MREGC5101
BASIC QUANTITATIVE
SKILLS FOR RELIABILITY
ENGINEERING
Course Guide
Prepared by
Assoc. Prof. Indra Gunawan
Sessional Academic, School of
Engineering, IT and Physical Sciences
t
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Prepared by:
Assoc. Prof. Indra Gunawan for the School of Engineering and Information Technology, Federation
University, in conjunction with the Off-Campus Learning Centre, Federation University
.
Produced and Published by:
Off-Campus Learning Centre,
Federation University,
Churchill, Victoria, Australia, 3842
Revised July 2020
This off-campus learning material is for a study course that is part of one or more of the Fed Uni postgraduate
programs in Maintenance and Reliability Engineering. These comprise the Graduate Certificate in Maintenance
Management, Graduate Certificate in Reliability Engineering, Graduate Diploma of Engineering Maintenance
Management, and the Master of Maintenance and Reliability Engineering.
It has evolved over some years of offering these courses. The material is reviewed each year and updated. Some
Reader resource items are retained despite their age because they are considered to be of ongoing value to
students.
If you are not a student, you are invited to consider enrolling in one of our programs. Studies run full year, starting in
late February, and each course has an associated website. You can see the latest details on the School website. For
further information, contact the Coordinator of the programs.
Contents
Course Guide 1
Introduction to MRE5101 1
Context of this course…………………………………………………………………………………………………………… 1
Introducing your Course Adviser ………………………………………………………………………………………….. 1
How to contact your Course Adviser …………………………………………………………………………………….. 1
Aims of this course ………………………………………………………………………………………………………………. 1
Course overview …………………………………………………………………………………………………………………… 2
Study materials …………………………………………………………………………………………………………………….. 2
Textbooks…………………………………………………………………………………………………………………………….. 3
Accessing your Moodle site 3
The MREGC Orientation Guide 3
Starting off ………………………………………………………………………………………………………………………………………..3
The materials needed for your studies…………………………………………………………………………………………………..4
Now you have started your studies……………………………………………………………………………………………………….4
Administration matters ………………………………………………………………………………………………………………………..4
About postgraduate study in MRE ………………………………………………………………………………………………………..4
As the end of the study year approaches………………………………………………………………………………………………4
When you have finished your studies ……………………………………………………………………………………………………4
Study program 5
Study calendar – 2020……………………………………………………………………. Error! Bookmark not defined.
Assessment 6
Policy on late submission of assignments …………………………………………………………………………….. 6
Submission of assignments………………………………………………………………………………………………….. 6
Examination details………………………………………………………………………………………………………………. 7
Sample examination …………………………………………………………………………………………………………………………..8
Assignments ………………………………………………………………………………………………………………………. 10
Assignments for Submission 11
Assignment 1 ……………………………………………………………………………………………………………………… 11
Assignment 2 ……………………………………………………………………………………………………………………… 14
Assignment 3 ……………………………………………………………………………………………………………………… 15
Assignment 4 ……………………………………………………………………………………………………………………… 16
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Course Guide
Introduction to MRE5101
Welcome to our course MRE5101 Basic Quantitative Skills for Reliability Engineering.
Context of this course
This course is one of the initial courses in the Graduate Certificate in Reliability Engineering, and is also
studied as an elective by Honours direct entry students in the Master of Maintenance and Reliability
Engineering. I think that you will find its content of interest and value whichever path you are following.
Introducing your Course Adviser
Associate Prof. Indra Gunwan
Assoc. Prof. Gunawan received his PhD in Industrial Engineering and MSc in Construction Management
from Northeastern University, USA.
He was a program coordinator for Maintenance and Reliability Engineering at Monash University, Gippsland
Campus and served as a faculty at Auckland University of Technology, New Zealand, where his teaching
and research focused on reliability engineering, project management, operations management and
applications of operations research. He was also the Head of Systems Engineering and Management
program at Malaysia University of Science and Technology previously.
Details of his publications on maintenance and reliability engineering journals and conferences can be seen
on the School website.
How to contact your Course Adviser
Do not hesitate to contact me if you have any questions, or want to share some information. I should be able
to respond inside a day or two, except when I am away. If and when you do, please include in your
message some indication of the details of the problems you are facing so that when I reply, I can have a
considered response prepared. There are several ways:
1. The best way is via email. Email me on indra.gunawan@federation.edu.au I can usually
access email when away from base.
