Exponential Distribution Archives

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…]

by Fred Schenkelberg 3 Comments

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.

Please review the slides and comment or ask questions – both Chet and I will attempt to help clarify any misunderstandings. I do think the slides are excellent and will do a great job providing a review of basic reliability math and the exponential distribution.

Slide set posted with permission of Chet Haibel.

Chet’s slides

Reliability math and the exponential distribution from FMS Reliability

Using The Exponential Distribution Reliability Function (article)

Basic Statistics (article)

The Exponential Distribution (article)

by Fred Schenkelberg 5 Comments

K Out of N

The design of a product includes the arrangement of all of the product elements. When considering the reliability of a system, the arrangement matters. Many systems are arranged serially. This means that with the failure of any one element, the system will not work. See the article on Series Systems for more details. [Read more…]

by Fred Schenkelberg 6 Comments

Common Formulas

Running through a couple of practice CRE exams recently (yeah, I know I should get out more…) found a few formulas kept coming up in the questions. While it is not a complete list of equation you’ll need for the exam, the following five will help in many of the questions. They seem popular maybe because the relate to key concepts in the body of knowledge, or they are easy to use in question creation. I do not know why. [Read more…]

by Fred Schenkelberg 12 Comments

Exponential Reliability

Down to the last week of preparation for the exam on March 2nd. Good luck to all those signed up for that exam date. Time to focus on preparing your notes, organizing your references and doing a final run through of practice exams. [Read more…]

by Fred Schenkelberg 2 Comments

Poisson Distribution Calculation

Let’s say the results of software testing averaged three defects per 10,000 lines of code. The criteria for release is 90% probability of 5 or fewer defects per 10k lines.

If this product ready for release?

The Poisson distribution is appropriate here as it is useful for modeling defects per unit, count per area, or arrivals per hour. If the data, in this case, the defect count per lines of code to be modeled by the Poisson distribution, the probability of an occurrence (defect in this case) has to be proportional to the interval (lines of code in this case). Also, the number of occurrences (defects) per interval must be independent (more on statistical independence in another post). [Read more…]

by Fred Schenkelberg 25 Comments

How to Calculate Warranty Failures

Let’s say we have a product that most often fails for one major component. Let’s say a fan (it could be anything, and while I don’t have anything against fans, it’s easy to picture).

Ok, this fan has a data sheet with the classic reliability claim of 50,000 hours MTBF. For those that know about my disdain for MTBF (www.nomtbf.com) rest assured I’m not going to get into it here. The basic approach for estimating the number of failure during any [Read more…]

by Fred Schenkelberg 1 Comment

Weakest Link

Each piece of gear used in rock climbing has the potential to be the weakest link. Often, based on accident reports, it the human decisions or lack of focus that is the most difficult to improve.

Ropes, anchors, harness, and carabiners and another equipment all have to work in the event of a fall. The design of each piece of equipment is to meet and hopefully exceed any possible load. And, to maintain the needed strength over years of harsh outdoor use. [Read more…]

by Fred Schenkelberg 1 Comment

Basic Statistics

Understanding the math is critical not only for the exam, but it is also important for your ability to function as a reliability professional.

Most of us did not enjoy our undergraduate statistics course. It was just another course to endure as part of being in an engineering or science track.

The basic concepts and approaches to working with data are fundamental for some many situations. [Read more…]