Movip

Modeling van Initiele Product Kwaliteit

+ .

Measure of Product Quality (ZHDR)

Zero Hour Defect Rate (ZHDR) reflects the number of products which failed at the customer, with respect to the number of products delivered to the customer during an agreed period of time. A “failure” is the unplanned occurrence that prevents the product from meeting its functional requirements under the specified operating conditions.
The time period in which a product fails is the Reliability Infact Mortality period. Most infant mortality failures will occur during the build of the product followed by the first year of use.
After this period the failure mechanism is life time related (reliability random failures and wear out).
Predicting the ZHDR is based on all contributing part and process risks indentified by the MoViP methodology. When measuring the ZHDR during this period of time the outcome of this must result in the ZHDR.

Product Design Failure Modes

When designing a product its evident that the risk of a failure increases with increasing the number of parts and as such the number of processes used to manaufacturer and assemble the part.

design_risks

Risk increases with #Parts

To determine the risk of failure during the infant mortality period the traditional methods such as a process FMEA's, early design involvement of manufacturing, building prototypes, ... works well for products manufactured in large quantities and not having the pressure of fast market introduction. When manufacturing low quantities these methods helps but are costly and time consuming and doesn't help in cost price or market introduction. For industries in this category a methodology is developed to identify the manufacturing, part and partial the design risks during the design phase.

When designing a product there are only three failure modes (Parts, Processes and Design failure modes) which contributes to the "Non" Quality of a product.
Parts are either vendor parts which are bought or manufactured parts which started from a material and ends up as a part manufactured according a drawing.
Processes are either the manufacturing processes (material -> part) or the assembly processes where vendor and manufactured parts put together lead to sub assembly(s) with in the end a product.
A design is the combination of parts when put together correctly deliver the required functionality.
The three failure modes are:

Possibly as fourth failure mode handling and transport is mentioned. This can be easely seen as a part which is packed and handled, stored or transported (process).

Failure Modes

Processes are always coupled to either a material or a part (vendor, manufactured or (sub)assembly). Based on this the Bill of Materials (BoM) contains everything to identify the part or material risks and based on the coupling of processes to either a material or a part also all processes. Each part or material and the coupled processes based on the BoM result in an Zero Hour Defect Rate (ZHDR) when added statistical correct.

part_process

Vendor parts - Material & Processes


The risks of a failure per part or process is based on the history of that part or process. To identify the risk of failure for the part of processes a number of defect opportunities are used.

Part Failure Modes/Defect Opportunities

When a part has a risk on failure a number of Defect Opportunities are possible. A part can be defect (not functioning at all), physical out of spec (scratched, dented, dirty, no threaded holes,...) or functional out of spec (funtioning not according specification). This is only true for parts which are bought. Parts which are manufactured have a failure mode which is build up out of the marterial failures and the failures introduced during the manufacturing.

Part Defect

Part Defect

Part Related Risks

Part Related Risks

Part related risk described for vendor parts.
What's the risk on not working at all (defect) or not physical according specification (physical out of spec) or not functioning accpording specification (functional out of spec).

Part Defect

A part is defect when the part is not functioning at all.

Examples: Hard disk is not functioning at all, a motor is not rotating.

Part is Defect

Part Defect

Part Physical out of Spec

Part is not conform the physical specifications. This can be a large number of physical defects.

  • Hole is missing
  • Hole is not threaded
  • Surface is scratched
  • Surface is dented
  • Part is not clean
  • Part has bend legs (Integrated Circuit)
  • ...

Example: Hard disk is either dented, scratched, has no threaded holes for mounting, connect broken, motor axis bend,...

Part is Physical out of Spec

Part Physical out of Spec

Part Functional out of Spec

Part functions not conform specification but is still working.

  • Motor turns slower than specified
  • Transmission lens is lower than specified
  • Bandwidth/noise is not within specification
  • ...

Example: Hard disk turn slower than specified rpm, access time slower,...

Assembly Defect Opportunities

Assembling is building together one or more vendor parts with one or more manufactured parts to create a new part ((sub)assembly or even product). The assembly process consist two steps (placement and connection). When creating a (sub)assembly or product each vendor or manufactured part must be placed. Connection takes only place when the part connects one to another part (screw, glue, bond,...).

Assembly Defect

Assembly Defect Opportunities

First step in the assembly process is always the placement of the parts.

Part Placement Risks

Part Placement Risks

Risks of placing the part in the (sub)assembly in the wrong way, forget or damage the part.

