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The problems of accelerated testing on durability are formulated and the basic definitions are given. The concept of so-called acceleration function is determined. In the case of linear model, integral function of distribution of time of failure-free operation of a device is determined on the basis of this concept. The criterions of linearity of acceleration function are formulated. The technique of accelerated testing is developed on the basis of correlation that conveys the generalized principle of Palmgren-Miner. This technique guarantees computation of reliability, when load increases permanently or stepwise.

The problem of forced testing on reliability, i.e. the problem of construction of probability models for forced testing is formulated as an interposition of a distribution function

In the particular case of forced testing, we are concerned in finding certain quantitative properties of the distribution

The problem of forced testing is reduced to definition of so-called “acceleration function”

The correlation of quantitative properties (moments) and the corresponding distributions

where

In the case of linear model, when

When acceleration function is linear, it is enough to offer a technique of deterministic, forced testing that gives estimation

It is more important that on the basis of acceleration function g, mathematical notation of so-called physical principle of reliability [

where

It is quite interesting to determine the criterions of linearity of acceleration function, because the problem of forced testing is essentially simplified for linear model. These criterions are formulated in the following form [

Let us assume that one of the two sets are tested with load X during interval

The physical principle of reliability in the form of (1) is essentially used for proving the above-mentioned theorem. Therefore, this theorem is realized only in those conditions, when hypothesis of N.M. Sediakin is correct.

We strictly prove [

A.G. Palmgren [

If we change the test a little bit and test the set of devices under load Y not during fixed time interval

This equation represents the basic correlation for definitive, forced testing with technique of so-called “destruction” [

That is spent by device in random time

This statement is true at any rule of distribution of random magnitude

In the model of stepwise load that is shown in

where index n, as well as

Average time of failure-free operation of device in normal conditions (under nominal load) is denoted with symbol

If we assume that in every described mode, time of failure-free operation of element has exponential distribution, then the following equations are true:

If we use property of additivity of resource of reliability and Equation (2) for the described two examples, then:

These equations represent mathematical notations of correlation of linear summation of failures in discrete and permanent modes.

We can describe considerable amount of reliability models for stepwise and permanent load, if we use mathematical notations of correlations of linear summation of failures that are based on the property of reliability resource.

For example, the following model is known:

where m is a certain constant. Many researchers have got the same result. For example, for ball bearings

For stepwise load, this model gives:

If load is permanent and load H varies in time x with constant “rate” v on the basis of linear rule

According to the work [

where E and m are certain constants.

For stepwise model and above-mentioned model, we get:

When load increases permanently with constant “rate” ν and failure is observed at the random moment

It is easy to see that the Equation (4) with assumption (3) and linear increasing load with initial value

Hence

On the basis of previous equation we conclude that in the case of described conditions, random value

The specifications of form and scale of this law is described with the following equations correspondingly:

These conclusions are based on a fact that if random value of time of failure-free operation of certain device is distributed according to Weibul’s law, then intensity of failure of this device is described with the equation

The result is important, because value m can be determined with the same statistical data that is given from the experiment with permanent load of the basic set of devices. It is sufficient to create the function of distribution of random value

The problems of accelerated testing on durability are formulated newly, the basic definitions are given and the concept of so-called acceleration function is introduced. In the case of linear model, integral function of distribution of time of failure-free operation of a device is determined on the basis of this concept. The criterions of linearity of acceleration function are formulated and the techniques of accelerated testing are developed on the basis of correlation that generalizes the principle of Palmgren-Miner. This technique guarantees computation of reliability, when load increases permanently or stepwise.

Described method is easily generalized to the case of chemical engineering kinetics and chemical rate phenomenon.

We would like to express our very great appreciation to Dr. David Gorgidze for his valuable and constructive suggestions during the planning and development of this research work. His willingness to give his time so generously has been very much appreciated.

We would also like to thank the staff of the Strength of materials Laboratory at the Georgian Technical University for enabling us to visit their offices to observe their daily operations.

Archil Prangishvili,Oleg Namicheishvili, (2016) Accelerated Testing of Devices on Durability and Fatigue Failure. World Journal of Engineering and Technology,04,200-205. doi: 10.4236/wjet.2016.42019