The MTFB … What, Why, How and What for.

(and other ins and outs)

Ghulam Mustafa, Ph. D. ©2016

MTBF – Training Plan

Day 1: All About the MTBF

- Common mis/conceptions. - What is MTBF? - How is it calculated? - How is it predicted? - What can be done with the prediction? - Answers to the questions. - Some further considerations.

Day 2: On the MTBF Report

- Assumptions of the Report. - Data and Analysis. - What actions can be taken? - What is missing? - How to do a MTBF prediction? - Answers to the questions. - Some further considerations.

Feedback

Common conception about MTBF

A system will not fail before MTBF.

A system has 50% chance of failure before MTBF.

If two systems have MTBFs M1 and M2 then the combined MTBF is the average M=(M1+M2)/2.

The MTBF of a system is constant throughout its life.

If a system is tested for MTBF multiple times, it will always show the same MTBF.

MTBF of a population increases when more systems are added to the population.

Life’s Big Question

1) Have a good definition of what x is – narrow it down to basics. 2) Find a way to quantify the uncertainty as it relates to x.

Yogi Berra

It’s tough to make predictions, about the future.

Life … is uncertain. Then x happens. (x=failure event)

MTBF

As far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.

Albert Einstein

accurate

MTBF – Test Scenario During a reliability test, 25 units were tested. Time to failure for each unit was recorded. The test was stopped at the last failure. The test was repeated 3 times.

Inst. MTBF v Failures

Confidence in MTBF estimate Improves with more testing

Prob(t<MTBF)

MTBF – Scenario – Observations / Conclusions

0 200 400 600 800 10000

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time0 200 400 600 800 1000

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Time

Artifact of Random Sampling

1. Each test results in a different value of MTBF. 2. Number of times the system fails before MTBF is greater than 50%. 3. Instantaneous MTBF stabilizes with failures (or longer test times)

Observations

1. MTBF is a random variable (with certain characteristics). 2. The probability that the system will fail before MTBF is 63%. 3. Confidence in MTBF increases with failures or longer test time.

Conclusions

Each failure is a sample drawn from a distribution

What is … MTBF

It is the mean (or the expected value) of the random variable – time to failure (TTF). TTF is assumed to be exponentially distributed. This means that the histogram of TTF is an exponential function.

0 0.01 0.02 0.03 0.04 0.05 0.060

200

400

600

800

1000

1200

1400

1600

Tim

e t

o F

ailu

re

1

n

tMTBF

i=Failure Rate (failures/hour)

Reliability

It is the probability that system will perform its intended function for the specified period of time under stated conditions.

368.0)( )( MTBFt eetR

63.2% chance the system will fail before MTBF

What is …

MTBF – 37% Reliable

Reliability after 5 yrs – 5%

Reliability after 1 yr – 62%

Reliability after 6 mo– 78%

MTBF

The MTBF of a unit was determined to be 2 year – how reliable is it?

What is … MTBF

We want the system to be 95% reliable after 2 yrs. What is the MTBF?

yrsMTBF

tR

hrstetR t

38/1

1092.2/)ln(

17250365242;95.0)(

6

Reliability after 2 yrs – 95%

Reliability after 5 yrs – 88%

How to Measure MTBF

We know that MTBF comes from TTF that are exponentially distributed and so each test for MTBF will result in a different ‘estimate’. There is an uncertainty associated with MTBF. The uncertainty can be accounted for by including an interval around the estimated MTF – this is called the confidence interval

Any estimation or specification of MTBF MUST include a confidence interval

MTBFkMTBF *

( * ) MTBF

Lower Bound Upper Bound

= % confidence for lower and upper bounds k = Constant depending on

How to Measure MTBF @ 90% Confidence

25 units were test for 5000 hrs. The test stopped at the last failure.

Estimated MTBF=5000/25=200hrs

95% Lower Bound 95% Upper Bound

1.45 0.71

200

( * ) Lower Bound Upper Bound

142 290

MTBF Prediction & Modeling (What is good about prediction)

Why do MTBF prediction: To determine the feasibility of the specification (is it possible to design this system). Means of measuring the progress against the specification. Improving designs to meet new / future requirements. System

R

Sub-System 1 R1

Sub-System 2 R2

Module 11

Module 11

Module 11

Module 1n

n

in

t

n

inMTBF

eRRRRR

...

1;....

21

)(

21

(1) Similar Item Analysis. Each item under consideration is compared

with similar items of known reliability

(2) Part Count Analysis. Item reliability is estimated as a function of

the number of parts.

(3) Stress Analyses. The item failure rate is determined as a function of

operational stress levels

(4) Physics-of-Failure Analysis. Using detailed fabrication and

materials data, each item or part reliability is determined using failure

mechanisms

MTBF Prediction & Modeling (What is good about prediction)

Why do MTBF prediction: To determine the feasibility of the specification (is it possible to design this system). Means of measuring the progress against the specification. Improving designs to meet new / future requirements.

System R

Sub-System 1 R1

Sub-System 2 R2

Module 11

Module 11

Module 11

Module 1n

Distribution Application

Normal 1- Failure due to wear, such as mechanical devices.

2- Manufacturing varaibility

Log Normal 1- Reliability analysis of semiconductors

2- Fatigue life of certain types of mechanical components

3- Maintainability analysis

Exponential 1- Reliability prediction of electronic equipment

2- Items whose failure rate does not change significantly with

age

3- Complex repairable equipment without excessive

redundancy

4- Equipment for which the "infant mortalities" have been

eliminated by "burning in"

Gamma 1- Cases where partial failures exist (e.g., redundant systems)

2- Time to second failure when the time to failure is

exponentially distributed.

