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.

# Articles tagged Probability concepts

## 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…]

## 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…]

## 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…]

## The Law of Large Numbers and the Gambler’s Fallacy

### edited by John Healy

## 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…]

## 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…]

## 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.

## 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…]

## 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…]

## 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…]

## 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…]