有序統計量的一些信賴度性質

Abstract

本論文首先推廣 Inperfect repair 和 Age-dependent minimal repair 的結果.探討在 DMRL,IMRL 中,當兩個有序統計量失敗率比值大於 1 的情 形.再由此證明當k小於(n+3)/2,假如X(k:n)是DMRL,則X(k+1:n+2)也是 DMRL.證明假如X(k:n)是IMRL,則X(k-1:n),X(k:n+1)和X(k-1:n-1)也是 IMRL.證明當k小於(n+3)/2,假如X(k:n)是IMRL,則X(k-1:n-2)也是IMRL. In this paper we develop theory helpful in the study of relia- bility properties of order statistics. We show two theorems with the assumption of F being absolutely continuous with pdf f. First, if p>1 and p is a constant, then F is DMRL(IMRL) implies that Fp is DMRL(IMRL), where F has failure rate r(t) and Fp has failure rate rp(t)=p*r(t). Second, if p(x)>1 and p( x) is increasing(decreasing), then F is DMRL(IMRL) implies that Fp is DMRL(IMRL), where F has failure rate r(t) and Fp has failure rate rp(t)=p(t)*r(t). We also use above results to verify that if X(k:n) is IMRL, so are X(k-1:n), X(k:n+1) and X( k-1:n-1). And if k<=(n+3)/2, X(k:n) is IMRL implies that X(k-1: n-2) is IMRL. And if k<=(n+3)/2, X(k:n) is DMRL implies that X( k+1:n+2) is DMRL.