A Proposal for an Alternative to MTBF/MTTF

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Does the DoD use the Wrong Reliability Metric?
A Proposal for an Alternative to MTBF/MTTF
James McLeish ASQ Reliability Division Webinar July 10, 2014
jmcleish@dfrsolutions.com

o Accurate measurements are essential for understanding, controlling and
improving processes and performance.
o For many decades the primary metric for measuring reliability in the
defense and aerospace industries has been the Mean Time Between or To
Failures (MTBF/MTTF (i.e. MTxF)) metrics.
o They are used despite the facts that these metrics are widely misunderstood
and misinterpreted, due to the incomplete view they provide of actual system
or equipment dependability performance across the entire product lifecycle.
o This often results in a misleading, overly optimistic reliability assessment that can
hide potential failure and safety issues.
o Yet the use of the MTBF/MTTF metrics continues because they have been
codified into numerous military standards, specs and handbooks.
o This webinar will review the origins of the MTBF/MTTF metrics and discuss what
they do and do not represent from a Physics of Failure point of view and
provide recommendations for Better Reliability Metrics.
o Note: This Webinar evolved an article Post at http://nomtbf.com/
o Replacing MTBF/MTTF with Bx/Lx Reliability Metrics
o http://nomtbf.com/2013/09/replacing-mtbf-bx/
Abstract

o Mean Time Between Failures (MTBF also known as Theta (Θ)):
o The statistical average of the time between failures across a population or fleet of
systems or components that are repairable or replaceable, calculated by dividing
the total accumulated population operating or field time by the number of failures.
o Mean Time To Failure (MTTF):
o The statistical average of the time between failures of a population or fleet of
systems or components that are not repairable or replaceable, calculated by
dividing the total accumulated population operating or field time by the number of
failures.
o The Inverse of MTxF is known as the Failure Rate (λ)
(Note: for Vehicles Mean Miles Between/To Failure is sometime used instead of time)
What is MTBF / MTTF
MTxF (Θ) =
Σ0
x( Unitsx * Each Unitsx Operating or Field Time)
Number of Failures
Failure Rate (λ) =
1 .
MTxF

o MTxF is used in various industries (especially defense & aerospace) to represent
reliability, but is widely misquoted, misunderstood & sometimes abused
o The most common misconception is that MTxF refers to the expected service life or
failure free operating period between failures OF A SINGLE DEVICE
o In reality MTxF is the inverse of the average failure rate of a fleet of devices
o Example: A MTBF of 1,000,000 fleet hours in a fleet of 10,000 units
o Results in a time to failure ever 100 fleet hours
o If the 10,000 unit fleet operates 24 hrs./day
o 240,000 Fleet hrs. are accumulated daily
o Then on average a failure can be expected somewhere in the fleet every 4.1667 days
o While this metric has value to Logisticians working to provide the needed spare parts to
support the deployment of a military division,
It does not represent actual reliability or service life.
o Many misconceptions could be avoided if the term
“Fleet or Population” Hours, Time, or Miles”
were used instead of simply Hours, Time or Miles
MTBF / MTTF Conceptions vs Reality

o “IF” a constant Failure Fate or MTxF applies,
the reliability at a point in time can be calculate by the equation:
o Example: R@2,400 hrs = e–2,400/1,000,000 = e-.0024 = 0.9976
= 10,000 units x (1-0.9976) = 23.97 Failures
(2,400 hrs, Operating at 24 hrs/day = 100 days)
R@8,760 hrs = e–8.760/1,000,000 = e-.008760 = 0.9912
10,000 units x (1-0.9912) = 87.2 Failures
(8,760 hrs/Operating at 24 hrs/day = 365 days = 1year)
o Unfortunately the constant failure (or Random Failure) Portion of the
hypothetical bath tub curve is not realistic, and
o If a constant failure rate period did exists, it can not last forever, wear-out
failures of the device would eventually limit its life much earlier than its MTBF
o Therefore, there is no direct correlation between the service life
of a device and its failure rate or MTxF
MTBF / MTTF & Reliability
Rt = e-λt = e-t/MTxF

