Statistical Assurance without failures

In order to be able to draw conclusions with regard to the reliability of a component or assembly, tests are conducted with a limited number of test samples prior to actual series production. This is a relatively reliable method of discovering fundamental design or manufacturing faults. On the other hand, the probability of determining faults that occur randomly and at low frequency is low if a considerably higher load cannot be applied in the test. This is generally the case in vehicle tests, in contrast to the special component tests conducted on component test rigs or in the laboratory, permitting an increase in load by a factor of 2 and higher.

Nevertheless, with the following method, a conclusion can still be drawn with regard to failure characteristics under normal load conditions where no "failures" occur. The prerequisite is that the number of test samples, that is always relatively low for cost reasons, is subject to longer test periods than is necessary in normal use.

If no failures occur in the test, using formula

 

 

The reliability R of the component can be determined with a statement probability of, generally, PA = 0.80.

n is the number of tests and Lvr the relative service life ratio. This represents the test time in relation to the required service life. b is the form factor at b = 2 or b = 3.5 (see rise of Weibull straight line).

 

An example: The number of components to be tested is to be found if a double test time compared to the required service life is possible and a minimum reliability of R = 80 % is required. No parts fail in the test. This results in n = 3 for a statement probability of PA = 0.80.

 

 

 

If a defined minimum reliability is stipulated and the requirement is what statement probability is achieved, the above-specified formula is to be correspondingly rearranged to result in b = 2 and R = 80 %.

It can generally be said that, for the statement probability or for determining the reliability, it is better to test less "samples" for longer than many samples for a relatively short testing time. On the other hand, however, with less samples the conclusion concerning the component scatter is also less reliable.

In any case, Lvr must be greater than 1.

 

The template LvRb20.vxg and LvRb35.vxg can be used for this approach.

 

If a conclusion is required with regard to the reduction in service life due to higher load, tests with concrete failures will be necessary, represented in a stress-cycle (Woehler) diagram.