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Comparing the importance of system components by some structural characteristics

Various results concerning importance measures and rankings of system components are presented. The vectors (of component states) which appear useful in studying various component importance measures are decomposed. In particular, a new method to compute Birnbaum importance measures of components is introduced. For some systems and components the Vesely-Fussell importance measure might not be suitable; thus a new importance measure is proposed. By using the notion of component criticality introduced by Boland, Proschan, Tong, several results are obtained which can be used to compare the relative importance of components when their reliabilities are unknown and/or when the calculation involved in assessing their importance measures become prohibitively extensive.