The $$\delta $$ -shock model is one of the basic shock models which has a wide range applications in reliability, finance and related fields. In existing literature, it assumed that recovery time system from damage induced by constant as well shocks magnitude. However, technical systems gradually deteriorate with time, takes more to recover this damage, whereas larger magnitude also results sam...

Envelope methodology is succinctly pitched as a class of procedures for increasing efficiency in multivariate analyses without altering traditional objectives [5, first sentence page 1]. This description comes with the additional caveat that gains obtained by envelope are mitigated model selection volatility to an unknown degree. Recent strides account have been made on two fronts: 1) developme...