MSR508

Unit Description and General Aims

This unit focusses on Interpretation of Failure rates. Starting with a discussion on the differences between success and failure domains, the unit meanders through various topics such as sources of failure data, accuracy, confidence levels, Cumulative Poisson curves, Chi-square tests, and the bath-tub curve for constant failure rates and the Weibull distribution for variable failure rates. The unit concludes that the extremely wide variability of failure rates of identical components under identical conditions obviates the need for complex reliability prediction models.

Learning Outcomes

On successful completion of this Unit, students are expected to be able to:

1. Compare and contrast failure data from various sources in terms of reliability, accuracy and confidence levels.

2. Apply correction factors to failure data to make it “fit for purpose”

3. Apply appropriate failure data to real-life situations

4. Employ appropriate statistical methods for data analysis and deductions

5. Interpret system failure rates and appreciate their limitations

6. Discuss Field data collection and Reliability Growth Modelling

Student assessment

Prescribed and Recommended readings

Required textbook(s)

1. 1. D.J. Smith and K.G.L. Simpson, Safety-critical systems handbook: a straightforward guide to functional safety: IEC 61508 (2010 edition) and related standards, 2010.

   OR

   1. D. J. Smith, Reliability, Maintainability and Risk, 2005.
   2. Kubiak, T. M. Benbow, Donald W.. (2017). Certified Six Sigma Black Belt Handbook (3rd Edition). American Society for Quality (ASQ). Retrieved from https://app.knovel.com/hotlink/toc/id:kpCSSBBH02/certified-six-sigma-black/certified-six-sigma-black
   3. Ebeling, C. E. (2019). An Introduction to Reliability and Maintainability Engineering, Third Edition (3rd edition). Waveland Press, Inc.
   4. Ayyub, B. M., & McCuen, R. H. (2016). Probability, statistics, and reliability for engineers and scientists. CRC press

Reference Materials

A number of peer-reviewed journals and websites (advised during lectures). Some examples are listed below.

• Reliability growth – Statistical test and estimation methods, Australian standard AS IEC 61164-2008.
• Equipment reliability – Reliability assessment methods, Australian standard AS IEC 62308– 2008.
• IDC /EIT notes and Reference texts as advised.
• Other material advised during the lectures

Unit Content

One topic is delivered per contact week.

Topic 1

Probability

1. Basic Concepts
1. Complementary Rule of Probability
2. Addition Rule of Probability
3. Contingency Tables
4. Conditional Probability
5. Independent and Dependent Events
6. Mutually Exclusive Events
7. Multiplication Rule of Probabilities
2. Distributions
1. Normal Distribution
2. Poisson Distribution
3. Binomial Distribution
4. t-Distribution (also known as Student's t-Distribution)
5. Exponential Distribution
6. Lognormal Distribution
7. Weibull Distribution

Topic 2

Basic Statistics

1. Basic Statistical Terms
2. Central Limit Theorem
3. Descriptive Statistics
1. Measures of Central Tendency
2. Measures of Dispersion
3. Other Useful Descriptive Statistics
4.  Determining Quartiles
4.  Graphical Methods
1. Frequency Distribution
2. Histogram
3. Scatter Diagrams
4. Normal Probability Plot

Topic 3

Measuring and Modelling Relationships between Variables

1. Simple Linear Regression
2. Value of the prediction equation
3. Assumptions
4. Checking assumptions through the residual plot
5. Confidence Interval for the Regression Line

Topic 4

Field Data Collection and Feedback

1. Reasons for Data Collection
2. Information and Difficulties
3. Spreadsheets and Databases
4. Best Practice and Recommendations
5. Analysis and Presentation of Results
6. Examples of Failure Report Forms

Topic 5

Data accuracy, databases and confidence limits

1. Data Accuracy
2. Sources of Data
3. Manufacturers' Data
4. Anecdotal Data
5. No-Fault-Found (NFF)
6. Data Ranges
7. Manufacturers' Data (Warranty Claims)
8. Overall Conclusion

Topic 6

Basic concepts of reliability - I

1. The study of Reliability and Maintainability
2. Concepts, terms and definitions
3. Applications
4. A brief history
5. Reliability Engineering as a Profession

Topic 7

Basic concepts of reliability - II

1. Defining Failure and Failure Modes
2. Failure Rate Function
3. Time to failure  and Time between failures
4. Interrelationships of Terms
5. Bathtub Curve
6. Conditional Reliability
7. Times to Failure
8. Down Time and Repair Time
9. Availability, Unavailability and Probability of Failure on Demand
10. Hazard and Risk-Related Terms
11. Choosing the Appropriate Parameter

Topic  8

Distribution analysis/Weibull analysis

1. Ranking of times to failure
2. Probability plotting
3. Estimate of the distribution parameters
4. Goodness of fit test
5. 3-parameter Weibull probability plot

Topic  9

Reliability Growth Modelling

1. The CUSUM ((Cumulative Sum Chart) technique
2. AMSAA (U.S. Army Materiel Systems Analysis Activity) model
3. Duane Plots

Topic 10

Data accuracy, databases and confidence limits

1. General procedure
2. Confidence intervals on sample statistics
3. Confidence interval for the mean
4. Factors affecting confidence interval and sampling variation
5. Sample size determination
6. Relationship between decision parameters and type I and II errors

Topic 11

Interpreting data

1. The four cases
2. Inference and confidence levels
3. The Chi-Square distribution and test
4. Confidence interval of MTBF/MTTR with time termination
5. Confidence interval of MTTR/MTTR with failure termination

Topic 12

Presentations and Unit Review

In the final week, students will prepare and present the main findings of their case study as part of Assessment 3. They will also have an opportunity to review the contents covered so far. Opportunities will be provided for a review of student work and to clarify any outstanding issues.  Instructors/facilitators may choose to cover a specialized topic if applicable to that cohort.

Software/Hardware Used

Software

• Software: N/A

• Version: N/A

• Instructions:  N/A

• Additional resources or files: N/A

Hardware

• N/A

Unit Changes Based on Student Feedback