“…This topic has posed many interesting problems to which many researchers have devoted themselves in the past decades; see, for example, Boland, El-Neweihi, and Proschan (1992); Shaked and Shanthikumar (1992); Singh and Misra (1994); Singh and Singh (1997); Mi (1998); Ramirez-Marquez and Coit (2004) ;Yalaoui, Chu, and Châtelet (2005); da Costa Bueno (2005); Valdés and Zequeira (2006); da Costa Bueno and do Carmo (2007); Hu and Wang (2009) ;Valdés, Arango, and Zequeira (2010) ;Brito, Zequeira, and Valdès (2011);Misra, Dhariyal, and Gupta (2009) ;Misra, Misra, and Dhariyal (2011a,b); Zhao, Chan, and Ng (2012) ;Zhao, Chan, Li, and Ng (2013a,b); Laniado and Lillo (2014) and the references therein. In general, there are two types of redundancies called active redundancy and standby redundancy commonly used in reliability engineering and system security.…”