ZE/ZE5 C J
Statistical Design
Interpreting Reliability by Fitting Theoretical Distributions to Failure Data Early failures can be used to predict future performance by W. S. Connor, The Research Triangle Institute
D v STUDYING the failure history of a device, one can estimate and, perhaps, also learn something about how to improve reliability. In the last column, failure distributions for a component of a missile were found to be incompatible with the Poisson distribution, but to be in good agreement with the negative binomial distribution. In this col umn failures are sorted into initial failures at point A (the point of manufacture) and failures which occurred after the units were shipped from point A. It turns out that the distribution of units according to the number of initial failures is the geometric distribution, and that the distribution of units accord ing to subsequent failures is de scribed by the Poisson distribution. The latter distribution is a function of the time elapsed since manu facture, and may be extrapolated to predict the failure distribution at some future time. Finally, a more elaborate failure mechanism is discussed.
Analysis of Unsorted Failures
In this section we shall briefly review the analysis of the failure data before the failures were sorted into initial and subsequent failures. Table I shows the observed fre quencies for the month of manu facture and four months later. It shows the numbers of units which failed 0, 1, . . . times, and also the numbers predicted by the Poisson and negative binomial frequency functions. For the Poisson distri bution the probability that a unit will incur exactly i failures is given by the formula Λ—m — 11 '
ι s= 0
1 '
'
* * *
'
and for the negative binomial distri bution the probability is given by
Table I.
Distributions of Units by Total Failures
Initial failures and failures after shipment
where r is a positive integer and 0
