11/7/2016
ReliabilityDataPlotting
LeastSquaresFit(Regression)
PropertiesofStraightLines
Slope:
Then
= (
)+
Forany(x,y)ontheline,
= (
y
)+
P2(x2 , y2)
y (rise)
=
P1(x1, y1)
x (run)
intercept 0
0
x
2
1
11/7/2016
LeastSquaresFit(Regression)
The sum of the
Exercise 2.6 page 36
Using the life distribution from exercise 2.1, calculate the
failure rate at 10 hours. Answers in both %K and FITs
]
1
Exercise 2.6 page 36
failure rate at t=10 hours. Answers in both %K and
FITs
h(t)=
=0.0111803
Whent=10,h(t)=0.00353
10/4/2016
Exampleof
KolmogorovSmirnov
GoodnessofFitTest
44
TheKolmogorovSmirnovTest
The Kolmogorov-Smirnov uses the empirical cumulative
distribution function as a tool for testing the goodness of fit of a
distribution.
Fn(x) = the proportion of observat
Reliability Concepts
1
Reliability
Topics
-Reliability Function
-Hazard Function
-Cumulative Hazard Function
-Failure Rate, average failure rate
-Bathtub Curve
-Renewal rate
-The Mean time to failure
-Relationships
2
Again: What is Reliability?
Reliabilit
IE5345 Reliability Theory - Fall 2016 TTU
1
Constructing a Frequency Distribution
Example:
The following data represents the ages of 30
students in a statistics class. Construct a
frequency distribution that has five classes.
18
Ages of Students
20 21 27
WeibullDistribution
Weibull Distribution
The exponential distribution applies only under the
constant failure rate assumption.
But what do we do if the
failure rate is increasing or
decreasing?
WeibullDistribution
Consideringthefollowingcumulativehazardf
11/2/2016
The Normal &
Lognormal
Distributions
Normal Distribution
Bell Shaped
Symmetrical
Mean = Median = Mode
Location is determined by the mean
Spread is determined by the standard
deviation
The random variable has an infinite
theoretical range: -<x<
F
Frequency Distribution
Random variable
IE 5345 Reliability Theory - Fall 2016 TTU
1
Random Variables
A random variable is a function that
assigns numbers; such as numbers of
heads or tails; to points in the sample
space
A Probability distribution is a fun