Missing Part

The risk that a part is not placed in the assembly.
Examples:

  • Washer is missing
  • O-Ring is missing
  • Electronic parts missing on a Printed Circuit Board (PCB)
  • Cover missing
  • ...

Part is missing

Missing Part

Wrong Part

Another part is placed in the assembly than specified in the Bill of material (BoM)

Examples:
  • Wrong electronic component (value) in a Printed Circuit Board Assembly (PCBA)
  • Magnetic fasteners where non magnetic fasteners are required
  • Bolt length
  • ...

Part is wrong

Wrong Part

Misoriented part

Part is placed with the wrong orientation in the assembly.

Examples:
  • Inside out
  • 90° rotated
  • ...

Part is misoriented

Misoriented Part

Misplaced Part

The part is not mounted on the specified position.

Part is misplaced

Misplaced Part

Part is damaged during placement

Part is damaged during placement. How bigger the part how easier the damage occurs. This is also true if a part is fragile.

Examples:
  • Sheet metal
  • Enclosures
  • ...

Excess parts

More parts are placed in the product than identified on the BoM.

Examples:
  • Washers
  • O-Rings
  • ...

Part Connection Risks

Second step in the assembly process is connecting the parts together.

Part Connection Risks

Connection Risks

Risks of connecting the part in the (sub)assembly not according specification. (screw not tigtening according torque, glue step not resulting in required strenght, connector misplaced,...

Missing Connection

Risk of not connecting at all.

Examples:
  • No glue dispenced
  • cable or hose not connected at all (hanging loose)
  • ...

Misplaced Connection

Risk of connecting at the wrong place.

Examples:
  • glue dispenced on wrong position
  • cable or hose not connected at the wrong place
  • ...

Misoriented Connection

Risk of connecting in the wrong orientation.

Examples:
  • Cable connected in the wrong orientation (3W3 sub D connector)
  • ...

Connection process

Risk of not correct connecting.

Examples:
  • Screw not tightened according specified/requirred torque
  • C able not connected correctly
  • Glue not according specified/required strenght
  • Solder not according IPC
  • ...

Connection

Part is Misconnected

Manufacturing Defect Opportunities

Manufacturing processes are either the manufacturing of a mono (manufactured part) or the common processes which lead to a (sub)assembly. mono parts assembly parts

Assembly Defect

Manufacturing Defect Opportunities

Manufacturing Process manufactured part

Manufacturing processes of a part are processes executed in a predefined sequence. Each manufacturing process contributes to the risk of not meeting the required manafuctured part quality. Where in assembly DPMO's are used as measure of the risk in manufacturing the Cpk, Ppk, sigma's are more used. When for each manufacturing step the Cpk, Ppk or sigma's are known these can be easely translated to DPMO's. Processes are:

  • Mill
  • Drill
  • Thread
  • Surface Threatment
  • ...

The manufactred part risk is noting more than the material riks and the 'added' process risks. the material risk can be treated as a vendor part risk without any process associated to it.

Manufacturing Process (sub)Assembly

Last step in the assembly process before it is a (sub)assembly or product are the common processes which take place on the (sub)assembly or product level.

  • Cleaning
  • Testing
  • Adjusting
  • .....

Theses processes are for all parts in the (sub)assembly the same and are associated to the (sub)assembly as a manufacturing process.

Determine Defect Opportunity Risk

To be able to calculate the product Zero Hour Defect Rate (ZHDR) for each defect opportunity a risk on occuring must be known. For calculation purpose the Defect Parts per Milion Opportunities (DPMO) is used. DPMO's are widely used or could be calculed from the Cpk, Ppk or sigma's.
When all DPMO's which can occur are known a product risk calculation can be done.

Zero Hour Defect Rate (ZHDR) Calculation

ZHDR Calculations

This calculation result in a product ZHDR. Based on this also a list of Part Risk and process risks can be created.

Risk Mitigation

When having calculated the Zero Hour Defect Rate (ZHDR) and this is larger than the specified product ZHDR there are three options to lower the ZHDR.

Zero Hour Defect Rate (ZHDR) realized

ZHDR Specified/Calculated

Design change is the first step in mitigation. Based on the list of part or process risks a design change must be made which avoids those risks. When not possible the second best option is to improve the processes which contribute most to the high ZHDr of the product. Last resort is to test the remaining risks which could not be solved with a design change or process improvement. Realize that a test when its detected a Not Ok lead to scrap and as such increasing the cost price.

Design Change

Select out of the list of risks those parts and/or processes which contribute to the not meeting the product ZHDR. For parts a replacement or avoidance is the only way to improve. For processes is take an other design which avoids those processes.

