Parts Failure Rate Reflects Parts Failure History, Which Depends on the Number of Opportunities to Fail

Here is a simple example of how to calculate parts failure rate, also called the Hazard Rate, using a drinking glass

Slide 15 – A Simple Example of How to Use Parts Failure and Maintenance History to Calculate Parts Failure Rate (also known as the Hazard Rate)

Reliability Engineering is the branch of statistics and probability used to calculate the failure rate of machines, equipment, and parts. The Reliability Engineer uses historic records of failure events to develop a failure rate curve for an item. Failure rate calculations are fundamental in reliability analysis. Below is described a simple failure rate example showing the approach taken.

We’ll use the drinking glass in the image above as a component and determine its failure rate curve. Explosions mark when a glass was broken, and they are colour-coded by the reasons they broke.

During our lives nearly all of us will break several drinking glasses. In the orange box in the slide are listed 15 causes of glass breakage: they can be dropped in a variety of ways, they can be knocked, crushed, shocked by temperature and vibration, they can be mistreated, and they can succumb to previous damage. You can probably think of a few other ways that drinking glasses can break.

Let’s say that a million of these drinking glasses and were made and sold in packs of 12 from stores around the world. The packs of 12 went to individual households, which means that 83,333 homes used the glasses.

Each household is different, some will have just one person living in it, others will have many people. Some houses will only have adults. Other homes will have families with young children. Still other houses will be a mix of elderly persons, adults, teenagers, and children. The more people in a house, the more times the glasses are used. Homes with frail, aged persons carry a greater risk the elders will break more glasses.

For the sake of the example we will use a house with an average of two glasses broken a year. That cannot be the truth for every house. It is a convenient assumption to permit the analysis to be done simply. What happens in a person’s house to break glasses is not exactly the same as what happens in your house, or in your neighbour’s house. To use a “typical household” as an example of all 83,333 houses around the world is a presumption that ought to be challenged as being unrealistic for most homes.

Each glass in the pack of 12 started its service life by being removed from the wrapping and put onto a shelf. From our experiences with drinking glass breakage, we realize a glass could be broken as it’s moved to the shelf.

At time zero the failure rate will not be zero, because with nearly 1,000,000 opportunities to be broken (12 x 83,333), some glasses will not make it from the pack to the shelf. The failure rate curve for a “typical household” begins at a point slightly above zero to allow for the occasional early life failure. The remaining glasses will not fail until they are broken by some event that happens during their lifetime. Acts of God and nature could be included in the analysis under their own category, but they are excluded from this basic example.

Before a failure event there first must be an opportunity for a glass to be used. Along the bottom of the plot we see many situations and events where glasses are needed. There are birthday parties, annual festivities, family gatherings, visits by friends, anniversaries, special occasions, and many other times where we bring out a glass to have a drink. Each use is an opportunity for a glass to be broken. Among the population of 83,000-plus households glasses will be broken every day.

Initially the failure rate will start to climb as each month goes by and more opportunities occur for a glass to be used. By the end of 12 to 18 months the range of opportunities will repeat. Annual events will re-occur, occasional random uses of the glasses will arise now and again. In time, a reasonably constant set of opportunities tend to reoccur in each household. If all homes were a “typical household,” then each year on average about 166,667 glasses around the world will be broken and need to be replaced.

Because the failure curve becomes a line after about 18 months we then have a steady rate of breakage at 166,667 per million glasses, which is an average failure rate of 0.167. The approach explained above is a simple example of determining the failure rate curve of an item.

It is best to model your own failure data. To do that you must have impeccable historic records of when items failed, and the history of how they were failed. The truth is hardly any company in the world collects failure data to that level of detail. And so, the Reliability Engineer must make assumptions and build some sort of model, even though the model will not be the truth.

 Consecutive slides from this series will be regularly posted at the Lifetime Reliability Solutions website page Plant Wellness Way EAM Tutorials until the enire series is complete. There will be a full description and explanation on the relevant content in each slide. You’ll have a comprehensive reference on how PWWEAM works, and how to use it to design, build, and embed a Plant Wellness Way enterprise asset life cycle management system that gets world class plant and equipment reliability. This series of slides is a companion to the new Industrial and Manufacturing Wellness book. The book has extensive information, all the necessary templates, and useful examples of how to design and build your own Plant Wellness Way enterprise asset life cycle management system. You can buy the book from its publisher, Industrial Press, and from Amazon Books. If you have any questions about this slide, please send us an email using the head office email address listed at the Lifetime Reliability Solutions website Contact Us page.