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1 www.hilti.com Confidential SCM 1.3_Information Hilti Guideline Quality Capability Statistics | 07/2012

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


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


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


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 problem-

free 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.


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


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.


Analytical statistics

investigation of a sample out of a

population

• Confidence intervals

• Hypothesis testing

• Correlation analysis

Descriptive statistics

often analyses of population

• Organizing data / features

• Plots of data / features

Which sub-areas of statistics are important for a

process capability analysis?

Calculation of population characteristics Design of a mathematical model out of samples


During a process capability study different

distribution models must be considerd

unimodal

non-

symmetrical

symmetrical

polymodal


The Quantile method is universally applicable

for the calculation of capability indices

U = upper specification limit

L = lower specification limit

a = specified tolerance U - L

= process location

= process spread

= XU - XL

= L + U

(= 99.73% of the distribution)

L = lower process variation

U = upper process variation

XL = lower variation range limit X0,135%

XU = upper variation range limit X99,655%

Lower Upper

Process capability index Prozessfähigkeitsindex Minimum process capability index


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

U = upper specification limit

L = lower specification limit

a = specified tolerance U - L

= process location

= process spread

= XU - XL

= L + U

(= 99.73% of the distribution)

L = lower process variation

U = upper process variation

XL = lower variation range limit

= X0,135%

XU = upper variation range limit

= X99,655%

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 Upper

Process capability index Prozessfähigkeitsindex Minimum process capability index


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.


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

1,6

2,4

2,0

1,2

0,8

Ppk or Cpk

1,33 1,33

1,00

Pp or Cp

1,67

Cmk

1,67

1,33

Cm

2,00

1,67

K-feature

H- and N-feature

Limit = minimum value for different features and qualification phases


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


Instantaneous distributions build up the

resulting distribution

Time-dependent distribution model the choice arises from the process study

Characteristic A1 A2 B C1 C2 C3 C4 D

Change of location

over time none none none random random systematic

systematic &

random

systematic &

random

Change of variation

over time none none random none none none none

systematic &

random

Instantaneous

distribution

Normally

distributed

unimodal, not

normally

distributed

Normally

distributed

Normally

distributed

Normally

distributed any shape any shape any shape

Resulting

distribution

Normally

distributed

unimodal,

not normally

distributed

unimodal,

not normally

distributed

Normally

distributed

unimodal,

not normally

distributed

any shape any shape any shape


Different qualification phases require different

measures

Process study before series production Start of series product.

Process study during series production

Measuring system analysis

↓

Gage R&R study

Short-term

process analysis

↓

Short-term

capability study

Preliminary process analysis

↓

Process performance study

Long-term process analysis

↓

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


PPM-3.2 TTM

Capability studies need to be aligned with PPM

and SCM tasks

G1 G2 G3 G4 G5 G6

SCM-1.3 Qualifizierung von Herstellprozessen

Planning Execution & Doc. Testing & Release Proof of Sustainibility

QN

Quality of 0-series

production and

product confirmed

QA

Plan for quality of

series product. test

PQA

Product

quality

assessment

Quality

assurance

plan

QEST

Quality of

development in

complete system

QN

Plan for quality of

0-series test

Planning of

qualification

steps

Prototype/Sample parts Pre-series parts Series parts

QA

Quality of series

production

Sample Inspection

(acc. SI overview)

(Cmk proven)

Sample Inspection

close to series

production.

Plant and SC

statements

(Cmk / Ppk prov.)

Sample Inspection

series production

(Cpk proven)

QEST

Quality of

development in

complete system

QE

Plan for quality of

system test


SCM 1.3 „Sample Inspection Guideline“ is

setting limits for the qualification

* Production allowed with Inspection waiver / deviation approval (ABE)

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 G6

P

Process conforming 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%


Today 2 guidelines for process capability

studies exist

Teil 2: Short-term capability study Short-term capability (formerly machine capability)

Quality capability indicators Cm, Cmk

Part 3: Process capability study Preliminary and long-term process capability

Quality capability indicators Pp, Ppk; Cp, Cpk

Link


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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