Process Improvement

When a design change is not sufficient to meet the product ZHDR process improvemnt is the next option.

Zero Hour Defect Rate (ZHDR) realized

ZHDR Specified/Calculated

In an assembly process, even with skilled/trained operators, perfect workinstructions, sign off lists, ideal environment or ... incidents happen. To avoid these process incidents the process must be controlled in itself. The most easy way is automating the process, or put in other words avoid manual labour. Worldwide is manual labour a risk. To get a feeling for the contribution of manual labour an average incident rate is 1000ppm (1 of the 1000).
When manufactured part processes contributes to not meeting the product ZHDR those identiefied process must be improved. When manual labour with manufactured part is the contributor the process must be improved. When there is no manual labour which can be improved an other strategy can be another machine or again avoid a process risk by relaxing the requirement which causes the risk.

Test

Even when the design changes and process improvements are not sufficient to meet the product ZHDR the last resort is testing.

Zero Hour Defect Rate (ZHDR) realized

ZHDR Specified/Calculated

Each part or process which is tested and is Not Ok results in scrapping the product. When testing not on product level but on part or (sub)assembly level the consequences are the same but the cost involved is lower. For design risks this will always lead to scrap.

Test Scrap

Process & Test resulting in OK/FOK/NOK

Calculation of the Zero Hour Defect rate (ZHDR) includes now the test coupled to the defect opportunity.For the test the slip is defined as:

0 > No slip (no process failure slips through)
1 > No test (all process failures slips through to next stage)

Zero Hour Defect Rate (ZHDR) Calculation

ZHDR Calculations including test

When testing identifies a Not Ok this mabey can be reworked. When reworked this can solve the NoK but also can introduce new risks. Testing the reworked product is mostly done on another test fixture than the test used for production.

Test Scrap Rework

ZHDR Calculations including test & rework

The assembly Zero Hour Defect Rate (ZHDR) can be calculated by taking for each Bill Of Material (BOM) item the part and mounting Defect Opportunity (DO) corresponding risks (7 per BOM item), from the schematic (Printed Circuit Board Assembly (PCBA)) or 3D drawings (mechanics, mechatronics, optics) the connection risks followed by the assembly processing risks.
  • Part Risks
  • Mounting Risks
  • Connection Risks
  • Assembly Process Risks
When the DPMO's of the risks are within a small band (5-10ppm or 20-30ppm) use the graph to determine the Zero Hour Defect Rate (ZHDR)

Zero Hour Defect Rate (ZHDR) Graph

When the DPMO's vary outside a limited band use the formula below

All these Defect Opportunity (DO) corresponding risks together, give an insight in which risk contributes most to the Zero Hour Defect Rate (ZHDR) of the assembly.

Contributors:

  • Part Risks
  • Mounting Risks
  • Connection Risks
  • Assembly Process Risks

Hierarchy

With complex assemblies the build sequence is mostly done in a hierarchical way. When encountering such a hierarchy each hierarchical level results in itself in a part with all the part, mounting, connection and assembly related risks. This part is treated as a part one hierarchical level up. When out of the design phase the build sequence is done in takts and can be treated the same way as a hierarchy.

Hierarchical connections

When connecting cables, hoses (fluids, gasses, vacuum, ..), this could be treated as a separate hierarchical level. The cable, hose in itself is treated as a part with a risk and as a connection with its connection risks. This methodology is needed to avoid counting risks more than once.

Printed Cicuit Board Assemblies (PCBA) connections

When connecting Printed Circuit Board Assemblies (PCBA) to each other, counting the risk more than once is not allowed. An approach could be to select the male or female connectors for determining the connection risk.

Risk Mitigation

If the calculated Zero Hour Defect Rate (ZHDR) is lower than the specified Zero Hour Defect Rate (ZHDR) then no mitigation of the risk is needed. If the calculated Zero Hour Defect Rate (ZHDR) is not within specification the risks must be mitigated.

Zero Hour Defect Rate (ZHDR) realized

If it is specified that a product requires a Zero Hour Defect Rate (ZHDR) of 1000ppm (1 of 1000 may fail) the risks must be mitigated to reach the specified Zero Hour Defect Rate. Starting point are the largest contributors of the Zero hour Defect Rate (ZHDR). Mitigation can be done in three ways.

Design Change

Avoiding the risks is the best way to mitigate. If the design can be changed in such way that the risks are avoided then this is to most preferable way of mitigation.

