How to calculate the mtbf of linux system

What is MTBF and how to calculate it?

MTBF index and calculation method

1) general general unit calculation

In a unit time (usually in years), the ratio of the total number of product failures to the total number of products in operation is called "failure rate", which is often expressed by λ. For example, there are 100 devices running on the Internet, and there are two failures in one year, so the failure rate of the devices is 0.02 times/year. When the life of a product obeys exponential distribution, the reciprocal of its failure rate is called mean time between failures (MTBF). Namely:

MTBF= 1/λ

For example, the MTBF time of a YY product is as high as 65438+600,000 hours. 160000 hours is about 18 years, which does not mean that every YY product can work for 18 years without failure. According to MTBF= 1/λ, λ =1/mtbf =18 years (assuming that the life of YY products obeys exponential distribution), that is, the annual average failure rate of YY products is about 5.5%, and within one year, the average failure rate is10000.

The reliability index of the whole machine is expressed by the mean time between failures:

MTBF=(T 1+T2+…Tn)/ rn

Where: mtbf-the mean time between failures of the whole machine, h;

Ti—— cumulative working time of the I-th machine under test, h;

Rn-the total number of failures of the machine under test during the test.

2) Calculate the total value through a single module in communication.

MTBF- mean time between failure refers to the time between two failures, which is a statistical average. The MTBF value is usually determined in two ways:

1) theoretical statistical method: according to the actual situation of devices, components and constraints, accumulate and average.

2) Empirical statistics method: according to the damage records of factories or laboratories, accumulate average data.

MTBF statistics of 1+0 stand-alone system

According to the composition block diagram of 1+0 stand-alone system, the total MTBF statistical value is given by the following formula:

1/MTBF total = 1/MTBF transmitting high frequency+1/MTBF receiving high frequency+1/MTBF modulation+1/MTBF baseband+1/MTBF power supply.

3) The difference of MTBF caused by series-parallel elements in communication network λ= 1/MTBF (h)

If two components work in series and one of them fails, the whole function will fail.

λ total =λ 1+λ2

Or MTBF total = 1/(λ 1+λ2)

For parallel or redundant structures, although one component fails, the functional integrity remains unchanged (100%);

1/λtotal =( 1/λ 1)+( 1/λ2)+( 1/(λ 1+λ2))

Or MTBF total = (λ 21+λ 65438+λ 2+λ 22)/(λ 265438+λ 2+λ 65438+λ 22)

4) MTBF calculation of general products

Mean time between failures (MTTF)

Assuming that N0 unrepairable products are tested under the same conditions, the total failure time is T 1, T2, ... TN0. Mean time before failure (MTTF) is:

MTTF = (T 1+T2+…Tn)/N0

Since the failure time is the life of unrepairable products, MTTF is also the average life.

When the life of the product obeys exponential distribution,

MTTF= 1/λ

Mean time between failure (MTBF)

A repairable product has N0 failures in use, and it is put into use again after each failure repair. It is measured that its working duration is T 1, T2, ... TN0, and its mean time between failures MTBF is:

MTBF=T/N0

Where t is the total working time of the product.

For a completely repaired product, the state after repair is the same as that of a new product, so the failure of a product N0 times is equivalent to the failure of N0 new products for the first time. Therefore:

MTBF=MTTF

When the life of the product obeys exponential distribution and the failure rate of the product is constant λ, then MTBF=MTTF= 1/λ.

Mean time to repair (MTTR)

The observed value is the ratio of the sum of repair time t to repair times: MTTR = (t1+T2+… TN)/n.

Where: Ti-the time of the I-th repair; N- maintenance times.

5) Simple calculation (according to temperature coefficient)

MTBF = total test time * acceleration factor/coefficient (refer to table)

Total test time = (sample size) * (test days) * (power-on time/day)

Acceleration coefficient = e (e/k) (1/TN-1/ta)

Ta = indoor combustion test temperature

Tn = normal temperature

coefficient

confidence

Number of fault levels (n)

0 1 2 3 4 5 6 7 8 9

manganese

(90%) 2.30 3.89 5.32 6.68 7.99 9.27 10.53 1 1.77 12.99 14.20

Acceleration factor = e (e/k) (1/TN-1/ta) This acceleration model is Arrhenius acceleration model.