Accendo Reliability

Your Reliability Engineering Professional Development Site

  • Home
  • About
    • Contributors
    • About Us
    • Colophon
    • Survey
  • Reliability.fm
  • Articles
    • CRE Preparation Notes
    • NoMTBF
    • on Leadership & Career
      • Advanced Engineering Culture
      • ASQR&R
      • Engineering Leadership
      • Managing in the 2000s
      • Product Development and Process Improvement
    • on Maintenance Reliability
      • Aasan Asset Management
      • AI & Predictive Maintenance
      • Asset Management in the Mining Industry
      • CMMS and Maintenance Management
      • CMMS and Reliability
      • Conscious Asset
      • EAM & CMMS
      • Everyday RCM
      • History of Maintenance Management
      • Life Cycle Asset Management
      • Maintenance and Reliability
      • Maintenance Management
      • Plant Maintenance
      • Process Plant Reliability Engineering
      • RCM Blitz®
      • ReliabilityXperience
      • Rob’s Reliability Project
      • The Intelligent Transformer Blog
      • The People Side of Maintenance
      • The Reliability Mindset
    • on Product Reliability
      • Accelerated Reliability
      • Achieving the Benefits of Reliability
      • Apex Ridge
      • Field Reliability Data Analysis
      • Metals Engineering and Product Reliability
      • Musings on Reliability and Maintenance Topics
      • Product Validation
      • Reliability by Design
      • Reliability Competence
      • Reliability Engineering Insights
      • Reliability in Emerging Technology
      • Reliability Knowledge
    • on Risk & Safety
      • CERM® Risk Insights
      • Equipment Risk and Reliability in Downhole Applications
      • Operational Risk Process Safety
    • on Systems Thinking
      • Communicating with FINESSE
      • The RCA
    • on Tools & Techniques
      • Big Data & Analytics
      • Experimental Design for NPD
      • Innovative Thinking in Reliability and Durability
      • Inside and Beyond HALT
      • Inside FMEA
      • Institute of Quality & Reliability
      • Integral Concepts
      • Learning from Failures
      • Progress in Field Reliability?
      • R for Engineering
      • Reliability Engineering Using Python
      • Reliability Reflections
      • Statistical Methods for Failure-Time Data
      • Testing 1 2 3
      • The Manufacturing Academy
  • eBooks
  • Resources
    • Accendo Authors
    • FMEA Resources
    • Glossary
    • Feed Forward Publications
    • Openings
    • Books
    • Webinar Sources
    • Podcasts
  • Courses
    • Your Courses
    • Live Courses
      • Introduction to Reliability Engineering & Accelerated Testings Course Landing Page
      • Advanced Accelerated Testing Course Landing Page
    • Integral Concepts Courses
      • Reliability Analysis Methods Course Landing Page
      • Applied Reliability Analysis Course Landing Page
      • Statistics, Hypothesis Testing, & Regression Modeling Course Landing Page
      • Measurement System Assessment Course Landing Page
      • SPC & Process Capability Course Landing Page
      • Design of Experiments Course Landing Page
    • The Manufacturing Academy Courses
      • An Introduction to Reliability Engineering
      • Reliability Engineering Statistics
      • An Introduction to Quality Engineering
      • Quality Engineering Statistics
      • FMEA in Practice
      • Process Capability Analysis course
      • Root Cause Analysis and the 8D Corrective Action Process course
      • Return on Investment online course
    • Industrial Metallurgist Courses
    • FMEA courses Powered by The Luminous Group
    • Foundations of RCM online course
    • Reliability Engineering for Heavy Industry
    • How to be an Online Student
    • Quondam Courses
  • Calendar
    • Call for Papers Listing
    • Upcoming Webinars
    • Webinar Calendar
  • Login
    • Member Home
  • Barringer Process Reliability Introduction Course Landing Page
  • Upcoming Live Events
You are here: Home / Archives for Probability concepts

Articles tagged Probability concepts

by Christopher Jackson Leave a Comment

How to not Suck at Probability and Statistics

How to not Suck at Probability and Statistics

A simple way of looking at our brain is by dividing it into the conscious, subconscious and unconscious minds. The conscious mind is all about what we are actively thinking about in the here and now. We might be navigating as we drive through the countryside. We might decide to take an exit from the main road because our conscious mind has worked out that the map we are looking at is showing us that’s what we need to do to get to where we want to go. 

[Read more…]

Filed Under: Articles, on Product Reliability, Reliability in Emerging Technology Tagged With: Probability concepts

by Fred Schenkelberg Leave a Comment

Data Outliers and Questions

Data Outliers and Questions

When looking at a pile of data, sometimes there is a data point that is not like the others. It attracts attention as it is different than the rest of the data.

When I spot something odd in a dataset, I wonder if there is something to learn here. Is this an opportunity to make a discovery or improve a process?

All too often it is tempting to remove the outlier as a mistake. Or to drop the outlier as it doesn’t make any sense and ‘messes up’ the analysis. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Probability concepts

by Fred Schenkelberg Leave a Comment

Why do statistical based testing?