With the changed design, the calculation must be repeated with the new Bill Of Material (BOM) and/or the changed connections and/or the changed assembly process. The recalculated Zero Hour Defect Rate (ZHDR) must be checked if it is within specification.

Part Related Risk Mitigation

Part risks are design related due to the fact that the Bill Of Material (BOM) is dictated by design. Part related risks can only be mitigated by changing those parts which contributes to the Part related Zero Hour Defect Rate (ZHDR).

Mounting Related Risk Mitigation

Avoiding mounting risks is done by at least following the rules of Designing For Manufacturing (DFM), Designing For Assembly (DFA) and respecting the industrialization rules. Yang, Kai, Design for Six Sigma, Chapter 10 (10 Tien-Chien Chang, Richard A. Wysk, and Hsu-Pin Wang. Computer-Aided Manufacturing, Second Edition, Pages 596 to 598 (11

Industrialization Rules:

  • Develop a modular design
  • Use of standard parts
  • Minimize number of parts
  • Minimize number of different parts
    • Use only one type of fastener, resistor, capacitor,.... (Wrong)
  • Minimize adjustments
  • Make adjustment accessible
  • Design parts to be multi-functional
  • Design for ease of manufacturing
  • No symmetrical mounting (Misoriented)
  • Minimize assembly directions
  • Use gravity when mounting parts
  • Use no hand tools
  • Minimize handling

Connection Related Risk Mitigation

Mitigating connection risks is done by avoiding those connection technologies in the design which contributes most to the connection related Zero Hour Defect Rate (ZHDR).

Assembly Processing Related Risk Mitigation

Mitigating assembly processing risks is done by not using these assembly processing technologies in the design which contributes most to the assembly processing related Zero Hour Defect Rate (ZHDR).

Calculate New Zero Hour Defect Rate (ZHDR)

Based on the design changes a new Bill Of material (BOM) is created and the Zero Hour Defect Rate (ZHDR) must be (re)calculated.

Zero Hour Defect Rate (ZHDR) Calculation

This results in a new Zero Hour Defect Rate (ZHDR) which must be checked if the Zero Hour Defect Rate (ZHDR) is within specification.

Zero Hour Defect Rate (ZHDR) realized

Manufacturing Process Change

When the design changes alone are not sufficient to reach the specified Zero Hour Defect Rate (ZHDR), the risks in the manufacturers process can be mitigated.

Part Related Risk Mitigation

The only exception which can't be mitigated in the manufacturing process are the part related risks. These can only be mitigated in the design, so only the mounting, connection or assembly process risks can be mitigated by changing/improving the manufacturing process.

Mounting Related Risk Mitigation

Mitigation of only the contributing mounting risks in the manufacturing process are required. (good is good) The categories in the calculated Zero Hour Defect Rate (ZHDR) are missing, wrong, misoriented, misplaced and must lead to a change in the manufacturing process to minimize the risk.

Examples of mitigation strategies are :

  • Missing (poka-yoke, lean process, ..)
  • Wrong (logistics)
  • Misoriented (poka-yoke, lean process, ..)
  • Misplaced (poka-yoke, lean process, ..)

Connection Related Risk Mitigation

Improving of only the contributing connection risks in the manufacturing process are required. The category in the calculated Zero Hour Defect Rate (ZHDR) is connection and must lead to a change to minimize the risk.

  • Screw (process improvements, Tools,...)
  • Glue (process improvements, Tools,...)
  • Solder (process improvements, Tools,...)
  • Press (process improvements, Tools,...)
  • Bond (process improvements, Tools,...)
  • Rivet (process improvements, Tools,...)
  • Staple (process improvements, Tools,...)
  • ....

Assembly Processing Related Risk Mitigation

Improving of only the contributing assembly processing risks in the manufacturing process are required. (good is good) The categories in the calculated Zero Hour Defect Rate (ZHDR) are coating, cleaning, excess parts, adjusting, testing, greasing, ... and must lead to a change in the assembly process to minimize the risk.

  • Coating (improve process,...)
  • Cleaning (improve process,...)
  • Excess parts
  • Adjusting
  • Greasing
  • Testing
  • .....

Calculate the New Zero Hour Defect Rate (ZHDR)

Based on the Manufacturing process change new processes are used and the Zero Hour Defect Rate (ZHDR) must be (re)calculated.

Zero Hour Defect Rate (ZHDR) Calculation

This results in a new Zero Hour Defect Rate (ZHDR) which must be checked if the Zero Hour Defect Rate (ZHDR) is within specification.

