Accendo Reliability

Your Reliability Engineering Professional Development Site

  • Home
  • About
    • Contributors
  • Reliability.fm
    • Speaking Of Reliability
    • Rooted in Reliability: The Plant Performance Podcast
    • Quality during Design
    • Way of the Quality Warrior
    • Critical Talks
    • Dare to Know
    • Maintenance Disrupted
    • Metal Conversations
    • The Leadership Connection
    • Practical Reliability Podcast
    • Reliability Matters
    • Reliability it Matters
    • Maintenance Mavericks Podcast
    • Women in Maintenance
    • Accendo Reliability Webinar Series
  • Articles
    • CRE Preparation Notes
    • on Leadership & Career
      • Advanced Engineering Culture
      • 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 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
      • ReliabilityXperience
      • RCM Blitz®
      • 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
      • Metals Engineering and Product Reliability
      • Musings on Reliability and Maintenance Topics
      • Product Validation
      • Reliability Engineering Insights
      • Reliability in Emerging Technology
    • 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
      • Integral Concepts
      • Learning from Failures
      • Progress in Field Reliability?
      • R for Engineering
      • Reliability Engineering Using Python
      • Reliability Reflections
      • Testing 1 2 3
      • The Manufacturing Academy
  • eBooks
  • Resources
    • Accendo Authors
    • FMEA Resources
    • Feed Forward Publications
    • Openings
    • Books
    • Webinars
    • Journals
    • Higher Education
    • Podcasts
  • Courses
    • 14 Ways to Acquire Reliability Engineering Knowledge
    • Reliability Analysis Methods online course
    • Measurement System Assessment
    • SPC-Process Capability Course
    • Design of Experiments
    • Foundations of RCM online course
    • Quality during Design Journey
    • Reliability Engineering Statistics
    • Quality Engineering Statistics
    • An Introduction to Reliability Engineering
    • Reliability Engineering for Heavy Industry
    • An Introduction to Quality Engineering
    • Process Capability Analysis course
    • Root Cause Analysis and the 8D Corrective Action Process course
    • Return on Investment online course
    • CRE Preparation Online Course
    • Quondam Courses
  • Webinars
    • Upcoming Live Events
  • Calendar
    • Call for Papers Listing
    • Upcoming Webinars
    • Webinar Calendar
  • Login
    • Member Home

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: Basic Probability Concepts

by Fred Schenkelberg 3 Comments

Create a Stem and Leaf Plot

Create a Stem and Leaf Plot

There are times when you do not have a computer available and would like to visualize the distribution of a small set of data. With paper and pencil, you can create a representation that is similar to a probability density function plot. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Discrete and continuous probability distributions

by Fred Schenkelberg Leave a Comment

Mood’s Median Test

Mood’s Median Test

This nonparametric hypothesis test tests the equality of population medians. While not as powerful as the Kruskal-Wallis Test, it is useful for smaller sample sizes, when there are a few outliers or errors in the data as it focuses only on the median value. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Hypothesis Testing (parametric and non-parametric), Non-parametric statistical methods

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: Basic Probability Concepts, Statistical Terms

by Fred Schenkelberg 1 Comment

Levene’s Test

Levene’s Test

Here’s an overview of the non-parametric test to evaluate if a set of samples have the same variance. If the variances are equal they have homogeneity of variances.

Some statistical tests assume equal variances across samples, such as analysis of variance and many types of hypothesis tests. It is also assumed for statistical process control purposes to determine stability (often done with range (r chart) or standard deviation (s charts). [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Non-parametric statistical methods

by Fred Schenkelberg 5 Comments

Contingency Coefficient

Contingency Coefficient

A contingency table, as in the chi-squared test of independence, reveals if two sets of data or groups are independent or not. It does not reveal the strength of the dependence. The contingency coefficient is a non-parametric measure of the association for cross-classification data. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Non-parametric statistical methods

by Fred Schenkelberg 2 Comments

Chi-Square Test of Independence

Chi-Square Test of Independence

The chi-square ( $- \chi^2 -$) test provides a means to determine independence between two or more variables. In this case, it works for count data.

