Narrow Results

This paper applies the inspection policy in reliability theory to social integrations. As a result of shortage of labor forces due to the declining birthrate, many developed countries are increasingly accepting immigrants. However, it has been shown that the acceptance of immigrants increases anti-immigrant sentiment among host citizens and leads to large-scale riots. While social integration policies such as language education for new immigrants and support for labor market can reduce anti-immigrant sentiment, they need high costs. It is necessary to detect the anti-immigrant sentiment based on regular public polls and implement social integration. However, there is no empirical study that proposes the expected costs until the anti-immigrant sentiment is detected and discuss the optimal checking times which minimize them. We formulate three stochastic models, replacing inspection of units with check of the social structure such as people’s feelings for immigrants and failure with riot. This paper proposes extended stochastic models of social structures considering the suppression of a riot. We obtain the expected costs until a riot ends and discuss optimal checking times which minimize them analytically and numerically. These methods used in this paper could be applied to some social problems occurred in the world.

Each system goes through several intermediate states between its initial state and the failure state, which are called degradation states. In addition, knowing these intermediate states allows us the building of an effective maintenance plan for the system under consideration. In this paper, we have considered a two-component parallel system where each component is subjected to two levels of degradation. Our first objective is to identify the mathematical (probabilistic) model associated with this system and this when the hypothesis of periodic inspection of the system is retained. Then, the main idea is to build the economic model encompassing the different average costs (inspection costs, preventive maintenance costs and corrective maintenance costs) spent during a renewal cycle. The latter will allow us to determine the optimal “inspection interval” while minimizing the average global-cost spent. Finally, in order to illustrate and analyze the sensitivity of the optimal inspection policy to the various maintenance costs, numerical examples are presented.

In this paper, we propose a computing algorithm to obtain optimal checking times which minimize the expected cost rate of sequential inspection models. This algorithm is applied to two modified inspection models with finite intervals such that the unit is checked at times $T_k$ ($k=1,2,\dots ,N$) for given $N$ and given $S\equiv T_N$. The modified algorithms are proposed and optimal checking times to minimize the expected cost rates are obtained. Numerical examples of each model are given to show how to use the algorithm. This method would be applied to other sequential inspection models by its suitable modifications.