Zero Hour Defect Rate (ZHDR) realized

Testing

Testing is the last resort which must be used when the design or manufacturing process changes are not sufficient to reach the required Zero Hour Defect Rate (ZHDR). Testing will always brings added risk, scrap, rework, cost and time by introducing testers.

Part Related Risk Mitigation

Part risks are design related due to the fact that the Bill Of Material (BOM) dictates these parts. Part related risks, which are not mitigated by a design change, needs to be tested to reduce those Part related Zero Hour Defect Rate (ZHDR).

  • Part Defects (Incoming inspection, Test in assembly, ....)
  • Part physical out of specification (Incoming inspection, Test in assembly, ....)
  • Part functional out of specification (Incoming inspection, Test in assembly, ....)

Mounting Related Risk Mitigation

Mounting risks are manufacturing process related and can only be tested during or after assembly.

  • Missing (Test in assembly, ....)
  • Wrong (Test in assembly, ....)
  • Misoriented (Test in assembly, ....)
  • Misplaced (Test in assembly, ....)

Connection Related Risk Mitigation

Connection risks are assembly process related and therefore tested during or after assembly.

  • Screw (test, ...)
  • Glue (test, ...)
  • Solder (test, ...)
  • Press (test, ...)
  • Bond (test, ...)
  • Rivet (test, ...)
  • Staple (test, ...)
  • ....


  •  

Assembly Processing Related Risk Mitigation

Assembly process risks are manufacturing process related and therefore tested after assembly.

  • Coating (test, ...)
  • Cleaning (test, ...)
  • Excess parts (test, ...)
  • Adjusting (test, ...)
  • Greasing (test, ...)
  • .....

Test Mitigation

Each part, mounting, connection or assembly processing risk can be mitigated with a test. Each implemented test can influence one or more risks (defect opportunities) or one or more parts.

For this the variable Slip is a measure of how much the risk is mitigated.

If the slip is 1 no mitigation takes place.
If the slip is 0 the risk is completely mitigated.

Slip

Mitigated Zero Hour Defect Rate (ZHDR) Calculation

The part, mounting, connection and assembly process risks (DPMO's) are multiplied with the corresponding part, mounting, connection and assembly process slip.

Zero Hour Defect Rate (ZHDR) Calculation

This results in a new Zero Hour Defect Rate (ZHDR) which must be checked if the Zero Hour Defect Rate (ZHDR) is within specification.

Zero Hour Defect Rate (ZHDR) realized

Design Failure Contributions

Even when an assembly is manufactured perfectly, there is still a chance that the assembly will not meet its specified functionality and thus fails.

Methodologies to get insight in the design failures early in the design phase (architecture) is a Design Failure Mode Effect Analasys (DFMEA) where based on experiences of the past risks are identified. These risks can be quantized in a Zero Hour Defect Rate (ZHDR). New designs where there is no experiences have a high risk and those risks should be avoided or get insight in the risks by building a functional model. Furthermore each specification must be guaranteed by design or a test must be created to ensure this specification. When the design is finished a design verification must be done which must at least verify al the specifications. The same methodology also applies here that when a specification is not met a test must be applied to secure the specification. Underneath the DFMEA, Specification calculation and verification are the part and design related risks.

This could be caused by either a part or the design, even when the design is assembled correctly, resulting in not meeting the specifications.

Part Related Risks

A part could be used outside its specified area.
A special case is when the part is used outside its Safe Operating Area which causes wear and affects the reliability on long term. This will be explained in Life Time Risks.

  • Part used outside specified area
  • Usage of non specified part behaviour
  • Part stress (internal, external mounting, thermal,..)

Part used Outside Specified Area

When a part is used outside its specified area the part is itself is correct but its usage not. Due to the not specified behaviour it is possible that the assembly will fail.

Examples:

  • Sensor linearity
  • Lens aberrations/transmission outside specified area

Usage of non specified Part Behaviour

All parts, even with the most extensive documented specifications, have hidden performances which are not guarantied.

Examples:

  • OpAmp Noise behaviour is only specified for low frequencies
  • Optical elements specifeid on optical axis
  • ...

Design Related Risks

When assembled, the tolerances of all parts could lead to an assembly out of specification. (Worst case Risks)

  • Timing violations (digital circuits)
  • Noise behaviour (analog circuits)
  • Offset (Sensor + acquisition system)
  • Build dimensions (mechanic parts)
other Design risks are thermal stress induced in the design.
  • Stress induced mounting
  • Stress induced by thermal cycling during opteration. (Infant mortality)
  • ....

