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31 October 1986 Some Statistical Aspects Of Tolerancing
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The effects of manufacturing errors are numerous and varied. They range from simple phenomena such as changes in focal length, spherical aberration etc to the complex functions, RMS wave error and MTF drop. One or more of these will be used as a criterion to judge the 'success' or 'failure' of a lens. The manufacturing errors, a., will have some probability distribution fi(ai), which are determined by the tolerance anA workshop practice. These will, in turn, determine the distribution, f (y), of the effect, y, of interest. Given fy(y) the designer can then predict the expgcted failure rate. Firstly we show how to predict the lower moments of f (y): mean, variance, skewness and kurtosis for linear effects of the errors: mean and variance for the non linear RMS wave error. Then we discuss approximations to the functional form of f (y), which we can specify by these moments. fy(y) only tend towards gaussian form for linear process. The RMS wave error is better modellgd by a chi-square distribution. Comparisons with Monte Carolo simulations are shown. Small production runs will cause the expected failure rate to fluctuate. Simple equations are given which predict this scatter. Finally the effects of using compensators are predicted and compared with simulations.
© (1986) COPYRIGHT Society of Photo-Optical Instrumentation Engineers (SPIE). Downloading of the abstract is permitted for personal use only.
Geoff Adams "Some Statistical Aspects Of Tolerancing", Proc. SPIE 0655, Optical System Design, Analysis, Production for Advanced Technology Systems, (31 October 1986);

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