2. Call my mobile, on +61 4 50062964. I should be able to reply inside a day. (We are on the
same time zone as Sydney – normally 10 hours ahead of GMT, but you can check on
www.worldtimeserver.com). If I am away for longer than 2 days, I will leave a message
accordingly. Please say your name clearly, and give a time when you are likely to be
contactable for me to call you back.
Aims of this course
The primary aim of this course is to introduce you to a range of quantitative analytical techniques which are
of use to reliability engineers.
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This will involve you in:
• the study of mathematical concepts and calculation techniques;
• the use of computer software (OREST, Reliasoft) for studying problems in reliability;
• the study of mathematical techniques for preventive replacement analysis;
• the study of techniques for capital equipment life cycle cost and age based replacement analysis, and
the use of computer software in this application; and
• the introduction to mathematical terms and concepts in maintainability and availability.
The benefits of studying quantitative techniques in reliability take three forms. Firstly, you may be able to
apply a specific quantitative technique in your work. Secondly, even when you cannot formally apply a
specific technique (due perhaps to lack of data), then the principles underlying the technique may help with
management planning and decision-making. Thirdly, a knowledge of quantitative techniques will enable you
to form a judgement about when and how these techniques may be applied and will help you to judge the
extent to which an organisation should commit itself to the application of any given technique.
Course overview
Welcome to the course on Basic Quantitative Skills for Reliability Engineering.
A wide range of quantitative techniques has been developed over the years in the area of reliability
engineering. This course is presented as an introduction to the following key techniques:
• Analysis of reliability data, including burn-in, random and wearout failures, and how to take account
of items which have not failed.
• Measurement of key parameters such as Mean Time Between Failures (MTBF),and the estimation
of confidence limits.
• Preventive replacement policy determination.
• Capital equipment cost analysis with discounted cash flow.
• Maintainability and availability.
• Introduction of sensors and Internet of Things (IoT) for condition data collection.
The range and depth of statistical analyses which have been developed, particularly in relation to life test
analysis, is substantial.
The best way to come to grips with this is by a study of the basic problems using hand calculations for
simplified problems, combined with the use of computer software to handle the more complex calculations
and to provide rapid results in the form of graphs and tables.
Study materials
The course study materials are available on the unit Moodle site. You can access these anywhere in the
world via a series of document files.
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An educational version of OREST software is available for download at no cost. OREST/Reliasoft can be
used in this unit to replace RELCODE software which has no longer been produced since 2012.
We seek to continuously improve our study material. I would very much appreciate any comments or
suggestions for improvements from you at any time, during the year or later.
Textbooks
The text prescribed for this unit is:
O’Connor, PDT Practical Reliability Engineering 5th edition Wiley, 2012.
It contains very useful material that supplements the software and study materials.
You can download the educational version of OREST software at http://www.banakinc.com/orest_demo/orest_demo.html
The OREST manual is posted on-line, and can be printed and taken into the examination if you wish.
Accessing your Moodle site
As explained in the MRE5000, we have a Moodle site for each of our MRE courses. Only the students
enrolled in a course will have access to this course site.
Visit http://federation.edu.au/ portal and enter your authcate and password, as you obtained when you set up
your Federation computer access. (If you have not yet done this, check the links on the portal under the
“Login to” heading, hit “Moodle (HE)”).
You will see all the courses you are studying this year. Among them you will see MRE5000 STUDIES.
Although this looks like a course of study, it is a Moodle site for our MRE programs in general. News,
updates, etc. will be posted on it throughout the year.
If you cannot log into Moodle because it says you have an invalid password, check with the Moodle support
that you are correctly enrolled.
The MREGC Orientation Guide
We have collated all the generic support material about your study in one place. This Guide will be posted,
along with any updates during the year, on the MREGC5000 STUDIES site: Topics included are:
Starting off
| |
Obtain your computer account Your portal Web Enrolment System (WES) Keeping in contact with us Moodle HE MREGC5000 Studies |
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Need help with Federation University computer services?