Mitigate Part or Design related Risks

Mitigation of the part or design risk is possible by either changing the design or selecting other parts so the risks are avoided.

Calculate the New Zero Hour Defect Rate (ZHDR)

Based on the design changes a new Bill Of material (BOM) is created and the Zero Hour Defect Rate (ZHDR) must be (re)calculated.

Zero Hour Defect Rate (ZHDR) Calculation

When a design change is not possible, the design must be tested on the risks to make sure that no part which could fail reaches the customer.
The same methodology also applies for the design related risks as for the assembly related risks. A test must be applied on the risks and the test slip multiplied with the risk DPMO.

Mitigated Zero Hour Defect Rate (ZHDR) Calculation

The Zero Hour Defect Rate (ZHDR) design risks are multiplied with the corresponding slip of the applied test.

Zero Hour Defect Rate (ZHDR) Calculation

This results in a new Zero Hour Defect Rate (ZHDR) which must be checked if the Zero Hour Defect Rate (ZHDR) is within specification.

Handling and Transport Failure Contributions

When an assembly is handled and transported, before its reaches the customer, the handling and transport risks must be taken into account.

Handling Related Risks

Assemblies are handled to go to a storage area or packaging area.

  • Electro Static Discharge (ESD)
  • Packaging Risks
  • Storage risks

Transport Related Risks

  • Transport damage risks

Calculate the New Zero Hour Defect Rate (ZHDR)

Based on the changes in the handling and transport process the Zero Hour Defect Rate (ZHDR) must be calculated.

Zero Hour Defect Rate (ZHDR) Calculation

Mitigated Zero Hour Defect Rate (ZHDR) Calculation

The Zero Hour Defect Rate (ZHDR) handling and transport risks are multiplied with the corresponding slip.

Zero Hour Defect Rate (ZHDR) Calculation

This results in a new Zero Hour Defect Rate (ZHDR) which must be checked if the Zero Hour Defect Rate (ZHDR) is within specification.

Life Time Failure Contributions

Reliabilty performance is mostly depicted by the bathtub curve which describes the three phases of the product life time (Initial, useful life, wear).

Relia bathtub Curve

Infant Mortality Related Risks

Random Life Time related risks

Structural Life Time related risks

Wear Life Time related risks

  • Heat

References

(1 First pass Yield (FPY)
(2 Yield
(3 Mcarthy, Thomas. The Six Sigma Black Belt Handbook, p. 307. 2004 McGraw Hill Education. ISBN10: 0071443290
(4 Througput Yield (TPY)
(5 Rolled Throughput Yield (RTY)
(6 Lunau, Stephan. Design for Six Sigma + Lean Toolset, p. 133. 2009 Springer-Verlag Berlin Heidelberg. ISBN 978-3-540-89513-8.
(7 Institute for Interconnecting and Packaging Electronic Circuits(IPC) IPC-7912A
(8 Yang, Kai, Design for Six Sigma, Chapter 11 2003 McGraw Hill, ISBN: 0-07-141208-5
(9 Mcarthy, Thomas. The Six Sigma Black Belt Handbook, p. 383. 2004 McGraw Hill Education. ISBN10: 0071443290.
(10 Yang, Kai, ''Design for Six Sigma'', Chapter 10 2003 McGraw Hill, ISBN: 0-07-141208-5
(11 Tien-Chien chang, Richard A. Wysk, and Hsu-Pin Wang. Computer-Aided Manufacturing, Second Edition, Pages 596 to 598. Prentice Hall 1998
(12 The bathtub Curve and Product Failure Behaviour (Part1)
(13 The bathtub Curve and Product Failure Behaviour (Part2)

Litirature on Quality

George, Michael l., ''What is Lean Six Sigma'', 2003, McGraw Hill, ISBN-10: 007142668X
George, Michael l., ''The Lean Six Sigma Pocket Toolbook'', 2004, McGraw Hill, ISBN-10: 0071441190
Morgan, John, ''Lean Six Sigma For Dummies'', 2012, Wiley Publishing, Inc., ISBN-10: 1119953707
Gygi, Craig, ''Six Sigma for Dummies'', 2005, Wiley Publishing, Inc., ISBN: 0-7645-6798-5
Webber, Larry, ''Quality Control for Dummies'', 2012, Wiley Publishing, Inc., ISBN-10: 0470069090
Kemp, Sid, ''Quality Management Dymistifeid'', 2006, McGraw Hill Education, ISBN: 0-07-144908-6