0 1 2 3 Time - Years 4 5 6 7
Focuses on 3 Separate & Individual Life Cycle Phases, each with Separate
Control & Improvement Strategies, Produced the Misguided Belief that
Reliability Efforts Should Focus Only On Random Failure Issues
The Traditional View of Quality, Reliability & Durability (QRD)
- Product Life Cycle Failure Rate “Bath Tub” Curve
ProblemorFailureRate
End of Useful Life
/Typ. Replacement
Decision Pt.
The Bath Tub Curve
(Sum of 3 Independent Phenomena)
Durability = Wear Out
(End of Useful Life)
Reliability = Random or Chance Problems
(Constant Unavoidable)
But “True” Root Causes Can Be Disguised by
Actuarial Assumptions that Make QRD Data Analysis
Easy to Perform & Administer
This is an Inaccurate & Misleading Point of View
Quality = Infant Mortality

Real failure rate curves are irregular, dynamic and full of valuable information,
not clean smooth curves to simplify the data plots.
A “PoF FAILURE MECHANISM” Based “REALISTIC” View
Reveals the True Interactive Relationships Between Q, R & D
ProblemorFailureRate
Manuf. Variation & Error
and Service Errors
That Cause Latent
Problems Throughout Life
“Cause & Effect” Root Causes
Can Be Disguised by Actuarial Statistics
Once Problems Are Accurately Categorized
You Have Realistic Picture of “True Root Causes”
Weak Designs That
Start to Wear Out
Prematurely
TRUE Random
Problems
Are Rare Once
Correlated to
“ACTS OF
GOD & WAR”
0 1 2 3 Years 4 5 6 7

A Constant MTxF/Failure Rate is a Statistical Aberration that
Doesn’t Occur in Reality
o Just because a distribution can be averaged does not mean that the average accurately
represents the entire distribution.
o The constant Failure Rate/MTxF concept is the result of statistical manipulations by 1960 era
actuarial principles used to simplify data crunching and reporting
o Physics of Failure Research has produced a Different Point of View & Classifications:
Infant Morality
Failures are Actually
due to:
Manuf. Errors.
Excessive Manuf.
Variation or
Design Errors that
Produce Defects or
Weaknesses
Can cause either
Initial Failures or
Latent Failures
Throughout Life
(Correlates to the
Safety Enrg. Definition
of Systematic Failures
In Weak Designs
Wear Out
Failure
Mechanisms
Can Start
Prematurely
Also Correlates
to the Safety
Enrg. Definition
of Random
“True” Random Failures are Due to Chance Encounters with “Overstress” Conditions
that Exceeds the Capabilities/Strength of the Device (Pot Holes, EOS, Vehicle Impacts)
- In Well Designed Products Random Failure are Rare Attributable to
“Acts of God or War”

o MTxF metrics are often used without an understanding of what they represent
o Basic and necessary assumptions on what constitutes a failure are not stated.
o MTXF does not characterize the expected failure free period or the useful life
o A single discrete number does not give any insight into the characteristics of the
actual distribution beyond the arithmetic mean.
o While MTxF may be one aspect of reliability,
it is insufficient to accurately represent
all attributes of Reliability.
o Which results in uncertainty on what
is the actual reliability of a device
MTBF is a Non-Intuitive Reliability “Buzz Word”.

MTBF/MTTF is Insufficient for Representing the Classical Definition of Reliability:
o “The Probability of an item to perform required functions,
under stated conditions, for a stated period of time”
o MTxF is a coarse metric with limited value for designing reliability into products
o An arithmetic mean is a poor metric for representing complex relationships
o Insufficient to represent the influenced of outliers spread and distribution of the
endurance / reliability of a population.
o Time to first failure, failures over time, usage/durability life & total
service lifetime failure are more useful reliability metrics.
o The misconception of a Constant/Random Failure Period can results in
qualification using short reliability demonstration tests
instead of Longer Durability Testing
3 Failure Distributions (with the same Mean)
But Vastly Different Times to 1st Failure
Identifying Equipment Durability and
Times to 1st Failure for
Various Failure Mechanisms & Operating Conditions
is More Vital than a MTxF or Mean Failure Rate

o MTxF is cited in numerous military standards, specs & handbooks.
o Caused the practice to spread throughout the defense, aerospace & electronic
industries as contractors were required to providing MTxF data.
o Further documented in numerous reliability text books and college courses
o Migrated to other engineering disciplines especially FAA & Safety Engineering
o The MTxF metric is desired in some industries
o Simplicity of a single number metric
o Easy alternative to implementing more comprehensive activities that better
address all reliability issues.
o Since MTxF DOES NOT represent the actual expected service life of a device
or its expected failure free period, this confusion may sometimes be
desired as a marketing scheme to produce a perception of High Reliability
that avoids addressing real reliability issue
If MTxF is so Misleading - Then Why is it So Widely Used

