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System Reliability: Computational Algebra Methods

Computer algebra systems are useful in calculating system reliability. We use several diverse examples to illustrate how a computer algebra system can be helpful in determining system reliability. The examples presented here are (a) analyzing a k-out-of-n system; (b) determining the mean time to failure of a parallel system with symbolic parameters; (c) determining the conditional survivor function for a system with a piecewise survival distribution; (d) determining the probability of mission success for a unit and two cold standby units; (e) determining a lower confidence bound on the system reliability from binary failure data collected on each of the independent components in a coherent system via bootstrapping; and (f) determining the exact distribution of a popular goodness-of-fit test statistic. 
 
 
Keywords: 
 
bootstrapping; 
coherent system; 
computer algebra system; 
exponential distribution; 
lifetime distributions; 
survival analysis; 
Weibull distribution