Question 1

FIT and MTTF / MTBF (1): What is MTBF (Mean Time Between Failures)?

Accepted Answer

A. Mean time between failure is the arithmetic mean (or average) time between failures of a given device or system and is normally measured in hours. This statistical value is meant to represent the average amount of time that will pass between random failures for a large sample over a long period of time for a given component. It is also an indicator of system reliability that is calculated from known failure rates of various components in the system.[3Ƽƽ]

MTBF calculations are used to predict behaviors for a large (or entire) population, not the behavior from a particular site or smaller subset of the population. Therefore MTBF only applies to the cumulative analysis of large numbers of components; it says nothing about a particular unit.[5] Figure 1 gives a visual overview of the concept.

Figure 1. MTBF Illustration.

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Question 2

FIT and MTTF / MTBF (2): What is the difference between MTBF and MTTF?

Accepted Answer

A. Ideally, the MTBF should be used as part of a model that assumes the failed system will be repaired immediately (zero elapsed time) as opposed to mean time to failure (MTTF), which measures average time between failures of non-repairable systems only. However, in practice, MTBF is commonly used for both types of systems, repairable and non-repairable.

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Question 3

FIT and MTTF / MTBF (3): What types of MTBF figures can be obtained from manufacturers?

Accepted Answer

A. Basically, there are two types of MTBF figures: Theoretical and operational MTBF. When a manufacturer introduces a new product to the market, there is no operational data on how the product will perform. Typically, a theoretical MTBF figure will be calculated based on similar products (in the case of multilayer ceramic capacitors, this figure will be based on similar materials and class). This number is primarily used as a benchmark for reliability. It is calculated from the FIT number. It is also important to note that these MTBF figures are estimated based on a theoretical model and they are limited by the assumptions upon which they were based. Therefore it cannot typically account for random or unusual conditions such as a temporary quality problem during the manufacturing process.

Operational MTBF is provided when a component has been in use for a period of time. Actual failures of the component can be analyzed and calculations can be made thereafter. This figure is derived by analyzing field information and is typically lower than theoretical MTBF because it includes some human element and unforeseeable problems not accounted for in theoretical MTBF.

*JEDEC Standard JESD85, "Methods for Calculating Failure Rates in Units of FITs", JEDEC Solid State Technology Association, Arlington, VA, July 2001.
*R. A. Dovich, "Reliability Statistics", ASQ Quality Press, Wisconsin, 1990.
*Zzyzx Peripherals, Inc., "Mean Time Between Failure （MTBF） and Availability – A Primer", Technical Paper, June 13, 2001 Revision A.

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Question 4

FIT and MTTF / MTBF (4): What is FIT/Failure Rate?

Accepted Answer

A. By definition Failure Rate is the total number of failures within an item population divided by the total number of life units expended by that population during a particular measurement interval under stated conditions. It is usually denoted by the symbol λ. The dimension of the failure rate is the reciprocal of time and the unit used is 10⁹/hr = 1 FIT (Failure in Time). In other words, 1 FIT means 1 fail in 1ꯠꯠꯠ hours.

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Question 5

FIT and MTTF / MTBF (5): What are the failure periods?

Accepted Answer

A. Typically in the operational life of a system, three distinct phases of failure rate will become apparent. Figure 2 shows the reliability bathtub curve with the three phases.

Figure 2. Failure Rate Curve.

The first phase or period is referred to as the infant mortality or early failure period. The second phase is the random or constant cause failure period. This phase is assumed to be the period when the product will be in service. The failure rate for this period is expected to be flat and thus remains (virtually) constant. The last phase is the wear-out period. This period is more predominant in mechanical systems than in electronic systems.[2ƻ]

Infant mortality failures generally result from manufacturing errors that are not caught in inspection prior to shipping. At TDK, all ceramic capacitors go through thorough inspections and 100% testing to ensure that every chip meets specification before being shipped to customers in order to minimize infant mortality failures. We also perform intentional stress tests to ensure that all of our chip capacitors exceed specifications and expectations of our customers.

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Question 6

FIT and MTTF / MTBF (6): What factors affect the expected life and failure rates of MLCCs?

Accepted Answer

A. TDK uses the Arrhenius model (revised by Prokopowicz and Vaskas) to describe failure caused by systematic degradation. This model assumes that the degradation of the dielectric of the capacitor depends both on the temperature and the applied voltage. Basically these are stress factors placed on the system and are collectively called Acceleration Factors. Acceleration Factors are calculated as Voltage Acceleration (AV) times the Temperature Acceleration (AT). The resulting Acceleration Factor will be used in calculating the final FIT number.

