Practical guidance for statistical analysis of operational event data Page: 78 of 83
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APPENDIX A
SAS PROGRAMS
This appendix gives SAS programs for finding the moments of various combinations of failures,
in terms of the moments of the more fundamental failures, and programs relating the moments to the
parameters of a beta distribution. All the programs are macros, and are intended to be invoked from
within a SAS data step.
%macro abtomom(a,b,mu,var);
* given parameters of beta(a,b) distribution, finds mean and
variance;
delta = &a + &b;
&mu = &a / delta;
&var = &mu * (1 - &mu) / (delta+1) ;
%mend abtomom;
%macro momtoab(mu,var,a,b);
* given mean and variance, finds corresponding parameters of
beta(a,b) distr.;
delta = ( ( &mu * (1 - &mu )) / &var ) - 1 ;
&a = delta * μ
&b = delta - &a ;
%mend momtoab;
%macro andgate(mul,varl,mu2,var2,mu,var) ;
* finds moments of P(first event and second event);
&mu = &mul * &mu2 ;
&var = &varl*&var2 + (&mul**2)*&var2 + (&mu2**2)*&varl ;
%mend prod;
%macro notgate(mul, var, mu2, var2);
* given moments of P(A), finds moments of P(not A) ;
&mu2 = 1 - &mul;
&var2 = &varl ;
%mend notgate;
%macro orgate(mul,varl,mu2,var2 ,mu,var) ;
* finds moments of P(first event or second event);
%notgate(&mul, &varl,munotl,varnotl);
%notgate(&mu2,&var2,munot2,varnot2);
%prod (munotl, varnotl, munot2 ,varnot2 ,munot, varnot)
%notgate (munot, varnot, &mu, &var);
%mend sum;
%macro abtopow (k, a, b,muout, varout) ;
* finds moments of p**k, where p has beta(a,b) distribution;
* muk=E(P**k), mu2k=E(P**2k) ;
muk =1 ;
mu2k=1 ;A-3
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Atwood, C. L. Practical guidance for statistical analysis of operational event data, report, October 1, 1995; Idaho Falls, Idaho. (https://digital.library.unt.edu/ark:/67531/metadc620674/m1/78/: accessed April 24, 2024), University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu; crediting UNT Libraries Government Documents Department.