Post on 16-Dec-2015
transcript
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
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 = 0.72972.9% chance system works
Parallel 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
90% 80% 75%
Parallel 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!80% 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
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
Solutions
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
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
Exponential Distribution MTBF = mean time between failures Probability no failure before time T
Probability does not survive until time T = 1- f(T)
e = 2.718281828459045235360287471352662497757
MTBFTeTf /)(
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%