Your Reliability Engineering Professional Development Site
As you may recall the probability density function describes the behavior of a random variable.
Like a histogram, the PDF when plotted reveals the shape of the distribution. The PDF also has the property that the area under the curve for is one. Another property is the PDF is defined across the entire sample space. [Read more…]
Before computers and statistical software, we relied on tables to determine values for common integration problems – the normal distribution in particular. There is no closed form solution for the integral of the normal distribution probability density function, it requires advanced numerical methods to estimate the area under the curve. [Read more…]
A continuous distribution is useful in many statistical applications such as process capability, control charts, and confidence intervals about point estimates. On occasion time to failure, data may exhibit behavior that a normal distribution models well. [Read more…]
Similar to the Weibull distribution yet with slightly heavier tails. While not as easy to interpret if the data shows early life or wear out features, the lognormal distribution often fits time to repair data accurately.
Transform the data by taking the natural log of each data point. The resulting values tend to be normally distributed if the original data fits a lognormal distribution.
You can use base 10 or base 2 or any base and the results will still tend to be normally distributed. It is common to use natural log, ln(). [Read more…]
A discreet distribution useful when counting events within a time period.
It models rates, such as the number of gophers in your garden, paint scratches on your car, or the number of shopping carts that arrive in the 5 minutes before you in line. Essentially it’s the count of something over a time period or defined area. [Read more…]
The exponential distribution is a model for items with a constant failure rate (which very rarely occurs).
If the chance of failure is the same each hour (or cycle, etc.), including the first hour, 100th hour, and 1 millionth hour or use, then the exponential distribution is suitable.
Many practitioners assume the failure rate either is constant or changes so little as to be essential constant in order to make reliability calculations simpler. [Read more…]
It may be possible to pass the CRE exam knowing one formula.
The math elements of the exam may take a bit of time to solve, and knowing reliability statistics well is a good plan heading into the exam. Knowing the exponential distribution reliability function is one that you should memorize. [Read more…]
The operating characteristic curve is useful to understand the capability of a lot sampling plan. It depicts a graphical relationship between the unknown lot’s defect rate and the probability of the specific sampling plan to accept the lot. Ideally, we want a sampling plan the correctly accepts good lots and rejects bad lots. [Read more…]
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…]
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…]
One of the most basic skills needed for the CRE exam is the ability to correctly read the Standard Normal Table.
Writing this short how-to article would be really easy if there were only one way to create the table. There isn’t. It seems every author has to create a unique way to tabulate the values. [Read more…]
For our use of the Weibull distribution, we typically use the shape and scale parameters, β and η, respectively. For a three parameter Weibull, we add the location parameter, δ. [Read more…]
A continuous distribution is useful for modeling time to failure data. For reliability practitioners, the Weibull distribution is a versatile and powerful tool. I often fit a Weibull when first confronted with a life dataset, as it provides a reasonable fit given the flexibility provided by the distributions parameters. [Read more…]
Last week I posted about the Binomial probability density function, and it is useful when calculating the probability of exactly x successes out of n trials given p probability of success for each trial.
Well, what happens if you want to know the probability of 2 or more successes for example? [Read more…]
There are many cases where the results of an experiment (or trial) are either it works or it doesn’t, pass/fail, success/failure. Only two possible outcomes one of which we define as success the other outcome as failure. The binomial distribution is suitable if the random variable (the set of experimental or trial outcomes) when