Contingency table or row and column (r x c) analysis are other common names for this analysis. It is useful when comparing results from different treatments or processes. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Non-parametric statistical methods

by Fred Schenkelberg 2 Comments

Kaplan-Meier Reliability Estimator

Kaplan-Meier Reliability Estimator

Here’s an overview of a distribution-free approach commonly called the Kaplan-Meier (K-M) Product Limit Reliability Estimator.

There are no assumptions about underlying distributions. And, K-M works with datasets with or without censored data. We do need to know when failures or losses (items removed from the evaluation or test other than as a failure. Censored items). [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Non-parametric statistical methods

by Fred Schenkelberg 1 Comment

Kruskal-Wallis Test

Kruskal-Wallis Test

This is a non-parametric test to compare ranked data from three or more groups or treatments. The basic idea is to compare the mean value of the rank values and test if the samples could are from the same distribution or if at least one is not.

The null hypothesis is the data from each group would receive about the same mean rank score. We are comparing rank values, not the actual values. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Non-parametric statistical methods

by Fred Schenkelberg Leave a Comment

Spearman Rank Correlation Coefficient

Spearman Rank Correlation Coefficient

This non-parametric analysis tool provides a way to compare two sets of ordinal data (data that can be rank ordered in a meaningful manner). The result, rs, is a measure of the association between two datasets.

You may want to know if two reviewers have similar ratings for movies, or if two assessment techniques provide similar results. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Non-parametric statistical methods

by Fred Schenkelberg 13 Comments

Kendall Coefficient of Concordance

Kendall Coefficient of Concordance

Comparisons for agreement

Let’s say we have data that is only rank order from two or more evaluators (people, algorithms, etc.) and we want to determine if the evaluators agree or not.

The agreement here meaning the results from one person or another are in agreement, or they are concordant. This is typically done with this non-parametric method for 3 or more evaluators. For a comparison of two evaluators consider using Cohen’s Kappa or Spearman’s correlation coefficient as they are more appropriate. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Hypothesis Testing (parametric and non-parametric), Non-parametric statistical methods

by Fred Schenkelberg Leave a Comment

Three Considerations for Sample Size

Three Considerations for Sample Size

Detecting a change or difference is often the aim of an experiment or set of measurements. We want to learn which vendor, process, or design provides a better result.

When we use a sample to estimate a statistic for a population we take the risk that the sample provides values that are not representative of the population. For example, if we use a professional basketball team to sample men’s height. We may conclude that the height of men in the general population is taller than the true population value. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: sample size, Sample Size Determination

by Fred Schenkelberg 2 Comments

Mann-Whitney U Test

Mann-Whitney U Test

The U test permits the comparison of two samples to determine if they came from the same population or not. This non-parametric test can use ordinal data, meaning it is in some rank order without containing information about relative distances between ranks. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Non-parametric statistical methods

by Fred Schenkelberg Leave a Comment

Laplace’s Trend Test

Laplace’s Trend Test

A test to determine if the homogeneous Poisson model (HPP) is applicable given the data from an individual system is subject to the non-homogeneous Poisson model (NHPP).

This is an alternative test to using the Kendall-Mann Reverse Arrangement Test. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability Tagged With: Poisson process models

by Fred Schenkelberg Leave a Comment

Failure Modes and Mechanisms

Failure Modes and Mechanisms

When something fails, what should we do?

A natural question when something fails is

Why did it fail?

The answer is not always obvious or easy to sort out.

One of my favorite examples was on a circuit board that had a small burn mark where a component exploded off the board. The customer didn’t notice that missing part, our engineering team did that. [Read more…]

Filed Under: Articles, CRE Preparation Notes, Probability and Statistics for Reliability, Reliability Management Tagged With: Discrete and continuous probability distributions, Reliability Terminology

  • « Previous Page
  • 1
  • …
  • 4
  • 5
  • 6
  • 7
  • 8
  • …
  • 10
  • Next Page »

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" ]

[/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