EE 515
Basic Reliability Models
The Failure Distribution
Prof Joel Harris
CSULA - ECST Department
7 April 2016
1
Comparison of MTTF, Median, & Mode
2
Design Life
Find tR such that R(tR) = R
For example:
Find that time, t.99 such that R(t.99) = .99
Then, t
EE 515 Chapter 5
Reliability of Systems
Serial Configuration
Parallel Configuration
Combined Series-Parallel
Prof. Joel Harris
CSULA
17 May 2016
1
Serial Configuration
Reliability
Block Diagram
E1 = the event, component 1 does not fail, and
E2 = the event
EE 515
Basic Reliability Models
The Failure Distribution
Prof Joel Harris
CSULA - ECST Department
5 March 2016
1
Rlw
(im
th)et=
rcfw_T
P
t0,R()
1,and
The Reliability Function
Let T = a random variable, the time to failure of a component
This is often call
EE 515
Basic Reliability Models
The Failure Distribution
Prof Joel Harris
CSULA - ECST Department
5 March 2016
1
Rlw
(im
th)et=
rcfw_T
P
t0,R()
1,and
The Reliability Function
Let T = a random variable, the time to failure of a component
This is often call
The Constant Failure Rate
Model
[The Exponential Probability
Distribution]
EE 515 -03
Prof Joel Harris
14 April 2016
1
The Exponential Distribution
Let:
(t) = ,
t 0
Then:
R(t) = e
- 0t dt
- t
=e
, t 0
2
The Reliability Function
3
The CDF and PDF
F(t)= 1
EE 515 System Performance
Analysis
Prof. Joel Harris
CSULA - CEST Department
29 March 2016
1
Things Fail!
1946 the fleet of Lockheed Constellation aircraft was
grounded following a crash killing four of the five crew
members.
1978 the Ford Pinto automobil
EE 515 System Performance
Analysis
Prof. Joel Harris
CSULA - CEST Department
29 March 2016
1
Things Fail!
1946 the fleet of Lockheed Constellation aircraft was
grounded following a crash killing four of the five crew
members.
1978 the Ford Pinto automobil
EE 515 Systems
Performance Analysis:
Time-Dependent Failure
Models
The Weibull Distribution
Minimum Extreme Value
Distribution
(Chapter 4)
Prof. Joel Harris
CSULA ECST Department
28 April 2016
1
Time-Dependent Failure Mode
b
(t) = a t , with a 0
We can re
EE 515
Basic Reliability Models
The Failure Distribution
Prof Joel Harris
CSULA - ECST Department
7 April 2016
1
Comparison of MTTF, Median, & Mode
2
Design Life
Find tR such that R(tR) = R
For example:
Find that time, t.99 such that R(t.99) = .99
Then, t
EE 515 Systems
Performance Analysis:
Time-Dependent Failure
Models
The Weibull Distribution (contd)
Prof. Joel Harris
CSULA
3 May 2016
1
Typical Example Problems Redux
Let T = a random variable.
The time to failure of a
circuit card T has a Weibull
distri
The Constant Failure Rate
Model
[The Exponential Probability
Distribution contd]
EE 515 -03
Prof Joel Harris
21 April 2016
1
Failure Modes and CFR
If a system consists of n independent,
serially-related components each with
its own CFR, then:
n
(t) = = i
EE 515 Chapter 5
Reliability of Systems
Combined Series-Parallel
System Configurations
Prof. Joel Harris
CSULA
19 May 2016
1
Combined Series - Parallel
Systems
R1
R3
R2
R4
R6
R5
2
Combined Series - Parallel Systems
(contd)
B
A
R1
R3
R2
R6
C
R4
R5
3
Combin
Study Guide: EE 515 Final Examination
Chapter 1: General Concepts Regarding Reliability
Be able to describe in words/written form, the difference
between deterministic and stochastic/random failure models
(e.g. single outcome versus multiple outcomes).
EE 515 Week 1 Homework Problems
1. A household appliance is advertised as having more than a
10 year lifetime. If the following is its PDF, determine its
reliability for the following 10 years, assuming it has survived
a one year warranty period.
f(t) = 0
EE 515 Systems Performance Analysis (4) Section 01
Prerequisite EE 513
Prof. Joel K. Harris
Spring 2016, TTH Tuesday-Thursday, 8-9:40 PM ETA 331
Office & Hours
~ 1 hour prior to class/as arranged
Email
[email protected]
Grading
Quizzes
Midterm
Final
Homework Problem Set 2 Solutions
Problem 1
Given that = 0.00305, we have to find the following:
MTTF
R (500 hours)
Rmedian
R(.95)
Solution:
MTTF of a constant failure rate model =
R(500) = e (-)(t) = e
Rmedian = .5 = e
R(.95) = e
(-0.00305)(500)
(-0.00305
More Sample Chapter 4 Problems
Problem 1:
An automobile engine has a total of 4 fan belts, that all demonstrate a Weibull failure
distribution. If the four fan belts have separate scale parameters/design lifetimes of
2300, 4500, 5700, and 7200 operating h
Homework Problem Set #3
Problem 1:
A power supply consists of 3 rectifiers connected in a series. Each of the
rectifiers has a Weibull failure distribution with a value (shape parameter) of
1.8. But, the 3 rectifiers all have different characteristic life
EE 515 Week 1 Homework Problems
1. A household appliance is advertised as having more than a 10
year lifetime. If the following is its PDF, determine its reliability
for the following 10 years, assuming it has survived a one year
warranty period.
f(t) = 0
Homework Set # 2
Problem 1:
Given a (hazard rate) = 0.00305, find the following:
The MTTF
R(500) - in units of hours
R.50 , or tmedian
R(.95)
Problem 2:
A hydraulic system is made up of five components having the following
individual constant hazard rates
In Class Example Problems:
Chapter 4
Problem 1:
A recirculation pump for a heat exchanger in an air conditioning unit installed
on the roof of an industrial building has been found to have a normal failure
distribution.
Given that the MTTF for this pump i
Assignment solution-3
Instructor: Dr. Shaurya Agarwal
EE-5600, Spring 2017
March 23, 2017
Instructions:
Please complete all the questions and prepare a hard copy.
Submit the assignment 23rd March, 2017 (in Thursday Class).
No scanned copies. No late su
Assignment-3
Instructor: Dr. Shaurya Agarwal
EE-5600, Spring 2017
March 20, 2017
Instructions:
Please complete all the questions and prepare a hard copy.
Submit the assignment 23rd March, 2017 (in Thursday Class).
No scanned copies. No late submissions