The Origins of MTBF/MTTF
o 1957 AGREE Commision Report - Task Group 1
Advisory Group on Reliability of Electronic Equipment
 Developed for use on the Computational
Technologies of the 1950’s
 Mechanical Adding Machines
& The Slide Ruler
 A Reliability Metric Tailored
to the Leading Electronic
Technology of the 1950’s
 The Vacuum Tube &
Vacuum Tube Assemblies
 Early Discreet Transistor & Diodes

The Need for a Review and updating of Reliability Tools and Paradigms
for Effectiveness and Best Practices
o The Quality profession is consistently innovating,
sharing best practices, developing new tools &
methods and being a change agent for Quality,
while maintaining & updating standards:
o Continuous Improvement
o ISO-9000
o 6- Sigma Quality Methods
o However, with many organizations &
branches of the reliability profession
continue to cling to outdated, concepts &
standards.
o Due to lack of effort to update and
maintain standards or spec templates
o Due to a lack of cross pollination of
best practices from other industries

14
Current Situation as defined by the U.S. Defense Science Board
Task Force on Developmental Test and Evaluation (DT&E)
o Non optimized Reliability Metrics may be a reason why
“In recent years, there has been a dramatic increase in
the number (~2/3) of (military) systems not meeting
suitability
requirements”.
o “RAM deficiencies comprise the primary shortfall areas”.
o The results have been:
o “Costly redesign & schedule
delays.”
o “High maintenance burden & costs
as field personnel must replace or
repair unreliable systems and
components that were deployed
without achieving reliability
objectives.”

Other Views on - The Need for Updating the Reliability Profession
o “Reliability engineering historically has been focused on statistical & probabilistic models
which often do not have valid traceability to physical failure mechanisms”
o Kirk Gray - Accelerated Reliability Solutions & Hobbs Engineering Instructor
“What Why When and How to Apply HALT & HASS”.
 “What started as a simple observation has developed into a personal
mission to stop the widespread misuse, misunderstanding and
misinformation circling around MTBF. The acronym, MTBF, stands for
Mean Time Between Failure. It is very likely the worst four letter acronym
in the reliability engineering profession.”
o Fred Schenkelberg at http://nomtbf.com/
Former ASQ Reliability Division Chairman
 "Unfortunately, the development of reliability engineering has been
afflicted with more nonsense than any other branch of Engineering."
o Patrick O'Connor Consultant &
Author of: “Practical Reliability Engineering”
 “In Reliability and Quality Engineering, Physics Always Trumps Mathematics”
o Dr. Andre Kleyner, Global Reliability Engineering Leader - Delphi Electronics
“Notable Quotes” ASQ Quality Progress Nov. 2013

Recommendation For An Improved Reliability Metric – Bx/Lx
- A Blast from the Past
o Bx/Lx - the Life Point (hrs., days, yrs. or cycles)
When No More Than x% of Failures Have Occurred.
o A single metric that includes a Performance AND Durability element
o Max. Allowable % Failures (i.e. 1-R% ) AND the a Durability Life Point.
o Life point where no more than 10% (R≥90%)
of failures occur in a population.
o A Time to “Early Failure” Focus
o Failure values other that 10% can be used
(i.e. 5%, 2%, 1%, 0.5% 0.1% . . . )
o Predates MTBF/MTTF
o Evolved from the B10 Bearing Life metric,
(also used in Machinery & Auto Industries)
o Promotes Weibull Analysis
o A Valid, Widely Used, Comprehensive Metric,
that the AGREE Commission failed to adapt to
Electrical Equipment, due to the desire for a
metric that related more to Logistics than
sustainability