The materials needed for your studies
| | Study materials |
| | Textbooks |
Now you have started your studies
| |
Library services Key dates and study loads Course Advisers (All matters concerning study in a course: questions, help, clarification, feedback, assessment, request for extensions, etc) Submitting your assignments: PDFs Plagiarism |
| |
Administration matters
| |
MRE program overall, course choice, variation, etc. Want to change your study program? Want to withdraw from all MRE study for a while? Who handles MRE administration? Updating your address, etc. details Fees query? Support in off campus learning? Personal problems affecting study? |
About postgraduate study in MRE
| |
What exactly is meant by “postgraduate” study? Higher education – what it is OBJECTIVES of the MRE programs |
As the end of the study year approaches….
| |
Examinations to normal program – if advice, sent about seven (7) weeks ahead, does not arrive? Exams: inability to sit on timetabled date Final grades for a course |
When you have finished your studies
| |
Graduation Promoting our programs: AMC, SMRP, PEMAC, SAMA, etc. |
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Study program
To study this course, it is best to work through the study guides, following the suggestions for the various
readings, calculation and other learning activities.
Once you feel confident about the material in the form presented here, you may wish to read other texts.
You should be aware that the range of mathematical and statistical topics covered and the various
approaches to reliability statistics is considerable, and can vary, at least superficially, from book to book.
Overall, it is expected that you will need to spend about 140 hours of quality study time to complete this unit
successfully. This is approximately an average of 4-5 hours per week over the study year.
If you are studying all of the units in the Graduate Certificate in Reliability Engineering in the one year, then
you should keep to the assignment due deadlines given in the table supplied to all students. This will
minimise clashing of due dates, and ensure that you have done adequate preparation through MRE5101,
MRE5102 and MRE5103 to manage the demands of course MRE5104 Reliability Applications.
If you are not studying those other courses this year, I invite you to schedule your own program to line up
with your other study commitments. The table below should help you schedule your program, with each row
suggested as taking equal time. Please be sure that you submit your last assignment to me no later than at
least two weeks before the examination.
| Calendar week |
Study Guide |
Topic | Completed record– your |
| 1 | 1 | Introduction to Reliability Statistics | |
| 2 | 2 | Weibull Analysis I | |
| 3 | 3 | Weibull Analysis II | |
| 4 | Complete Assignment 1 | ||
| 5 | 4 | Computer-based techniques | |
| 6 | 5 | Random failures and confidence limits | |
| 7 | Complete Assignment 2 | ||
| 8 | 6 | Preventive replacement | |
| 9 | Complete Assignment 3 | ||
| 10 | 7 | Financial Analysis | |
| 11 | Complete Assignment 4 | ||
| 12 | 8 | Availability and Maintainability | |
| 13 | Revision | ||
| Examination period |
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Assessment
To give you feedback on your progress, each assignment will be graded, according to the:
• familiarity with the topic being presented,
• application of information which has been supplied during the course,
• evidence of individual research and literature surveys,
• application of original ideas to problems,
• standard of technical communication, which includes presentation (layout), spelling and grammar.
…..with one of these categories (which are not necessarily exactly the same as the final course grading):
| HD | High Distinction | Outstanding level of achievement | 80%-100% |
| D | Distinction | High level of achievement | 70%-79% |
| C | Credit | Satisfactory, sound work | 60%-69% |
| P | Pass | Just OK – more effort desirable | 50%-59% |
| N | Fail | Not good enough – more effort is required to pass | Below 50% |
Policy on late submission of assignments
Extensions to the due date will be granted for good reasons (eg. illness or extraordinary work requirements)
if the request is received by me in writing, by facsimile, or email, BEFORE the due date.
Assignments received after the due date without a request for extension will be subject to the following
penalties:
| (a) (b) |
One grade per week or part thereof up to two weeks late. No assessment of the assignment if received later than two weeks after the due date. |
Submission of assignments
Write the texts of your assignments as a WORD document, number the pages, and put the following on
every page with two spaces between each item:
• Your name
• Your authcate
• The course code (e.g. MRE5101)
• Assignment Number
Example: “FBloggs fblo25 MRE5101 Assignment 2”
Send this to me as an attachment to an email message. Please put the course code and assignment number
in the subject/title of the message (to help quick location and filing of your messages and assignments). If
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you wish to do so, select “reply requested” on your mailer so that I can acknowledge that I have received
your work.
It goes without saying that you are expected to provide original work, and copying from others is not
countenanced.
