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

## The chance of failure for equipment parts can be calculated from their history of failing and maintenance while in service

#### Slide 16 – 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 having frail, aged persons carry a greater risk the elders will break more glasses because their bodies are not as strong and responsive.

For the sake of the example we will use a house with an average of two glasses broken a year. That is not the truth in every house. It is a convenient assumption to permit the analysis to be done simply. What happens in another persons 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 from the package 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 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, or Hazard rate, of 0.167 (provided each broken glass is replaced soon after breakage to keep the usable population at a million glasses).

The approach explained above is a simple example of determining the failure rate curve of an item in a stable population of items. If the failed glasses are not replaced, then the population shrinks by 166,667 annually. Because the opportunities to use glasses are reasonably consistent each year, the number of glass breakages will remain at the “typical” level year to year. In the second year of our “typical” two-glass-breakage-per-year household, another 166,667 glasses will be broken world-wide. But since the initial population was 833,333 (1,000,000 – 166,667). The Hazard rate would then be 0.2 (166,667 / 833,333). Each year the Hazard rate would rise as the remaining population decreases.

It is best to model your own failure data. To do that you must have impeccable historic records of when your 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.

 This slide 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-of-reliability. Get the book from its publisher, Industrial Press, and Amazon Books.Use the head office email address on the Contact Us page if you have questions about this slide.

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