Introduction to MTBF principle and calculation method

Ⅰ. MTBF concept

MTBF: Mean time between failures

English name: Mean Time Between Failure

Definition: It is the most important indicator to measure the reliability and stability of a product (especially electrical products). It belongs to the international industry standard and the unit is "hour".

It reflects the time quality of the product and reflects the ability of the product to maintain its function within the specified time. Specifically, it refers to the average working time between two adjacent failures, also known as the average failure interval. It is only applicable For repairable products, it also stipulates that the ratio of the cumulative working time to the number of failures during the total use phase of the product is MTBF.

Remarks: MTTF (Mean Time To Failure) = Mean Time To Failure Applicable to non-repairable products

Ⅱ. MTBF test principle

1. Accelerated Life Testing

1.1 The purpose of carrying out the life test is to evaluate the service life of the product in a given environment.

1.2 Routine tests take a long time and require a lot of money, and product reliability information cannot be obtained and improved in time.

1.3 Accelerated life test can be used in the laboratory to evaluate the service life of the product within an acceptable test time.

1.4 In terms of physics and time, it accelerates the cause of product deterioration, and uses a short time test to estimate the life or failure rate of the product in normal use. However, the basic condition is that the original design characteristics cannot be destroyed.

1.5 In general, the three factors considered in the accelerated life test are environmental stress, the number of test samples and the test time.

1.6 The reliability mode and acceleration mode of parts in general electronics and industrial control industries can almost all be found from U.S. military specifications or related standards, or they can be tested and analyzed by themselves to obtain their mathematical experience formulas.

1.7 If temperature is the only acceleration factor for the product, the Arrhenius Model can be used, which is the most commonly used.

1.8 The introduction of stresses other than temperature, such as humidity, voltage, mechanical stress, etc., is the Eyring Model.The products applicable to this model include electric lamps, liquid crystal display components, capacitors, etc.

1.9 The Inverse Power Law is applicable to metal and non-metal materials, such as bearings and electronic equipment.

1.10 Combination Model is suitable for electronic materials that consider temperature and voltage as environmental stress at the same time (for example, the following formula for capacitance is the calculation formula for the life of electrolytic capacitor)

1.11 Under normal circumstances, active electronic parts are fully applicable to the Ashford model, and electronic and information products can also be applied to the Ashford model, because the failure mode of the finished product is composed of most active electronic components. Therefore, the Ashford model It is widely used in electronics and information industries.

2. Acceleration factor

2.1 The Ahrmann model originated from the Ahrmann reaction equation proposed by the Swedish physical chemist Svandte Arrhenius in 1887.

R: speed of reaction

A: Temperature constant a unknown non-thermal constant

EA: activation energy (eV)

K: Boltzmann constant, equal to 8.623*10-5 eV/0K.

T: is the absolute temperature (Kelvin)

2.2 The principle of acceleration factor: The acceleration factor is the ratio of the life of the product under the conditions of use (Luse) and the life of the product under high test stress (Laccelerated).

If the product life is applicable to the Aristotle model, its acceleration factor is:

AF=e[Ea/K×(1/Ts-1/Tu)]

Ts: room temperature + constant 273

Tu: high temperature + constant 273

K: Boltzmann constant, equal to 8.623*10-5 eV/0K.

3. Calculation of activation energy Ea in acceleration factor

3.1 The Ea of general electronic products that fail in the early death period is 0.2~0.6Ev, and the Ea that fails in the normal useful period is close to 1.0Ev; the Ea that fails in the aging period is greater than 1.0Ev.

3.2 According to the test specifications of HP Reliability Engineering (CRE), Ea is the average value of Ea of all parts of the machine. If the Ea of the new model cannot be calculated, Ea can be set to 0.67Ev and treated as a constant.

3.3 If the calculation is based on the average value of Ea of all parts of the machine, you can refer to the following examples

Ⅲ. MTBF calculation method

1. According to the definition of MTBF, it is stipulated that the ratio of the cumulative working time of the product in the total use phase to the number of failures is MTBF, and the exponential distribution is the most common probability distribution used in reliability statistical analysis. The MTBF value of the exponential distribution is failure The reciprocal of the rate λ, so once the value of λ is known, the reliability of the product can be estimated from the reliability function.

MTBF = Total Operating Time (Hrs) / Total Failures Total Failures

The estimated value of MTBF conforms to the principle of chi-square distribution, and its syntax is:

CHIINV(probability,degrees_freedom)X2(probability,degrees_freedom)

So there are the following formulas:

T = Total Hours

r=Number of failures

Φ=Confidence interval

Note: If there are no failures, then: MTBFlower = T/-ln(Confidence Interval)

2. DMTBF calculation

DMTBF: Mean Time Between Failure Verification

English full name: Demonstration Mean time Between failures

Calculation method: temperature is used as the accelerated life test, and the Accelerated life mode of Ah's life is adopted.

Calculation formula: (In actual use, if necessary, you can multiply the numerator by 24Hrs to facilitate the calculation of hours)

Duration =(MTBFspec* GEMfactor)/(DC*Sample size*Afpowr*AF)

Duration: continuous test time

MTBFspec: Mean Time Between Failures

GEMfactor: General Exponential Model composite index

DC: Duty cycle

Sample size: number of samples

Afpower: acceleration factor

AF: acceleration factor

2.1. Duration: continuous test time, that is, the total time that a unit or several units of samples need to be tested during the life test

2.2. GEMfactor: General Exponential Model composite index, this index is generally taken as a constant, and its value standard is based on the Confidence Level (confidence level), the commonly used value is 80% confidence level is 3.22; and 90% confidence level is taken 2.3026.

2.3. DC: Duty cycle duty cycle, that is, the percentage of the running time to the total time during the switching operation of the test. (For example, 45min ON/15min OFF, the DC value is: 45min/(45min+15min)=0.75

2.4 Sample size: the number of samples, the number of samples for life test confirmed according to actual conditions

2.5 MTBFSpec: Mean time between failures, the number of MTBF time described in the experimental product specification

2.6 AFpower: Acceleration factor, that is, the ratio of the sum of ON and OFF time for 1 hour during the switching operation of the experimental product. For example, when the experimental product is selected as 25min ON/5min OFF, the Afpower value is: AFpower=60min/(25+ 5)min=2

2.7 AF: Acceleration factor, the ratio of the life of the product under use conditions (Luse) and the life under high test stress conditions (Laccelerated)