RELIABILITY - College of Business
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Transcript RELIABILITY - College of Business
RELIABILITY
Dr. Ron Lembke
SCM 352
Reliability
Ability to perform its intended function
under a prescribed set of conditions
Probability product will function when
activated
Probability will function for a given length
of time
Measuring Probability
Depends on whether components are in
series or in parallel
Series – one fails, everything fails
Measuring Probability
Parallel: one fails, everything else keeps
going
Reliability
Light bulbs have 90% chance of
working for 2 days.
System operates if at least one bulb is
working
What is the probability system works?
Reliability
Light bulbs have 90% chance of
working for 2 days.
System operates if at least one bulb is
working
What is the probability system works?
Pr = 0.9 * 0.9 * 0.9 = 0.729
72.9% chance system works
Parallel
90%
80%
75%
Parallel
90%
0.9 prob. first bulb works
0.1 * 0.8 First fails & 2 operates
0.1 * 0.2 * 0.75 1&2 fail, 3 operates
=0.9 + 0.08 + 0.015 = 0.995
99.5% chance system works
80%
75%
Parallel – Different Order
80%
75%
90%
Parallel
80%
0.8 prob. first bulb works
0.2 * 0.75 First fails & 2 operates
0.2 * 0.25 * 0.90 1&2 fail, 3 operates
=0.8 + 0.15 + 0.045 = 0.995
99.5% chance system works
Same thing!
75%
90%
Parallel – All 3 90%
0.9 prob. first bulb works
0.1 * 0.9 First fails & 2 operates
0.1 * 0.1 * 0.9 1&2 fail, 3 operates
=0.9 + 0.09 + 0.009 = 0.999
99.9% chance system works
Practice
.95
.95
.75
.80
.9
.95
.9
Solutions
1: 0.95 * 0.95
2: Simplify
0.8 * 0.75 = 0.6 and
0.9 * 0.95 * 0.9 = 0.7695
Then 0.6 + 0.4 * 0.7695
= 0.6 + 0.3078 = 0.9078
Practice
.9
.95
.95
.95
Solution 2
Simplify:
0.9 * 0.95 = 0.855
0.95 * 0.95 = 0.9025
Then
0.855 + 0.145 * 0.9025 =
= 0.855 + 0.130863 = 0.985863
Practice
.95
.90
.75
.80
.9
.95
.9
Simplify
0.9 * 0.95 = 0.855
0.8 * 0.75 = 0.6
0.9 * 0.95 * 0.9 = 0.7695
.855
.60
.7695
Simplify
0.6 + 0.4 * 0.7695 = 0.6 + 0.3078
=0.9078
.855
0.9078
0.855 + 0.145 * 0.9078 = 0.855+0.13631
=0.986631
These 3 are in parallel
0.855 + 0.145 * 0.6 + 0.145*0.4*.7695
=0.855 + 0.087 + 0.044631
= 0.986631
.855
.60
.7695
Lifetime Failure Rate
3 Distinct phases:
Failure
rate
Infant
Mortality
Stability
Wear-out
time, T
Exponential Distribution
MTBF = mean time between failures
Probability no failure before time T
f (T ) e
T / MTBF
Probability does not survive until time T
= 1- f(T)
e = 2.718281828459045235360287471352662497757
Example
Product fails, on average, after 100
hours.
What is the probability it survives at
least 250 hours?
T/MTBF = 250 / 100 = 2.5
e^-T/MTBF = 0.0821
Probability surviving 250 hrs = 0.0821
=8.21%
Normally Distributed Lifetimes
Product failure due to wear-out may
follow Normal Distribution