Reliability In Static Failure

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The principal objectives of design for reliability are to reduce infant mortality and extend useful life. To accomplish these objectives, we turn to the notion of safety factor in stress.

The accepted definition of safety factor for static failure is as followsThe traditional method of guarding against stress related failure is to specify a safety factor that is significantly greater than one.

This definition assumes the values of stress and strength are known exactly and the difference between them provides a margin of safety for overloading and reduction of strength over time (due to corrosion, cracking, etc.).

If the safety factor is high enough, it should guard against failure even though there may be uncertainty in loading, usage and material properties. However, the higher the stress safety factor, the heavier, bulkier and more expensive the part. Obviously designing to avoid stress-related failure involves trade-offs.

There is uncertainty in strength measurements and stress calculations, so let us change our outlook on stress and strength and consider them to be random ...
... variables that follow normal distributions with mean values and variances.

This means that the stress of half of the parts will be higher than the calculated mean value and the strength of half of the parts will be lower than the published mean value. Conceivably a large value of stress could be found in a part with a low value of strength.

This would produce a failure or, at least, a much smaller safety factor than was calculated. If there is a sufficiently large safety factor, the stress and strength distributions might appear as Fig. 5. 2(a). If the safety factor is reduced a little, the distributions might appear as in Fig. 5. 2(b). If the safety factor is reduced a lot, the distributions might appear as in Fig. 5. 2(c).

From the three previous graphs, it is fairly obvious that when the probability distributions of stress and strength are taken into account the concept of safety factor must be revised to account for normal random variation in stress and strength. Let us refer to traditional safety factors as mean safety factors since they are computed with mean or expected values.

Any overlap between the probability distributions of stress and strength represents a probability of static failure. To reduce the probability of failure, we could redefine the concept of safety factor to include the variation of stress and strength, which are assumed to be normally distributed. By looking at the amount of overlap between the two distributions, assuming the same level of reliability for stress and strength, we get the following revised safety factor equation.

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