MEM 361: Engineering Reliability
Final Project
(Relevance to ak outcomes: a, b, c, d, e, f, g, h, k)
(due: Tuesday, March 15, 2011; noon)
Submit a printed report
(include the effort sheet)
Problem 1. (60%)
In the attached sheet are data collected from a
Problem 2. (Prb. 6.3 in Text)
The failure rate for a highspeed fan is given by
(1)
where t is in hours of operation. The required designlife reliability is 0.95.
a. How many hours of operation should the design life be?
In order to solve this, the equat
MEM 361: Engineering Reliability
Midterm Examination #2
(Relevance to ak outcomes: a, b, c, d, e, f, g, h, k)
(due: Thursday, February 24, 2011; in class)
Submit a printed report
(include the effort sheet)
In the attached sheet are data collected from a
5.6
Spreadsheet of falure times in days for proof test of new product
F(t) vs t
Weibull Distribution
Lognormal Distrobution
x= t
y=F(t)=i/(N+1)
x=ln(t)
y=ln(ln(1/(1F(t)
x=ln(t)
y=normsinv(F(t)
12.276826
0.0384615385 2.50771342 3.238550275
2.5077134203

MEM 361: Engineering
Reliability
Dr. Ajmal Yousuff
Dept. MEM
Drexel University
Multiple Units
Systems of Multiple Units
Yousuff
InSeries Models
InParallel Models
SeriesParallel Models
Redundancy
Markov Models
MEM361:Reliability
2
Systems with Multiple
MEM 361: Engineering
Reliability
Markov analysis (Chap. 11)
Dr. Ajmal Yousuff
Dept. MEM
Drexel University
overview
Failure interaction
Yousuff
Independent failures
Sharedload systems
Standby systems
Repaired systems
MEM361:Reliability
2
Location of redu
Dr. Ajmal Yousuff
Dept. MEM
Drexel University
Acceptance/Rejection Limits
target, spec
Assume ontarget, m = t.
yield
t D
reject
reject
D
LSL
Yousuff
m
quality requirement
tolerance, spec
D
USL
MEM361: Reliability
2
The Yield
Reject if X < LSL
Reject if
Dr. Ajmal Yousuff
Dept. Mech. Engg. And Mechanics
Drexel University
Censored Reliability Test
Censored Ungrouped Data
Censored Grouped Data
Accuracy of estimates
Yousuff
MEM 361 Reliability
2
Sometimes, a test maybe suspended before failure
occurs. This
MEM 361: ENGINEERING RELIABILITY
Winter 20152016
Midterm exam 2 (takehome, team project)
March 01, 2016: in class (printed report, no electronic submission)
(Performance indicators: 1,2,5,6,13,14,18,20,21,30)
A. The data given (in the attached sheet mar
MEM 255 Fall 2015 Example Midterm
Problem 1:
a) Write the differential equation for the following transfer function G(s)
b) Find the final value for the transfer function with a ramp input r(t)=tu(t)
c) Evaluate c(t) at time t=5 for the step input r(t)=u(
MEM361 Engineering Reliability
A. Yousuff, PhD
Dept. MEM
Drexel University
WEIBULL Distribution
Introduction
2parameter Distribution
The Gamma Function
Example
Fitting Sampled data
Example
Yousuff
MEM361 Reliability
2
Introduction
Recall:
1. Normal
Ajmal Yousuff, PhD
Dept. MEM
Drexel University
Small # of sampling N unreliable predictions.
Use ranking statistics cpdf, rather than pdf.
Equal ranking
Mean ranking
Median ranking
Fitting samples to distributions
Normal
Lognormal
Weibull
yousuff
Reli
MEM361 Engineering
Reliability
(chapter 12)
Dr. A. Yousuff
Dept. MEM
Qualitative System Analysis
Systems are composed of subsystems/components
Components critical to the function of the system
Critical chain of components
cut set and path set
Design/
MEM 361: ENGINEERING RELIABILITY
Winter 2016_2017
Home work #3
Due: 01/31/2017
Solution:
Problem 1 (20%)
a.
b.
c.
d.
P(BC) P(B). NOT independent.
P(BC) 0. NOT mutually exclusice.
P(ABC) = P(ABC)P(BC) = 0.5 * P(BC)P(C) = 0.5 * 0.6 * 0.4 = 0.12
P(BCA)
MEM 361: ENGINEERING RELIABILITY
Winter 2016_2017
Home work #
Due: 02/23/2017
This is NOT a team home work. Individual work and submissions are required.
