Stress
PROBABILITY OF FAILURE
John Toksoy Cummins Inc.
November 7, 2002
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QUIZ 1!
DESIGN = MARGIN Strength Design Stress
50 45 Fatigue Strength (ksi) 40 35 30 25 20 15 10 5 0 A B C D Material Types
§ Which one of the
materials would you choose for a higher fatigue strength?
§ Would you pay a
premium for material “D” over material “A”?
Stress &Strength Interference
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VARIATION IS THE ENEMY… § Would the additional information like the variation in
strength change your answers?
50 45 Fatigue Strength (ksi) 40 35 30 25 20 15 10 5 0 A B C D Material Types
Stress & Strength Interference
§ Is material “C”
better then “B”? quantify the difference between these materials?
$2.6 / kg $2.2 / kg
VARIATION
§ How would you
$1.5/ kg
$1.7 / kg
§ Is design margin
alone a good criteria to select a material?
AVE
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Early Practice
- Design Margin
§ Early practice in stress-strength relationship
dealt almost entirely along the lines of design margin.
Factor of safety!
§ Design margin approach use the mean value
of stress & strength ignoring the natural scatter that each may possess.
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§Utilization of design margin is justified when
It is based on considerable experience Component design changes are not too different than the existing design. Ø Geometry, processing, function
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Stress & Strength Interference
Recent Practice
– Probability of Failure
§ The variation in stress and strength results
in a statistical distribution and a natural scatter in these variables.§ When these two distributions interfere,
that is when stress becomes higher than strength, failure results. a practical engineering sense and means of calculating the resulting interference (probability of failure) is the heart of this seminar.
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§ Means of expressing these distributions in
Stress & Strength Interference
Outline
§ Definition of failure - Unreliability §Reliability in simple terms § Part Strength & Stress § Normal Distribution § Probability of failure § Reliability quantified § Example
Stress & Strength Interference
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Definition of Failure - Unreliability
§ Failure
n
The inability to meet customer required function The manner in which the item fails, not the display of the failure Ø It is very important to identify the root cause andseparate the failure modes When mission is interrupted such that the item cannot or should not be operated until repair occurs
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§ Failure Mode
n
§ Mission Disabling Failure
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Stress & Strength Interference
How Do Customers Talk About Reliability
§ “ A system that does what I want
(function), when and where I want to use it (conditions), for as long as I want to use it (time) ”
§“ No surprises - no unscheduled downtime” § “ Get me up and running quickly when
failures occur ”
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This is as important as not having a failure in the first place.
Stress & Strength Interference
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Definition of Reliability
§ “The ability of an item to perform a
required function under stated conditions for a stated period of time”
§ “Quality over time” § “It is alsodefined and/or measured as the
probability that an item performs…”
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It is with this definition that we can quantify Reliability.
Stress & Strength Interference
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Reliability Measures
§ Cumulative failure rate at a stated time
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Repairs Per Hundred (RPH) within warranty period Failure rate per hour, month, mile in service Mean Time Between Failures (MTBF) B10 life – time at which10% of the items have failed
§ Instantaneous failure rate or hazard rate
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§ Time it takes to fail
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§ Probability of failure
Stress & Strength Interference
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Causes of Different Failure Types
§ Infant Mortality
n n n
Manufacturing & assembly issues Quality control issues Supplier Issues
Titanic
§ Random Failures
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Interference of inherent strength and...
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