Weibull General distribution which can model a wide range of life

distributions of different classes of engineered items.

MTBF Prediction & Modeling (What is good about prediction)

System R

Sub-System 1 R1

Sub-System 2 R2

Sub-System n R5

Module 11

Module 12

Module 13

Module 10

n

in

t

n

inMTBF

eRRRRR

...

1;....

21

)(

21

=0.001

=0.001

=0.001

=0.001

=0.01

MTBF1000

MTBF1000

MTBF1000

MTBF1000

MTBF100

MTBF20

customer cassettes

Operator interface

Wafer aligner

Dual arm robot

Robot track

Processor Electronics rack WhisperScan Beamstop Vacuum chamber

Maintenance

interfaceVacuum robot Single wafer

loadlocks

PFS flange

Injector Booster Beamline Processor Factory Interface

We need system and module boundaries

Reliability Block Diagram

16 |

Reliability Block Diagram

System (100%)

Carousel (10%)

Shuttle (35%)

Gripper (17%)

Shuttle Horizontal Drive (10%)

Active Ports (15%)

Controls (10%)

DARTS Sys Cont.

FAB Int. Cont.

Drive Track FOUP Sensing

Belt Lift Belt Take-up Com/PWR Wiring Shuttle Cont PCB Interlocks

Controller Grip Mech. Sensors. Interlocks

Drive Rail Guides Flex Cable

Control PCB Vert. Drive Horizontal Dr.

E84 Func. Motion Cont. By-Pass Mode I/O Board

Ethernet Switch SW

Stationary Shelf (3%)

FOUP Sensing RF ID Connector Board

(%) is the module failure contribution to the system

MTBF in Closed-Loop Feedback (What is good about prediction)

MTBF prediction sets the goal for product reliability.

Step 1: Predict MTBF of the system under design. Step 2: Design the system to meet the MTBF. Step 3: Test the system to verify design and MTBF. Step 4: Is the MTBF goal met? Step 5: Perform F/A and take corrective actions. Step 6: Repeat 3-5 until D=0.

System Under Test

(Field Operation)

D Measured MTBF

Failure Analysis Corrective Actions

Predicted MTBF

Failure in Electronic Components

Failure in Incandescent Lamps

Initial Failures

Random Failures

Incandescent lap test data: after the initial infant mortality, the failure rate approaches a constant values. The failures are due to random causes – small defects grow with use and components become susceptible to failure due to small random variations.

You have questions In your expert opinion, when should the MTBF (complete product or system level) calculation be performed, Prototype, Pilot, or Production, phase? MTBF should be calculated as early as possible - it can

reveal design weakness and areas that need improvement. MTBF should be verified during prototype by testing - it should be validated during production. Should MTBF be done with individual components or tested

as a complete unit? Critical components are the weak links in the MTBF chain should be tested individually. System MTBF must be verified by system test.

Which parts (electrical/mechanical components) is most affected by MTBF? Which are likely to have short vs. long life?

Electrical components are generally more reliable (provided used correctly). Mechanical components are subject to variability and hence susceptible to premature failure.

Should we do MTBF on mechanical parts at system level?

Accelerated cycle testing is an efficient method for mechanical parts.

How would we determine buttons and switches MTBF?

Mechanical parts should be tested with accelerated cycling. Most of the electrical parts will have 5 years plus of MTBF. Should we do MTBF on mechanical parts only? Mechanical part testing -> Integrated System Test.

What are the common mis-understandings of MTBF calculations? There are many - MTBF alone is not enough.

Parts count MTBF, Problems and concerns regarding this method/better method? Part count is a good last resort if no other information is

available. Knowledge of system architecture helps in identifying weak links.

You have more questions Is MTBF created with testing in lab environments or hash environments? MTBF is a prediction - it should be verified by testing.

Software like Realcalc etc. worth the time, cost and effort? There is always an initial investment regardless of the SW tool - but it pays off over the product life cycle as real data is incorporated from field.

FITs number generation, where and what method is recommended. Best data comes from the vendor Do you know of any independent (consumer) databases that lists industry components that have been proven to be reliable, or at least within its advertised MTBF?

217 is old but reliable (read conservative). JEDEC is up to date.

HDBK 217 ground benign qa level 1 is the current basis for MTBF, is there a better or recommended standard? 1) Vendor 2) JEDEC 3) 217

What is your experience and suggestions regarding calculated MTBF and measure MTBF 1) First calculate MTBF 2) Verify MTBF by testing 3)

Determine delta 4) Improve MTBF How do correctly interpret an MTBF report – So a design eng can relate that to a potential problematic circuit? What parts on the Soundwaves product can we not do an MTBF on?

Best is to break it down into subsystem, module, submodule, assembly, subassembly … level and look at the weakest lowest level. Understanding when MTBF isn’t available, what do you do? MTBF is always available - as prediction, from lab test, from field, from customer … just have to find it. When published MTBF is not the reality, what is the

discrepancy? 1) Incorrect use of part data 2) Incorrect use of part.

Common conception about MTBF

A system will not fail before MTBF.

A system has 50% chance of failure before MTBF.

If two systems have MTBFs M1 and M2 then the combined MTBF is the average M=(M1+M2)/2.

The MTBF of a system is constant throughout its life.

If a system is tested for MTBF multiple times, it will always show the same MTBF.

MTBF of a population increases when more systems are added to the population.

M=1/(1/M1+1/M2)

You increase the failure rate – reliability decreases

MTBF is a random number

63%