(Performance indicators: 1,4,20, 30
(marks: 50)
Solution
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
MEM 361: ENGINEERING RELIABILITY
Winter 2016_2017
Home work #4
Due: 02/09/2017
(Performance indicators: I(N/A), II(2), III all problems(1,2)
(marks: II(10points), III(25 points total; ie. 5 points each)
I.
(need not submit; this is a reading assignment) E
MEM361 Engineering Reliability
(reliability, failure: Chap. 6)
Dr. A. Yousuff
Dept. MEM
Drexel University
Quantities of measure
Probability density function, f(t)
t
F (t ) f ( )d
Cumulative pdf, F(t)
0
Reliability function, R(t) R(t ) 1 F (t ) t f ( )d
Fa
MEM 361: Engineering Reliability
Midterm Exam 2
(Perf. Indicators: 1,2,5,6,13,14,18,19,20,21)
(due: Tuesday, March 07, 2017; in class)
Submit a printed report
(include the effort sheet)
Problem:
In the attached sheet are data collected from a tensile stre
MEM 361: ENGINEERING RELIABILITY
Winter 2016_2017
Home work #4
Due: 02/09/2017
(Performance indicators: I(N/A), II(2), III all problems(1,2)
(marks: II(10points), III(25 points total; ie. 5 points each)
I.
(need not submit; this is a reading assignment) E
MEM 361: ENGINEERING RELIABILITY
Winter 2016_2017
Home work #
Due: 02/23/2017
This is NOT a team home work. Individual work and submissions are required.
(Performance indicators: 1,4,20, 30
(marks: 50)
Problem 5.2 (variation)
Fifty measurements of the ult
MEM 255  Fall 2015
Homework 1
October 7, 2015
Name:
1. Write the differential equation for the following systems:
X(s)
F (S)
=
1
s2 +2s+7
X(s)
F (S)
=
s+2
s3 +8s2 +9s+15
2. Plot the poles and zeros for the following systems:
C(s)
R(s)
=
10
s2 +15s+54
C(s
MEM 255  Fall 2015
Homework 2
October 15, 2015
Name:
1. Write, but do not solve, the equations of motion for the following mechanical system in matrix form.
2. Solve for the transfer function G(s) =
2 (t)
T (t)
3. Solve for the transfer function G(s) =
L
MEM361: ENGINEERING RELIABILITY
(SAMPLING & DISTRIBUTION; CHAPTER 5)
Dr. A. Yousuff
Dept. MEM
Drexel University
Yousuff
WEVE SEEN
Random events (S) and variables (X)
Their pdf (f(x), f(xi), and cpdf (F(x),F(xi).
Two ways of getting pdf:
Probabilistic (t
Dr. Ajmal Yousuff
Dept. MEM
Drexel University
Normal distribution may not always be appropriate
Distribution may be skewed.
Other candidate distributions are:
Lognormal
Weibull
Extremevalue
Exponential
Beta
Gamma
MEM361 Reliability
yousuff
2
MEM 361: Engineering Reliability
Ajmal Yousuff, PhD
Dept. MEM
Drexel University
2
MEM 361 Reliability
Todays agenda
Administration
Overview of course
Yousuff
3
MEM 361 Reliability
Introduction  Instructor
Dr. Ajmal Yousuff
Associate Professor, Dept.
NPTEL > Mechanical Engineering > Modeling and Control of Dynamic electroMechanical System
Introduction to Dynamic System Modelling
Dr. Bishakh Bhattacharya
Professor, Department of Mechanical Engineering
IIT Kanpur
Joint Initiative of IITs and IISc  Fun
NPTEL > Mechanical Engineering > Modeling and Control of Dynamic electroMechanical System
Information Organization through
Signal Flow Graph
Dr. Bishakh Bhattacharya
P f
Professor,
D
Department
t
t off M
Mechanical
h i l Engineering
E i
i
IIT Kanpur
Join
NPTEL > Mechanical Engineering > Modeling and Control of Dynamic electroMechanical System
Module 1 Lecture 2
Information Organization through Block Diagram
Dr. Bishakh Bhattacharya
Professor, Department of Mechanical Engineering
IIT Kanpur
JointInitiati
NPTEL > Mechanical Engineering > Modeling and Control of Dynamic electroMechanical System
Dynamic Modelling of Mechanical Systems
Dr. Bishakh Bhattacharya
Professor, Department of Mechanical Engineering
g
g
IIT Kanpur
Joint Initiative of IITs and IISc 