O failure reliability

[sabrina]

Hello,

A few parts are getting a sequence of different accelerated stresses ( accelerated test times are different according to the kind of stress).
eg temperature storage 1500 hours at 85°C
then thermal cycling 400 cycles -40°C+100°C
There is no failure , it is a validation plan .

How could I calculate the demonstrated reliability after these different tests?

Many thanks
Regards

[Pantelis]

First, and wrt to Reliability Demonstration Tests (under non-accelerated conditions, and with zero failures) one could approach this from a Cumulative Binomial perspective
(see refs below). Other options may include making the assumption of a constant failure rate and using an exponential distribution.

Now having briefly addressed the demonstration aspect, what you are asking is how one accomplished this under accelerated conditions. To do that one needs to quantify what is the effect of the acceleration (the higher stress) on the life of the component, or an acceleration factor (see refs below). Classical accelerated testing methods can be applied to determine this effect; however classical methods for determining an acceleration factor require that failures are observed. With no failures it is impossible to determine what the effect of the elevated stress is on life, or how much you are accelerating it.

In the absence of failure data one can assume an acceleration factor, from prior or similar designs. Then the assumed acceleration factor can be applied to the demonstration test time as determined under non-accelerated conditions. Having said that I also need to point out that even though one could do the above, it is rather dangerous to do so because your assumption of an acceleration factor (one not computed from data) will heavily influence the results…

Hope that helps…

Refs for Cumulative Binomial Test Design:
• 1455 95 535 1128977841 Pantelis First, and wrt to Reliability Demonstration Tests (under non-accelerated conditions, and with zero failures) one could approach this from a Cumulative Binomial perspective
(see refs below). Other options may include making the assumption of a constant failure rate and using an exponential distribution.

Now having briefly addressed the demonstration aspect, what you are asking is how one accomplished this under accelerated conditions. To do that one needs to quantify what is the effect of the acceleration (the higher stress) on the life of the component, or an acceleration factor (see refs below). Classical accelerated testing methods can be applied to determine this effect; however classical methods for determining an acceleration factor require that failures are observed. With no failures it is impossible to determine what the effect of the elevated stress is on life, or how much you are accelerating it.

In the absence of failure data one can assume an acceleration factor, from prior or similar designs. Then the assumed acceleration factor can be applied to the demonstration test time as determined under non-accelerated conditions. Having said that I also need to point out that even though one could do the above, it is rather dangerous to do so because your assumption of an acceleration factor (one not computed from data) will heavily influence the results…

Hope that helps…

Refs for Cumulative Binomial Test Design:
• http://www.reliasoft.com/newsletter/2q2001/cumulative_binomial.htm
• http://www.weibull.com/LifeDataWeb/test_design.htm

Refs for Accelerated Testing:
• Simple ALT example: http://www.reliasoft.com/newsletter/1q2001/accelerated.htm
• Accelerated Testing eTextbook: http://www.weibull.com/acceltestwebcontents.htm

[Harry]

It looks your product is a two-index product. The life of this product can be calculated in terms of time and cycle. Many products are two-index product, like the light ball, car battery. Whenever you start your car, there is a cycle of the battery and the battery also will operate for some time. The total life of the battery depends on these two index.

For your problem, I will discuss it in these two aspects. 1. Temperature, 2. Cycle.
1. 1461 95 535 1129565314 Harry It looks your product is a two-index product. The life of this product can be calculated in terms of time and cycle. Many products are two-index product, like the light ball, car battery. Whenever you start your car, there is a cycle of the battery and the battery also will operate for some time. The total life of the battery depends on these two index.

For your problem, I will discuss it in these two aspects. 1. Temperature, 2. Cycle.
1. Temperature test,
For this one, you should use Arrhenius model to get the AF(acceleration factor).
Step 1:
AF=exp{Ea/K*(1/Tuse ?1/Ttest)}
Tuse: temperature in usage condition.
Ttest: temperature in test condition.
Be sure the temperature is in unit of absolute temperature.
Ea: activation energy, it depends on the material you test. The range is 0.4-1.4. you can check the handbook according to your product.
K; constant, 8.6*10^-5.

Step 2: Get the MTBF under accelerated test.
MTBF1=2Total_Time/chi_squared value, please refer to www.weibull.com (http://www.weibull.com) for detail. You should pre-give a confidence level.

Step 3: Get the MTBF under usage condition.
MTBF2=AF*MTBF1.


2. Cycle test
For this one, you should use Coffin-Manson model.
Step 1:
AF=(Delta_T_test/Delta_T_use)^n
Delta_T: the range of the temperature in a cycle.
n: a factor depends on your product material. You can Google it.

Step 2: Get the MTBF under accelerated test.
MTBF1=2Total_Cycles/chi_squared value, please refer to www.weibull.com (http://www.weibull.com) for detail. You should pre-give a confidence level.

Step 3: Get the MTBF under usage condition.
MTBF2=AF*MTBF1.