By A. D. S. Carter (auth.)
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3! 1) in which the successive terms represent the probabilities of zero, one, two and so on, occurrences of a truly random event. Hence the zero occurrence is given by the first term. 2) 41 THE VARIATION OF RELIABILITY WITH TIME where X is some arbitrary constant and tis time. 3) For infinitely rough loading, then, the reliability will always decrease with time according to a negative exponential law in which the constant (X) is equal to the failure rate. 2. As our theme develops we shall encounter the constant failure rate depicted above on many occasions.
We shall approach the problem of repeated loads in the same way as we tackled multiple components, by first examining physically the extreme cases of infinitely smooth and infinitely rough loading. ). Dealing then with infinitely smooth loading, if the load could be given a unique value I then it is obvious that all components whose strengths were less than the load I would fail on the application of the first load, while all components whose strength is greater than I would never fail, no matter how many times the load were repeated.
The manufacturing process will also introduce variations of an entirely different nature in that absolute dimensional accuracy cannot be attained and variations within specified tolerances are a necessary feature of all manufactured products. Thus any general theory of reliability must take into account substantial variation in the strength of all items. The same applies to load, but more so; for one instinctively feels that most 18 MECHANICAL RELIABILITY 40 30 20 10 City :t. c:: ~ ..... "'c. 0 ] c.