-series
production and
product confirmed
Quality
assurance
plan
QE
Plan for quality of
system test
QN
Plan for quality of
0-series test
QA
Plan for quality of
series product. test
G6
Series parts
QA
Quality of series
production
SCM-1.3 Qualifizierung von Herstellprozessen
Planning
Planning of
qualification
steps
Execution & Doc.
Testing & Release
Sample Inspection
(acc. SI overview)
Sample Inspection
close to series
production.
Plant and SC
statements
(Cmk proven)
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(Cmk / Ppk prov.)
Proof of Sustainibility
Sample Inspection
series production
(Cpk proven)
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SCM 1.3 „Sample Inspection Guideline“ is
setting limits for the qualification
The SI-Level target refers to the SI sample inspection summary and the rating roles in the SI policy
TTM Gate
SI-Level
G4
G5
P
Process conforming
G6
100%
A
Quality conforming
60%
80%
100%
B
Partly quality conforming
*
40%
20%
0%
C
Not quality conforming
0%
0%
Open
Not rated yet
0%
0%
* Production allowed with Inspection waiver / deviation approval (ABE)
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Today 2 guidelines for process capability
studies exist
Teil 2: Short-term capability study
Part 3: Process capability study
Short-term capability (formerly machine capability)
Preliminary and long-term process capability
 Quality capability indicators Cm, Cmk
 Quality capability indicators Pp, Ppk; Cp, Cpk
Link
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What are the key messages out of the new
guidelines?
● Description of a complex study 
This policy does not replace basic statistical skills that are absolutely
necessary in order to fully understand or even interpret results.
● By integrating international, statistical formulas and standards terms and
definitions are clearly set.
● Different qualification phases require different measures.
● Through distribution and process models, the time dependencies of technical
processes are recorded over time.
● The handling of discrete features is explained.
● Emphasizes the dependence on sample sizes.
● For a complete capability study the use of an appropriate statistical software for
process qualification (HILTI: qs-STAT) is mandatory.
● Defining of limit values for process capability indices.
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