Why do statistical based testing?

Edited by John Healy

There is a lot of probability, statistics and data analysis involved with reliability engineering. Why is that? Have you considered why our field of endeavor includes the use of these tools?

Let’s say there were no statistical tools. We would not be able to accurately infer a conclusion based on an observation of a few samples. We might react to everything that we observe – constantly spinning our wheels on minor issues. We might make decisions based on factors that did not include the random variation of the items. We might track failure rates, yet not really know how to determine if the few failures we observe were an indication of a major issue or not. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Probability concepts

by Fred Schenkelberg Leave a Comment

Retro Standard Deviation Calculation

Retro Standard Deviation Calculation

Edited by John Healy

You use your calculator or spreadsheet, or even a statistics software package to calculate standard deviation, which is an estimate of the population standard deviation. Yet, understanding how one could calculate standard deviation without such advanced tools may prove useful. The knowledge of basic sum of squares methods provides a foundation for ANOVA and DOE analysis techniques. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Probability concepts

by Fred Schenkelberg 5 Comments

The Law of Large Numbers and the Gambler’s Fallacy

The Law of Large Numbers and the Gambler’s Fallacy

edited by John Healy

This theorem is a fundamental element of probability theory. The law is basically that if one conducts the same experiment a large number of times the average of the results should be close to the expected value. Furthermore, the more trails conducted the closer the resulting average will be to the expected value.

[Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Probability concepts

by Fred Schenkelberg 7 Comments

The Range Rule

The Range Rule

When time is short and you just want a rough estimate of the standard deviation, turn to the range rule to quickly estimate the standard deviation value.

The standard deviation is approximately equal to the range of the data divided by 4. That’s it, simple. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Probability concepts

by Fred Schenkelberg 7 Comments

Expectation and Moment Generating Functions

Expectation and Moment Generating Functions

In statistics and reliability, we use distributions to describe time to failure patterns. The four functions commonly used in reliability engineering include

  • The probability density function
  • The cumulative distribution function
  • The reliability function
  • The hazard function

We often use terms like, mean, variance, skewness, and kurtosis to describe distributions (along with shape, scale, and location). The mean is defined as the use of a moment generating function. First though let’s first back up to the concept of center of gravity (cog) from mechanics. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Probability concepts

by Fred Schenkelberg 3 Comments

Reliability Math

Reliability Math

Recently a question came to me about the difference between hazard rate and failure rate. A lot of literature and reference use these two terms interchangeably. I have long thought there is a difference, and to check my understanding I asked a good friend and reliability engineering consultant Chet Haibel. He provides a slide set (below) that described the various functions we use working reliability statistics and he details out the functions when using the exponential distribution.

[Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Exponential distribution, Probability concepts

by Fred Schenkelberg Leave a Comment

Chebyshev’s Inequality

Chebyshev’s Inequality

As with the Markov Inequality, we may find useful information from a list of values, say time to failure data. Again, none of the numbers may be negative for this to apply, yet with life data that is rarely the case.

Short on time- a common situation for reliability engineers; we have only the mean, standard deviation and number of values in a list. And, we need to say something about the data and the number or fraction of value above a specific value. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Probability concepts

by Fred Schenkelberg Leave a Comment

Markov Inequalities

Markov Inequalities

If we have a list of numbers, saw cycles to failure for a test. None are negative. And, we do not have time for a complete analysis before being asked about the results.

What can we do?

In this case, the Markov Inequality may prove useful for a quick assessment of the results. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Probability concepts, Summary Statistics

by Fred Schenkelberg Leave a Comment

Permutations and Combinations

Permutations and Combinations

A foundational element of probability and statistics is counting. How many ways could something occur? A simple example is a pass or fail criteria, thus when evaluating a product there are two possible outcomes. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Probability concepts

by Fred Schenkelberg 2 Comments

Top Tips for Probability Analysis

Top Tips for Probability Analysis

This is provided courtesy of Amanda at

Egerton Consulting Ltd
Visit our website at www.egertonconsulting.co.uk

<They have a great newsletter and worth subscribing. Fred> [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Probability concepts

CRE Preparation Notes

Article by Fred Schenkelberg

Join Accendo

Join our members-only community for full access to exclusive eBooks, webinars, training, and more.

It’s free and only takes a minute.

Get Full Site Access

Not ready to join?
Stay current on new articles, podcasts, webinars, courses and more added to the Accendo Reliability website each week.
No membership required to subscribe.

[popup type="" link_text="Get Weekly Email Updates" link_class="button" ][display_form id=266][/popup]

  • CRE Preparation Notes
  • CRE Prep
  • Reliability Management
  • Probability and Statistics for Reliability
  • Reliability in Design and Development
  • Reliability Modeling and Predictions
  • Reliability Testing
  • Maintainability and Availability
  • Data Collection and Use

© 2025 FMS Reliability · Privacy Policy · Terms of Service · Cookies Policy