Your assignments are preferably sent by email addressed to indra.gunawan@federation.edu.au
I aim to respond to you within 2 weeks, but no longer than 30 days after the stated due date, provided it is
submitted on or before the due date. (If you request and are granted an extension, then the 30 days applies
from the extension date).
Examination details
The date and time of the examination will be notified to you nearer the time, and will be available via your
portal. It is of 3 hours duration, and open-book (this means that you can take anything into the examination
except a computer).
When you check the portal for your examination details, you will find the details of your venue by clicking on
the link in the table that appears. If any problems (e.g. if you have moved away from near the examination
location that you notified to us on your initial application form), contact the Examinations Unit promptly.
There will be several questions in the examination, all of which are to be attempted. Each question carries
equal marks.
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Sample examination
It is suggested you might use these questions as part of your revision when studying for the final
examination.
1. (a) Explain the meaning of the following terms:
| (i) (ii) (iii) (iv) (v) (vi) (vii) (viii) (ix) (x) |
Failure. Reliability. Bath Tub Curve of Reliability. Burn-In Failures. Random Failures. Wearout Failures. Failure Probability Density Function. Reliability Function. Distribution Function. Hazard Function. |
| (b) | Describe the Weibull distribution and explain why it has become accepted as a standard distribution model in reliability analysis. |
2. A new design of computer disk drive is tested and the following data reported from a test sample:
| Time to Failure (Hours) | Number of Failures |
| 0-200 | 17 |
| 200-400 | 8 |
| 400-600 | 6 |
| 600-800 | 6 |
| 800-1000 | 7 |
| 1000-1200 | 32 |
| Survivors at 1200 hours | 84 |
Plot the following:
(a) Failure Frequency Histogram.
(b) Cumulative Percent Failures.
(c) Hazard Function.
What phases of failure are exhibited by the disk drives?
3. A door locking mechanism in suburban trains is causing reliability problems. The data tabled on the next
page is available. Note that the volume of data has been reduced for ease of calculation. When the
locking mechanism fails, it is replaced by a new one.
Draw up a table showing the observed times to failure or suspension of the locking mechanisms.
Prepare data in a form suitable for a Weibull Probability Plot. Plot the data on the Weibull probability
paper provided and estimate the shape and scale parameter. What type of failure pattern is indicated
and what is the mean life?
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| Door Number | Cumulative Cycles Operated by Door |
Event |
| 1 | 3 057 | Failure |
| 1 | 10 196 | Running |
| 2 | 10 196 | Running |
| 3 | 6 990 | Failure |
| 3 | 10 196 | Running |
| 4 | 4 913 | Failure |
| 4 | 9 092 | Failure |
| 4 | 10 196 | Running |
4. (a) What conditions are necessary for the preventive replacement of components to be economically
worthwhile?
(b) Explain the meaning of the following replacement strategies:
| (i) (ii) (iii) |
Replace only on failure. Age-based preventive replacement. Block preventive replacement. |
(c) Describe how costs typically vary with the various replacement policies.
5. Over a period of one calendar month, 312 air conditioners are run continuously and five failures occur.
Estimate the MTBF and give a 90% confidence band.
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Assignments
Assessment will be by four assignments and a final examination.
The assignments and their “standard” due dates are:
| Assignment No. |
Title | Due date |
| 1 10% |
Introduction to Reliability | 28 August |
| 2 10% |
Reliability analysis – computer-based techniques |
7 Oct |
| 3 10% |
Preventive replacement | 21 Oct |
| 4 10% |
Financial analysis of capital equipment replacement |
4 Nov |
All the assignments and the examination are compulsory. To pass the course, the total of your marks for all
the assessment components must show a satisfactory level of achievement: that is, above 50%.
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Assignments for Submission
Assignment 1
Introduction to reliability
Value: 10%
Answer all three questions and submit them for assessment.
Question 1
(a) Describe in your own words the significance of the “bath tub curve” of reliability.
| (b) | How does the Weibull distribution relate to the bath tub curve and what is the significance of the shape parameter (BETA)? |
Question 2
Table A1 shows reliability data for 100 gas discharge lamps.
| (a) | Plot a histogram of failure frequency for this data. It should be similar in style to Figure 1.6 in Study Guide 1 (page 10). |
| (b) | Plot the cumulative percent failure against age of lamp. The graph should be similar to Figure 1.7 in Study Guide 1 (page 12). |
| (c) | Use Weibull probability paper to plot this data. The graph should be similar to Figure 2.16 in Study Guide 2 (page 39). |
(d) What type of failure (Burn-In, Random, Wearout) is exhibited by the Gas Discharge Lamps?
