Stochastic Properties of a Sequence of Interfailure Times Under Minimal Repair and Under Revival

Closure and Monotonicity Properties of Nonhomogeneous Poisson Processes and Record Values

“…In the same section, we give a physical argument which helps to understand why record values arise in the context of successive repairs of an item in which, upon each failure, the item is instanta-neously restored to its condition immediately prior to failure. This scheme will be called "minimal repair"; see Ascher [1], who refers to minimal repair as the "bad-as-old" (BAO) model, and Balaban and Singpurwalla [3] for some practical examples of minimal repair actions. Baxter [6] employed the relevation transform of Krakowski [12] to study the minimal repair process (although he did not use the latter expression).…”

Cost evaluation for an imperfect-repair model with random repair time

“…0, where r(t) is the failure rate function without any failure. Such a model has been discussed by many authors, including Blumenthal et al (1976), Balaban and Singpurwalla (1984), Block et al (1985), Sheu and Griffith (1992) and Lim et al (1998). Most of the system failures have severe negative economic consequences, not only because of the immediate expenses incurred by the necessary repairs or by the component replacements following each failure but also, more importantly, because of many other negative effects suffered following the system failure, such as late delivery of products and the loss of credibility for the product.…”

Multivariate age‐dependent imperfect repair

“…However, it is sometimes more realistic to assume that the life distri bution of a repaired item is different from the life distribution of a new item; e.g., it may be stochastically less. It has been assumed by some authors (e.g., Blumenthal, Greenwood, and Herbach [4], Brown and Proschan [5], Balaban and Singpurwalla [1], and Block, Borges, and Savits [3]) that a failed item, on repair, may return to a "good as old" state (imperfect repair). Thus, if the original life distribution of the item when it was new is F, then the item upon repair wilj^ have survival function F, where t is its age at failure and F,(x) = F(t + x)/F(t).…”