Geodesic
Some examples of non-monotonicities in a two-unit redundant system
Applications of Mathematics, Tome 29 (1984) no. 2, pp. 143-148

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A cold-standby redundant sytem with two identical units and one repair facility is considered. Units can be in three states: good $(I)$, degraded $(II)$, and failed $(III)$. It is supposed that only the following state-transitions of a unit are possible: $I\rightarrow II$, $II\rightarrow III$, $II\rightarrow I$, $III\rightarrow I$. The paper deals with the comparison of some initial situations of the system and with a stochastical improvement of units (stochastical increase of time of work in state $I$ and/or stochastical decrease of times of repairs of the types $II\rightarrow I$ and/or $III\rightarrow I$) and shows on examples that some surprising non-monotonicities can take place.
A cold-standby redundant sytem with two identical units and one repair facility is considered. Units can be in three states: good $(I)$, degraded $(II)$, and failed $(III)$. It is supposed that only the following state-transitions of a unit are possible: $I\rightarrow II$, $II\rightarrow III$, $II\rightarrow I$, $III\rightarrow I$. The paper deals with the comparison of some initial situations of the system and with a stochastical improvement of units (stochastical increase of time of work in state $I$ and/or stochastical decrease of times of repairs of the types $II\rightarrow I$ and/or $III\rightarrow I$) and shows on examples that some surprising non-monotonicities can take place.
DOI : 10.21136/AM.1984.104077
Classification : 60K10, 90B25
Keywords: times to system failure; cold-standby redundant system 
Lešanovský, Antonín. Some examples of non-monotonicities in a two-unit redundant system. Applications of Mathematics, Tome 29 (1984) no. 2, pp. 143-148. doi: 10.21136/AM.1984.104077
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[1] A. Lešanovský: Analysis of a two-unit standby redundant system with three states of units. Apl. mat. 27 (1982), 192-208. | MR

[2] A. Lešanovský: Characterization of the first operating period of a two-unit standby redundant system with three states of units. Apl. mat. 27 (1982), 341-351. | MR

[3] A. Lešanovský: Stochastical ordering in a two-unit standby redundant system with three states of units. To appear in the journal Mathematische Operationsforschung und Statistik - Series Optimization. | MR

[4] D. Stoyan: Qualitative Eigenschaften und Abschätzungen stochastischer Modelle. Akademie-Verlag, Berlin (1977). | MR | Zbl

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