![]() t1 is the future age of the piece of equipment.t0 is the current age of the piece of equipment.The curve in the CDF plot represents this function. D(t) is the cumulative distribution function, or the failure probability at time t for a new piece of equipment.If you specify a failure probability, the GE Digital APM system will use this value to calculate the future age of the equipment. P(t1|t0) is the failure probability at any given time assuming that the equipment has not yet failed at the current age.And so, Reliability Engineers must make assumptions and build some sort of model, even though the model will not be a true reflection of reality. The unfortunate truth is that hardly any company in the world collects failure data to that level of detail. ![]() To do that you must have impeccable historic records of when your items failed, and the history of how they were failed. Each year the Hazard Rate would rise as the remaining population decreases.Īs we can see from this example, it is best to model your own failure data. In the second year of our “typical” two-glass-breakage-per-year household, another 166,667 glasses will be broken world-wide. 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. If the failed glasses are not replaced, then the population shrinks by 166,667 annually. This approach is a simple example of determining the failure rate curve of an item in a stable population of items. This Hazard Rate assumes that each broken glass is replaced after breakage to keep the usable population at a million glasses. If all homes were a “typical household,” then each year on average about 166,667 glasses around the world will be broken and replaced.īecause the failure curve becomes a line after about 18 months, we have a steady rate of breakage at 166,667 per million glasses, which is an average failure rate, or Hazard Rate, of 0.167. In time, a reasonably constant set of opportunities tend to reoccur in each household. Annual events will re-occur, occasional random uses of the glasses will arise now and again. By the end of 12 to 18 months the range of opportunities will repeat. Initially the failure rate will start to climb as each month goes by and more opportunities occur for a glass to be used. Among the population of 83,000-plus households’ glasses will be broken every day. Each use is an opportunity for a glass to be broken. Acts of nature are excluded from this basic example.Īlong the bottom of the plot are situations and events where glasses are needed. The remaining glasses will not fail until they are broken by some event that happens during their lifetime. So, the failure rate curve for our “typical household” begins at a point slightly above zero to allow for the occasional early life failure. At time zero the failure rate will not be zero, because with nearly 1,000,000 opportunities to be broken, some glasses will not make it from the pack to the shelf. Each glass in the pack of 12 started its service life by being removed from the wrapping and put onto a shelf. In this situation, we will assume that a “typical household” has an average of two glasses broken a year.īefore a failure event there first must be an opportunity for a glass to be used. Those with young children and elderly people carrying a greater risk of glass breaks. Houses with more people in a house, the more times the glasses are used and a higher Hazard Rate. Houses with only one adult living it in will have a lower Hazard Rate. The packs of 12 were purchased by individual households, which means that 83,333 homes used the glasses.Įach household is different, and so carries its own hazard risk. This includes dropping, knocked, crushed, shocked by temperature and vibration, they can be mistreated, and they can succumb to previous damage.įor this example, we will assume that a million of a particular type of drinking glass and were made and sold in packs of 12 from stores around the world. The box lists 15 potential causes of glass breakage. Explosions mark when a glass was broken and are color-coded by the reasons they broke. In the image below, a drinking glass is used as an example component. Failure rates are fundamental in reliability analysis. A reliability engineer uses historic records of failure events to develop a failure rate curve of an item. BlueReliability engineering is a branch of statistics and probability that is used to calculate the failure rate of machines and parts.
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