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Engineering Design Handbook - Development Guide for Reliability - Part VI; Mathematical Appendix and Glossary

The common tractable hD'S (probability 
distributions) have no magic power to 
transform sample data into absolute knowl- 
edge, but many people act as if they did. 
Some important cautions are listed: 
(l) Avoid assuming that the selected PFD 
represents the physical data outside the range 
of the sample data, merely because the sample 
data might reasonably (statistically) have 
come from it. Gross extrapolation beyond the 
range of the data is very misleading. 
(2) DO not use point estimates Of the 
parameters of the HD without calculating 
some measure of their uncertainty such as 
s-confidence• limits or a standard deviation. 
(3) Avoid fitting sample data too closely 
by brute force, possibly by using a multi- 
parameter PFD for each of several segments of 
the random variable. If one wishes a very 
close fit, there are several old fashioned 
methods such as power series which do not 
clothe brute force in a comely cloak. In 
samples Of less than 10 or so, there can be 
tremendous scatter in the shape of a sample 
pdf, all from the same PFD. 
(4) Avoid fitting a PFD to the data merely 
because it can be done. 
(5) Avoid extensive calculations that select 
the farally of PFD's which gives the best fit (in

some sense) to the sample data. If that is the 
only reason for choosing a family ofPrD's, it 
is not a good enough reason. It is especially 
bad practice when the desired results depend 
heavily on the shape of the PFD outside the 
region of the data. 
The reason for all the cautions to the 
amateur analyst (and even some professional 
analysts) is not that he will violate some 
purist theory, but that he will outsmart 
himself. After having outsmarted and fooled 
himself, he will proceed to mislead others. 
One of the main functions of statistics in 
reliability engineering is to tell the engineer 
what he does NOT know from the data. 
The main purpose of fitting a PFD to the 
data is for a summary. Once the data are 
presumed to be a random sample from a HD, 
there is no need to save the data.