Benefits of the Bx/Lx Reliability Metric
o A More Comprehensive Reliability Metric Requires:
o Reliability Values Correlated to a Point in Usage or Field Time
o Under Application Appropriate Usage and Environmental Stress Conditions
o The Bx/Lx - Life Point can de defined in Hrs., Days, Yrs., Miles, Cycles . . .
as appropriate to the durability characteristic of interest in an application
o A Time to “Early or First Failure” Focus
o Failure values other that 10% can be used (i.e. 5%, 2%, 1%, 0.5% 0.1% . . . )
o Improvement over the Traditional (MTBF/MTTF) Reliability Metric
o Mean Time Between Failure / Mean Time To Failure
o Represents when 50% of the failures in a diverse population have occurred
during only the useful life phase (assumes wearout does not occur)
o Arithmetic mean is a poor metric since it is greatly influenced
by outliers and the spread/distribution of the population.
o Can be used in conjunction with MTxF
o Since many organization are familiar/comfortable with MTxF and use it for logistic,
there would be resistance to eliminating MTxF
o Would be easier to add Bx/Lx metrics along side MTxF

Physics of Failure Durability Simulation Modeling - Failure Risk Life Curves
for each Failure Mechanism Tallied to Produce a Combined Life Curve
o Bx/Lx Over Time
o Detailed Design & Application Specific PoF Life Curves are Far More Useful
than a simple single point MTxF value.
PTH Thermal
Cycling Fatigue
Wear Out
Thermal
Cycling
Solder
Fatigue
Wear Out
Vibration
Fatigue
Wear Out
Over All
Module
Combined
Risk
Cumulative Failures from
Generic, Actuarial, Constant Mean
Failure Rate Tables in MIL-HDBK-217
Example of a Physics of Failure
Failure Risk Over Time Plot from
the Sherlock ADA
Durability Simulation CAE App.
Ref.
http://www.dfrsolutions.com/software/
Over All Mean Life

o First, stop using MTBF yourself.
o Take and use the life data you already have and instead of calculating the MTBF,
calculate appropriate reliability function.
Fit to Weibull or Lognormal or whatever is appropriate
o Second, show others the information produced by directly using Reliability
data rather than using MTBF.
o Show the real life data to your customers, vendors, suppliers &engineering teams
o Show to marketing, finance, sales & especially decisions makes data
o Show that using an accurate reflection of reliability data permits better decisions
o It will save you time, money, resources, and frustration
o Be amazed at how quickly others understand the value of real reliability data
o Even managers will get it.
o Third, if require translate your work back to MTBF
o Provide the MTBF value with the duration over which it is appropriate
o Show the impact of assuming a constant failure rate when it isn’t true
o Focus on the value of making good decisions and the cost of making poor decisions.
What Can You Do If Your Industry Uses MTBF?
(From Fred Schenkelberg : http://nomtbf.com/2014/06/industry-mtbf-use/#more-1374)

Random Failure Definition Differences
Between Safety & Reliability Professionals
o Emerging Function Safety Standards
o IEC 61508 E/E Equipment
o ISO 26262 Automotive E/E Systems
o Risk-based safety standard, where the risk of hazardous failure operational
situations are qualitatively assessed and safety measures are defined to:
o Avoid or control Systematic Failures
o Detect, control or mitigate effects of Random Hardware Failures
o Requires commonly recognized industry sources be used to determine the
hardware part failure rates and the failure mode distributions
 IEC/TR 62380, IEC 61709, MIL HDBK 217 F notice 2, RIAC HDBK 217 Plus,
UTE C80-811, NPRD 95, EN 50129:2003, Annex C, IEC 62061:2005, Annex D, RIAC
FMD97 and MIL HDBK 338.
o Preparation of Self Driving Robotic Vehicle
o Examples: Google Car, Autonomous Drones
o Revealing fundamental difference in definition in
MTxF /Random Failure Rate between the
Safety Engineering & Reliability Engineering Professions