(e) By what age would you expect 10% of lamps of this type to fail?
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Table A1: Gas discharge lamps failure data
| Hours | Number of Failures |
| 0-400 | 5 |
| 400-800 | 9 |
| 800-1200 | 6 |
| 1200-1600 | 5 |
| 1600-2000 | 7 |
| 2000-2400 | 6 |
| 2400-2800 | 8 |
| 2800-3200 | 2 |
| 3200-3600 | 6 |
| 3600-4000 | 6 |
| 4000-4400 | 4 |
| 4400-4800 | 2 |
| 4800-5200 | 0 |
| 5200-5600 | 0 |
| 5600-6000 | 12 |
| 6000-6400 | 0 |
| 6400-6800 | 0 |
| 6800-7200 | 0 |
| 7200-7600 | 0 |
| 7600-8000 | 8 |
| unfailed at 8000 | 14 |
| Total | 100 |
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Question 3
When the number of failures is small the cumulative probability of failure associated with the ith failure from a
population of N items is given by the Median Rank.
Median Rank is approximated by the formula:
Failure probability = (i – 0.3) / (N + 0.4)
Six bearings have been run for a period of time and the following ages at failure observed.
Table A2: Bearings failure data
| Bearing | Age of Failure (Weeks) |
| 1 | 24 |
| 2 | 8 |
| 3 | 14 |
| 4 | 12 |
| 5 | 16 |
| 6 | Not failed at 24 weeks |
Use Weibull probability paper to determine the distribution of time to failure and estimate the mean life of the
bearings.
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Assignment 2
Reliability analysis
Value: 10%
Question 1: Confidence limits for the MTBF
Data relating to manpack radios is shown in the following table, use mid-points of the utilisation ranges:
| Utilisation Hours | Number of Sets | Number of Failures |
| 0-50 | 100 | 8 |
| 50-100 | 200 | 8 |
| 100-150 | 200 | 10 |
| 150-200 | 100 | 4 |
Use chi-squared tables to estimate the MTBF and give a 90% confidence interval. Show your full working.
Question 2: Maintainability
An aircraft maintenance check takes the following times in minutes to complete on six successive occasions:
49, 59, 43, 65, 55 and 58
Find a suitable distribution to fit these data and estimate the maintainability, given a maintenance constraint
of 60 minutes. (Note: The maintainability is the probability that the maintenance is completed within the
maintenance time constraint.)
Question 3
State the conditions which must apply if the preventive replacement of a component or assembly is to be
economically worthwhile.
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Assignment 3
Preventive replacement
Value: 10%
Question 1:
Describe the three alternative replacement policies:
| (i) (ii) (iii) |
Replace only on failure. Age-based preventive replacement. Block replacement. |
Question 2:
Suppose that, on the average, 3 “strong” earthquakes occur in a certain region every 7 years. For this
region,
a) Determine the probability of getting 3 strong earthquakes in 7 years.
b) What is the probability of having at least 2 strong earthquakes in 5 years?
Question 3:
Three nominally identical temperature sensing elements are connected to nominally the same point on a
process plant. A shutdown signal is designed to be given if any one or more of these temperature sensors
record a temperature above a certain prescribed level. The times to failure of each element are
exponentially distributed with a mean value of 5,000 hours.
What is the mean time to complete failure of the alarm system?
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Assignment 4
Financial analysis of capital equipment replacement
Value: 10%
Canmade Limited wants to determine the capital replacement age for its turret sideloaders to minimise total
discounted cost. Historical data analysis has produced the following information (all costs in present day
dollars):
| Year | Average Operating and Maintenance Cost ($/year) |
Resale Value at End of Year ($) |
| 1 | 16 000 | 100 000 |
| 2 | 28 000 | 60 000 |
| 3 | 46 000 | 50 000 |
| 4 | 70 000 | 20 000 |
The cost of a new turret sideloader is $150 000, and the interest rate for discounting purposes is 12%.
Carry out calculations using a hand calculator to solve this problem. Show your detailed working.
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