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Chapter
Introduction
It has been wellknown that Probability arose in the letter from Pascal to Fermat around 1654 on such questions as the fair division of the stakes in the game of change [1, p. 239].
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Chapter
Random Age Replacement Model
We consider the age replacement model in which the unit is replaced at time T or at failure, whichever occurs. The following five policies based on the age replacement are taken up: (1) Random replacement, (2) ...
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Chapter
Periodic Replacement Models
We consider the replacement model in which the unit is replaced at periodic times JT ( \(J=1,2,\dots \) ...
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Chapter
Which is Better for Standby or Parallel Systems
High system reliability can be achieved by redundancy and maintenance. It was shown by graph that the system can operate for a specified mean time by either the preventive replacement or increasing the number ...
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Chapter
Which is Better Problems in Backup Models
The data in a computer system are frequently updated by adding or deleting them, and are stored in a computer database system. However, data files in the database are often broken by several errors due to nois...
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Chapter
Replacement Model with Minimal Repair
We consider the replacement model in which the unit undergoes minimal repair at failures, and is replaced at a planned time T, at a working time N or at a failure number K.
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Chapter
Extended Replacement Models
The following three extended replacement models are considered: We take up age replacement with two failure modes such as major minor failures in Sect. 5.1.
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Chapter
Which is Better Problems in Shock and Damage Models
We consider an operating unit for the total damage due to random shocks which should operate for an infinite time span [1–5].
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Chapter
Which is Better Problems in Checkpoint Models
It is of great importance to develop the design of computer systems high reliability as human technologies have been rapidly growing up. Most systems consist of computing units which need high reliability an...