Chapter 5: Block Replacement

Overview

If a system consists of a block or group of units, their ages are not observed and only their failures are known, all units may be replaced periodically independently of their ages in use. The policy is called block replacement and is commonly used with complex electronic systems and many electrical parts. Such block replacement was studied and compared with other replacements in ^[1], ^[2]. Furthermore, the n-stage block replacement was proposed in ^[3], ^[4]. The adjustment costs, which are increasing with the age of a unit, were introduced in ^[5]. More general replacement policies were considered and summarized in ^{[6] [7] [8] [9] [10]}. The block replacement of a two-unit system with failure dependence was considered in ^[11]. The optimum problem of provisioning spare parts for block replacement was discussed in ^[12] as an example of railways. The question, "Which is better, age or block replacement?", was answered in ^[13].

This chapter summarizes the block replacement from the book ^[1] based mainly on our original work: In Sections 5.1 and 5.2, we consider two periodic replacement policies with planned time T in which failed units are always replaced at each failure and a failed unit remains failed until time T. We obtain the expected cost rates for each policy and analytically discuss optimum replacement times that minimize them ^[14]. In Section 5.3, we propose the combined model of block replacement and no replacement...