# Support  Calculation method of MTTF and L10：

1. According to fan datasheet , find the corresponding life expectancy base on sleeve or ball bearing.
For example：SPEC： 5-1-13 Life Expectancy(L10) 75,000 Hours At40℃(Bearing)

2. Calculation method: According to Webiull.
L10：Life expectancy of 90% reliability
MTTF: Mean Time To Failures
MTTF=7xL10
Ts: Test temperature
Tu: Pre-conversted temperature
AF:Acceleration factor
AF=1.5Λ ((Ts-Tu)/10)（When the temperature increases by 10 ℃, the life decreases by 1.5 times）

T1: Required test time with zero failure
n：Quantity of Test Devices
Βr;c: The confidence Level is  base on GEM (90%) , Zero failure value =2.3026

Generalized Exponential Model Table
Confidence Level(%) Number of failure
0 1 2 3 4 5 6 7 8 9 10
90 2.3026 3.8897 5.3223 6.6808 7.9936 9.2747 10.5321 11.7709 12.9947 14.286 15.4066
T1= 1.036 × MTTF × [ ( Βr;c ) / n ] Λ 0.91 ÷ AF

T2: Actual test time with zero failure.
(T2 Actual test time > T1 expected required test time , it means fan life is ok).

Temperature conversion formula：

T3：Expected temperature L：Expected life expectancy Tu：Pre-converted temperature  L1：Pre-converted temperature corresponding life.
L1=L/1.5Λ ((Tu-T3)/10)
For example: ( Expected life expectancy :75000H at 40℃, conversion life at 60℃).
L1=75000/1.5Λ ((60-40)/10)
=75000/2.25
=33333H

3. For example：
3-1. According to the formula to calculated the temperature of 40℃ environment, MTTF Life expectancy.
MTTF=7XL10=7X75000=525000 hours

3-2. According to AF formula to calculated the temperature of 75℃, converted  AF value.
at 40℃

AF=1.5 Λ ((Ts-Tu)/10)= 1.5 Λ ((75-40)/10)= 1.5 =4.13

3-3. According to the formula, calculated how long it takes to test(T1) at 75℃ to meet the fan used in an environment of 40℃, L10 can reach the expected life).
T1= 1.036 × MTTF × [ ( Βr;c ) / n ] Λ 0.91 ÷ AF
=1.036×525000×（2.3026/100） ÷4.13
=4255 hours

3-4. Under the temperature of 75℃, the actual test time( T2) , the conversion temperature is 40℃, MTTF and L10 time.
For example: 75℃ actual test time – 4272hours
MTTF=T2/(1.036x [ ( Βr;c ) / n ] Λ 0.91 ÷ AF)
=4272/（1.036 x（2.3026/100） ÷4.13）
=527196hours
L10=MTTF/7=527196/7=75314hours  