Device Reliability


Device Reliability

When searching for reliability figures, the mean time between failure (MTBF)  value is a metric commonly used. So, what is the relation to the life expectancy of the device? Unfortunately, none. MTBF and life expectancy have no direct relationship. The reason for this lies in the way MTBF is calculated.

If you look at Figure 10, you see a curve expressing the relationship between the number of failures over time for a population of devices. As you can see, the largest number of failures will occur in the beginning (called early life failures) and after a certain amount of time has passed (wear-out failures). In between these two periods, there is a phase where failures are rare and rather constant. This is called the useful life.

MTBF values are based on failure rate during this useful life. So no early life and no wear-out failures are taken into account. This means that the mean time between failure will be much higher than the life expectancy, since failures are more likely to occur during the two phases that are not taken into account.

 
Figure 10. Failure Rate Bathtub Curve

So what can you do with an MTBF value? One way to use this value is introducing it into the Poisson formula to make a quantitative estimation of reliability. To do this, we need to convert the MTBF to a new value: failure rate .

Failure rate will be expressed as a probability of failure during one machine month (MM). One machine month is rounded to 730 hours. This means that the failure rate will be equal to the inverse of the MTBF (expressed in hours) times the hours per machine month.

If we have, for example, an MTBF value of 100,000 hours, the failure rate will be 1/100,000 failures per machine hours, or 730/100,000 failures per machine month.

So, the failure rate expresses the probability (p) of a single event occurring in a selected time period. Table 3 shows an overview of the MTBF and this probability.

MTBF (Khrs) 100 200 300 400 500 600 700
p (Fails/MM) 0.0073 0.00365 0.00243 0.00183 0.00146 0.00122 0.00104

Table 3. Relationship of Failure Probability to MTBF

Note: This table is based on an MTBF calculated with a 100% duty cycle. Some publications will show an MTBF with a lower duty cycle.
To convert these, multiply the published MTBF with the duty cycle percentage used and divide by 100.

What is usually of interest however, is an estimate for the probability of a certain number of failures during a defined time period. To do this, we will use the Poisson distribution function.

 
Where:

n    Number of trials
   p    Probability of a single event during a selected time period (Fails/MM)
   x    Number of events
   P(x)    Probability of x events occurring in n trials


How can we use this formula now? Let's say we have 10 devices, and we want to check them over a time period of 12 months. This means that the number of trials will be 120 (one trial is defined as one machine during one machine month). The value p can be obtained from Table 3. We can now calculate the probability of a number of failures occurring during one year on these 10 devices.

MTBF
(Khrs.)		 Probability of no
failures (x=0)		 Probability of one
failure (x=1)		 Probability of two
or more failures
(x>1) P(>1)
100 .416 .365 .219
200 .645 .283 .072
300 .747 .218 .035
400 .803 .176 .021
500 .839 .147 .014
600 .864 .126 .010
700 .882 .110 .008


n=120 trials

Table 4. Probability of an Error Occurring on 10 Devices during 12 Months

Another item that is mostly unpublished in MTBF claims is the preventive and scheduled maintenance that is done. This could significantly extend MTBF. The main thing to remember is that when comparing MTBFs, extreme caution should be used.

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