Software tools are a cornerstone of modern Reliability Engineering, enabling reliability practitioners to perform their analysis without getting bogged down in the details of the underlying mathematical processes. There are many software tools available for reliability engineering, some of which are tailored to this application, while others are more general statistical tools which can be adapted to the needs of reliability engineers. One thing these tools have in common is their graphical user interface (GUI). The GUI requires only a basic level of knowledge to operate, but with a few clicks of the correct buttons, the desired task can be achieved with relatively little mental effort. It is the user friendly GUI that draws reliability engineers to select such applications as their tools of choice for performing reliability engineering analyses.

# Articles tagged Statistics distributions and functions

## Calculating the Probability of a Sample Containing Bad Parts

Received a question from a reader this morning that will make a nice tutorial.

A box contains 27 black and 3 red balls. A random sample of 5 balls is drawn without replacement. What is the probability that the sample contains one red ball?

So here’s my thinking and two ways to solve this problem. Instead of red and black balls in an urn type problem, which is pretty abstract, let’s say we know 3 bad parts are in a bin of 30 total parts.

## How to Estimate the Number of Failures Next Month

Let’s say you have shipped 1,000 products to your customer on January 1^{st}. All are immediately placed into service. And each month since you have received a few product returns, what we are going to call failures. We also have fitted the data to a Weibull distribution. Then in May, your boss asks you to estimate how many failures to expect in June.

This is a simple example as we’re not shipping units every month, nor changing the product design or assembly process. We also have worked out the fitted Weibull parameters already. That leaves the calculation of how many failures we should expect over the next month. [Read more…]

## The 3 Parameter Triangle Distribution 4 Formulas

This is part of a short series on the common distributions.

The Triangle distribution is univariate continuous distribution. This short article focuses on 4 formulas of the triangle distribution.

The distribution becomes a standard triangle distribution when a = 0, b = 1, thus it has a mean at the $- \sqrt{{c}/{2}\;} -$ and the median is at $- 1-\sqrt{{\left( 1-c \right)}/{2}\;}-$. The distribution becomes a symmetrical triangle distribution when $- c={\left( b-a \right)}/{2}\;-$.

The triangle distribution is used to approximate distributions when the actual distribution is unknown and bounded, often useful for Monte Carlo simulations. Other applications include subjective representation when there is evidence of bounds and a mode, or as a substitution to the beta distribution since it is bounded. [Read more…]

## The 2 Parameter Uniform Distribution 7 Formulas

This is part of a short series on the common distributions.

The Uniform distribution is a univariate continuous distribution. This short article focuses on 7 formulas of the Uniform Distribution. A common application is as a non-informative prior. Another application is to model a bounded parameter. The uniform distribution also finds application in random number generation. [Read more…]

## The 1 Parameter Poisson Distribution 4 Formulas

This is part of a short series on the common life data distributions.

The Poisson distribution is a discrete distribution. This short article focuses on 4 formulas of the Poisson Distribution. It is also known as the rare event distribution. It has application in a homogeneous Poisson princess and with renewal theory. [Read more…]

## The 2 Parameter Pareto Continuous Distribution 7 Formulas

This is part of a short series on the common life data distributions.

The Pareto distribution is a univariate continuous distribution useful when modeling rare events as the survival function slowly decreases as compared to other life distributions. This short article focuses on 7 formulas of the Pareto Continuous Distribution also known as the Pareto distribution of the first kind (there are three kinds, apparently). [Read more…]

## The 2 Parameter Binomial Discrete Distribution 4 Formulas

This is part of a short series on the common life data distributions.

The Binomial distribution is discrete. This short article focuses on 4 formulas of the Binomial Distribution.

It has the essential formulas that you may find useful when answering specific questions. Knowing a distribution’s set of parameters does provide, along with the right formulas, a quick means to answer a wide range of reliability related questions. [Read more…]

## The 2 Parameter Birnbaum-Saunders Distribution 7 Formulas

This is part of a short series on the common life data distributions.

The Birnbaum-Saunders distribution is a univariate continuous distribution. This short article focuses on 7 formulas of the Birnbaum-Saunders Distribution. This distribution was designed to model the Miner’s rule, thus allowing for non-constant fatigue cycles through accumulated damage.

If you want to know more about fitting a set of data to a distribution, well that is in another article.

It has the essential formulas that you may find useful when answering specific questions. Knowing a distribution’s set of parameters does provide, along with the right formulas, a quick means to answer a wide range of reliability related questions. [Read more…]

## The 4 Parameter Beta Distribution 7 Formulas

This is part of a short series on the common life data distributions.

The Beta distribution is a univariate continuous distribution. This short article focuses on 7 formulas of the Beta Distribution.

If you want to know more about fitting a set of data to a distribution, well that is in another article.

The Beta function is not used to describe life data very often yet is used to describe model parameters that are contained within an interval. For example given a probability parameter constrained from 0 ≤ p ≤ 1 the use of the Beta distribution is well suited to model such a parameter.

The Beta distribution is also known as a Pearson Type I distribution. [Read more…]

## The 2 Parameter Logistic Distribution 7 Formulas

This is part of a short series on the common life data distributions.

The Logistic distribution is univariate continuous distribution. This short article focuses on 7 formulas of the Logistic Distribution.

If you want to know more about fitting a set of data to a distribution, well that is in another article.

It has the essential formulas that you may find useful when answering specific questions. Knowing a distribution’s set of parameters does provide, along with the right formulas, a quick means to answer a wide range of reliability related questions. [Read more…]

## The 2 Parameter Normal Distribution 7 Formulas

This is part of a short series on the common life data distributions.

The Normal distribution is a continuous distribution widely taught. It is commonly used to describe items, measurements, or time to failure data when there are many additive perturbations that comprise the results. This short article focuses on 7 formulas of the Normal Distribution.

## The 2 Parameter Lognormal Distribution 7 Formulas

This is part of a short series on the common life data distributions.

The Lognormal distribution is a versatile and continuous distribution. It is similar to the Weibull in flexibility with just slightly fatter tails in most circumstances. It is commonly used to describe time to repair behavior. This short article focuses on 7 formulas of the Lognormal Distribution.

## How to Calculate Reliability Given 3 Different Distributions

On occasion, we want to estimate the reliability of an item at a specific time.

Maybe we are considering extending the warranty period, for example, and want to know the probability of no failures over one year instead of over the current 3 months.

Or, let’s say you talked to a bearing vendor and have the Weibull parameters and wish to know the reliability value over 2 years.

Whatever specific situation, you have the life distributions parameters. You just need to calculate reliability at a specific time. We can do that and let’s try it with three distributions using their respective reliability functions: exponential, Weibull, and lognormal. [Read more…]

## A Primer on Probability Distributions

The most common types of engineering data are measurements. There can be a few, thousands, or millions of data points to analyze. Without analytic tools, one can get lost in the data.

This article presents

- Dotplots
- Data if frequently clustered about a central value and displays variation.
- Frequency histograms
- Distribution characteristics
- Normal Distributions