Graphing Reliability Using Excel

The reliability of a component is measured by the mean time between failures (MTBF). It is the average time until failure and is typically provided in hours or years. A MTBF of 10 years means that, on average, every 10 years a failure occurs, based on a large sample. These numbers are typically provided in the component data sheets of the hardware manufacturers.

There are two problems associated with using the MTBF:

1. The values for MTBF can vary significantly, especially for components with moving parts like disk drives. This is because the MTBF depends greatly on the quality of the individual production batch which is far from constant. Manufacturers obviously try to detect quality problems, but this is not easy, as the manufacturing of complex components is more an art than a science. There are many variables, like calibration of machinery, impurities in the clean room, quality of materials, etc.

2. The appearance of failures does not follow a uniform distribution. The failure rate is high for new equipment (early mortality) and if equipment reaches its end of life. The time in-between is when we want to use the equipment for production.

However, manufacturers provide very impressive numbers for MTBF. For example, 106 hours (about 114 years) for a disk drive is a standard value nowadays.

The inverse of the MTBF is the failure rate. The annual failure rate (AFR) is defined as the average number of failures per year:

 AFR = 1/MTBF years = 8760/MTBF hours

 The AFR is a relative frequency of occurrence. It can be interpreted as a probability p(A) if AFR < 1, where p(A) means the probability that the component fails. If you multiply the AFR by the time interval you are considering, you will get the expected number of failures.

For example, consider a disk drive with MTBF of 300000 hours or 34 years. The corresponding AFR is 0.029 failures per year. If your disk array contains 200 such drives, you can expect one failure every 2 months. The following table lists typical mean time between failures (MTBF) and annual failure rate (AFR) values for common computer components:

 

MTBF Hours

MTBF Years

AFR

Disk Drive

300000

34

0.0292

Power Supply

150000

17

0.0584

Fan

250000

28

0.0350

Interface Card

200000

23

0.0438

 

 Excel Reliability Calculation Example

The formula used to calculate Reliability is: e-t/MTBF (Stevenson, 2019). In my MGT 350 Operations Management class, we create a worksheet similar to the Microsoft Excel example below. Using Excel, this formula is represented as =EXP(-A5/$B$2). To finish the worksheet, we simply copy everything down to row 2005:


 Next, add a graph for a range of 0 to 2,000,000 hours to illustrate the rapid decline and flattening of the curve: 


It is interesting to observe how quickly Reliability declines. At 300,000 hours, the reported MTBF, Reliability is only 36.79% and as we get farther out, the curve approaches 0%. We do a case study in MGT 350 for an autodetailer and there are a few vaccuums still working after 15 years. As they say "It was a good day at the factory!"

Source: High Availability and Disaster Recovery: Concepts, Design, Implementation

Authors: Schmidt, Klaus

Year: 2006

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