Voltage Acceleration is one of the two Acceleration Factors used to calculate FIT and MTBF. TDK uses the equation below to calculate this factor.

V = Test Voltage
V₀ = Operating Voltage
α = Voltage Acceleration Coefficient

Temperature Acceleration is the other factor of the two Acceleration Factors used to calculate FIT and MTBF. TDK uses the equation below to calculate this factor.

T = Test Temperature in °C
T₀ = Operating Temperature in °C

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Question 7

FIT and MTTF / MTBF (7): How does TDK calculate Failure Rate of MLCCs (Multilayer Ceramic Capacitors)?

Accepted Answer

A. TDK estimates Failure Rate using JIS C5003 standard and a combination of the number of life test failures, the total device-hours at stress temperature and voltage, temperature acceleration factor, and voltage acceleration factor. Failure rate (λ) is calculated with 60% confidence level.

•r = Number of failure
•Σ t = Total number of equivalent device hrs
•k = Coefficient for confidence level
(If r = 0, then use k = 0.917 only for 60%; otherwise use r x k, e.g. 2 x 1.55 for 2 failures)

Observation	k Value
Observation	60%	90%
0 failure	0.917	2.30
1 failure	2.02	3.89
2 failures	1.55	2.66
3 failures	1.39	2.23
4 failures	1.31	2.00
5 failures	1.26	1.85

Table 1. k values which correspond to r

For calculating Failure Rate with operating condition (λ0), the below equation is used:

Example:
To calculate the Failure of a CGA2B3X7R1H104K capacitor, assuming the customer uses the capacitor at 85 degree Celsius and half the rated voltage (25V) @ 60% confidence level with life test conditions @ 125°C, 1.5xRV, and 77pcs for 1ꯠ hours:

One unit of FIT = 1 x 10^-9:

MTBF/MTTF is the reciprocal of FIT. Below is the equation to illustrate this.

Based on this formula, lower failure rate would equate to higher mean time to failure. In regard to the previous example, MTBF would equal 4140.9 years.

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Question 8

FIT and MTTF / MTBF (8): How do users use MTBF and FIT values?

Accepted Answer

A. These numbers are mainly used to calculate the probability a system will remain in working condition for a given time frame. They are often misinterpreted and misused.
These numbers are in no way a guarantee that the part will last for the stated amount of time. Obviously, the higher the MTBF, the higher chance a part will perform for a longer period of time at the given conditions. MTBF is not related to life expectancy of the operating life of the product and therefore has nothing to do with product lifetime.

For example, let us suppose a TDK capacitor has a MTBF number of 6꽶 years (16.5 FIT), this does not mean that the capacitor will last for that long (obviously no one will be able to test the part for that amount of time). If we assume that there are 8께 hours in a year (365 days x 24 hrs per day) and we want to find out what the probability the capacitor operating without failure for 10 years is, we can do the following math:

6꽶 yrs x 8께 hrs/yr = 60긹꺈 hrs
10 yrs x 8께 hrs/yr = 87길 hrs
87길 hrs/60긹꺈 hrs = 0.0014455
e-0.0014455 = 0.99856

Since probability is a percentage, this simply means that the part has a 99.9 percent chance of functioning correctly in the 10 year period.

It is obvious that 6꽶 years is a ridiculously long time for a capacitor to fail. However, it is important to take into account that a capacitor does not function by itself. It is part of a circuit that performs some function for a larger system. Sometime, if a component in the circuit failed, the whole circuit will cease to operate. This will result in downtime for the system and render the product unavailable for use. To calculate the MTBF for the whole system, take the inverse of the sum of all the FIT figures. Let’s look at an example to get a clearer understanding of what a FIT number means. Let’s say that there are 70 capacitors in use for a particular circuit. All of these capacitors have a FIT number of 16.5 (same as previous example). To find the MTBF you would do the following calculations:

MTBF = 1/(16.5 x 70) = 0.0008658008658
0.0008658008658 x 10⁹ = 865꼀 hours

For 70 capacitors in the circuit, the MTBF of all of them combine has dropped significantly. If we want to know the chance of the circuit still being operational after 10 years, it will result in only a 90.3% chance following the same calculation steps for the previous example. Also, notice that the MTBF is now more reasonable, 865꼀 hours is roughly 98 years. Also consider that this is in terms of operating hours. So for something that runs 24/7, the average fail time would be 9.88 years. However, if it is used in a car, for example, then it would be much longer.

Assume that a car will operate 4 hours per day, 1460 hours per year; the MTBF will be 865꼀/1460, or 593 years. The probability of the car not failing in 10 years would now be e-(10/593) = 0.983, or 98.3%. This is much better compared to 90.4%. Another way to used MTBF figure is in the calculation of availability of a system.

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