Failure Definition Differences Between Safety & Reliability Professionals
o In Safety Engineering faults which lead to failures are classified as
either Random or Systematic:
o Random Faults are due to physical causes
(such as corrosion, thermal stressing and wear-out . . . etc.)
o To safety professions “Random Failure are not assumed to have a Constant Failure Rate
o However they due reference averaged failure probability & risk derived from statistical
analysis from testing and historical data.
o Systematic Faults are produced by human error during system
development & operation.
o Can be created in any stage of the system’s life (i.e. specification, design,
manufacture, operation, maintenance, decommissioning).
o Since it is difficult to predict the occurrence of systematic faults and their effect
on safety the implementation of best practices to prevent errors and defects are
employed

Definition of Random Failure Differences
Between Safety & Reliability
Professionals
The Safety Profession used a
“Common Sense Definition”
Unfortunately Classical Reliability Professionals
& the “Recognized Industry Sources”
use a Different Definition
Developed by Actuaries & Defined in the 1960’s
US DoD AGREE Commission Report
(Advisory Group on Reliability of
Electrical Equipment)
http://safetyengineering.wordpress.com/2008/04/09/systematic-and-random-failure/

Failure Definition Differences Between Safety & Reliability Professionals
o In Classical Reliability Engineering Random Failures are denoted by the “Flat”
(i.e. Constant Failure Rate portion) of the hazard function (bathtub curve) between:
o A Presumed Short Infant Mortality Phase (denoted by a “Decreasing” Failure Rate)
o A Presumed Distant Wear out Phase (denoted by an “Increasing” Failure Rate)
o Therefore the “recognized industry sources” in theory do not account for Infant Mortality or
Durability Wearout issue that the safety professional at expecting to be quantified.
Random Means Constant
i.e. Equally likely to occur,
at any time,
in the usage life
Random Failure Rate λ
The Inverse of the Random Constant Failure Rate is Known as the Mean Time Between Failures
1 / λ = MTBF

Summary: Mean Time Between or To Failures (MTBF / MTTF)
o The MTxF reliability metric is widely cited & often criticized
o It is the average usage time between repairable or permanent failures, of a fleet of items
o The inverse of the average failure rate (λavg) i.e. MTBF = 1 / λavg
o Characterizes a system often for logistic maintenance spare parts purposes
o Often misinterpreted as a failure free life period of a single system
o A single “number” that attempts to describe a complex life time
o By assuming that failures occur at a constant rate because:
o Quality related infant mortality failures are insignificant due to screening
o End of life wearout failures occur outside of the useful service life
o Results in an over simplification that misrepresents reality.
o Better Reliability Metrics correlate reliability or failure
to a point in operating or in service durability time or
are plots across a time line, Examples .
o Bx/Lx Reliability Metrics
o Physics of Failure Durability Simulation plots

In Conclusion:
o Reliability Metrics that are Better Than MTxF Exist
o Is it Now Time of All Segments of the Reliability Profession to Update from
50-60 Year Old AGREE Commission Principles?
o Especially with the introduction of Functional Safety REquirements
 If Not, Preventable QRD Issues May Continue
into the Far Future and Galaxies Far, Far Away!

Want to Know More – Suggested Reading

Questions & Discussion
Thank you for your attention
For More Information
or a copy of the Presentation Slides
Contact: jmcleish@dfrsolutions.com

Today’s Speaker
Bio: James McLeish is a senior technical staff consultant
and manager of the Michigan office of DfR (Design for
Reliability) Solutions, a Failure Analysis, Laboratory
Services and Reliability Physics Engineering Consulting
Firm headquartered in Beltsville Maryland.
Mr. McLeish is a senior member of the ASQ Reliability Division and a core
member of the SAE’s Reliability Standard Committee with over 32 years of
automotive and military E/E experience in design, development, validation
testing, production quality and field reliability. He has held numerous technical
expert and management position in automotive electronics product design,
development, vehicle electrical system integration, product assurance,
validation testing and warranty problem solving as an E/E Reliability Manager
and E/E Quality/Reliability/Durability (QRD) technical specialists at General
Motors.
James McLeish

Who is DfR Solutions?
The Industry Leader in
Quality-Reliability-
Durability
of Electronics
0 Fastest Growing Companies in the Electronics Industry
- Inc Magazine
2012 Global Technology Award Winner
Best Design Verification Tool
- Printed Circuit Design

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