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The purpose of this paper is to study the performance metrics of redundant repairable machining system which is applicable in various systems like computer and communication system, manufacturing and production system, etc.

In the present investigation, the authors develop Markov model for the system consisting of identical active operating machines which are prone to breakdown. The operating machines are under the care of one permanent repair facility that provides time-sharing basis repair services. The maintenance is facilitated with the provision of standby machines of mixed type and permanent as well as additional repair facility. From the economic point of view, F-policy and N-policy to control the service and arrival of failed machines effectively are included.

For the performance analysis of the system in long run, the authors compute steady-state probabilities using product-type solution method recursively. Sensitivity analysis is performed numerically for various parameters by developing code in MATLAB.

The performance prediction done may be helpful for the system designers and decision makers for the improvement of the existing machining systems in various industries.

Markovian model for the performance prediction of fault tolerant multi-identical operating and standby machines redundant system is developed in generic frameworks by incorporating many noble features which were not all taken together by other researchers working on the same lines. The key concepts incorporated for the modeling of the concerned system is: F-policy, N-policy, time-sharing, and sensitivity analysis of availability and cost function.

This study aims to explore the government’s subsidy preference and pricing decisions of a manufacturer who produces traditional and green product simultaneously under different government subsidy policies.

The authors establish a model consisting of a government, a set of heterogeneous consumers and a manufacturer. Three government subsidy policies are investigated without government subsidy (NS), government subsidy to consumer (CS) and government subsidy to the manufacturer (MS).

The results show that the government subsidy can increase both the green product’s demand and the manufacturer’s profit. The subsidy level and government’s utility under the CS policy are equal to those under the MS policy. Furthermore, if the government’s subsidy level is exogenous, there exists a Pareto improvement region when social welfare for unit greenness level is high. That is, if the government’s subsidy level under the CS policy is higher than that under the MS policy, both government and manufacturer prefer the CS policy; otherwise, they prefer the MS policy.

This paper considers the market where there is a monopoly green manufacturer and a government that only provides subsidy policy. In fact, competition from traditional manufacturers and carbon taxes are also worth exploring in future research.

This study provides some suggestions for government subsidy and provides guidance for the manufacturer’s pricing decisions under different government subsidy policies.

This paper is the first to compare government subsidy to consumer with a government subsidy to the manufacturer and investigate the pricing decisions of a manufacturer who produces traditional and green product simultaneously by considering an endogenous subsidy level of government.

The purpose of this paper is to investigate preventive‐repair warranty policies for repairable deteriorating systems using Zhang's geometric process repair model.

The paper aims to establish the importance of preventive repair during warranty. Three cost models have been developed using the average cost rate for the system as the objective function, employing N‐policy for two models therein.

The models have practical applications in warranty cost analysis, as product warranty is an important factor in designing an optimal maintenance policy.

The paper observes that product warranty has not been considered in the study of maintenance policies for repairable deteriorating systems using monotone processes. The numerical example given illustrates that a preventive repair during warranty with N‐policy is preferable compared with a non‐warranted product or a warranted product without preventive repair.

The purpose of this paper is to generalize Yeh and Zhang's 2004 random threshold failure model for deteriorating systems.

An N‐policy was adopted by which the system was replaced after the Nth failure.

The model was found to have practical applications in warranty cost analysis.

By identifying the instance of a shock as the failure of the system and the threshold times as the warranty period offered and changing the definition of lethal shock (system failure in this case) as the occurrence of a shock within a threshold period in our generalized model, one can study the renewing warranty cost analysis.

Using a two bank, two-period game-theoretic model, this chapter shows that contingent purchase and assumption policy under which the choice of acquirer for a failed bank is contingent on the surviving banks’ risk-taking behavior is generally most effective in reducing moral hazard problems, particularly for countries with low levels of competition and high regulatory barriers. Moreover, we find that to minimize the probability of future bank failures, the choice of acquiring bank should be based not only on the short-term goal of resolving the insolvencies of financial institutions, but also on the long-term effects of ex ante risk-taking incentives.

Technological advancements and growing complexity of many real-time systems, namely, communication, transportation, defense systems, etc., necessitate the importance to adopt a well-planned repair process such as phase type quasi-renewal process contributing to an improved system performance. Further, in an attempt to boost the role of maintenance as a financial benefactor, repairman’s multiple vacation policy is incorporated. Also, the significance of the degree of repair is illustrated while indicating the suitability of the matrix-analytic approach via the phase type quasi-renewal operating/repair times in reliability. The paper aims to discuss these issues.

The optimal replacement policy is obtained by employing the matrix-analytic method and minimum average cost rate.

The considered models make a significant contribution towards establishing that the matrix-analytic method, using the phase type quasi-renewal process, aids in reducing the computations and also fills the gap in the literature in the study of deteriorating systems. Availability and rate of occurrence of failures are evaluated in transient and steady-state regime.

This model differs from the existing models, in that, a repairman’s multiple vacation, delayed repair time and representation of the failure occurrence by a mixed Poisson process have been incorporated into the analysis. Also, time-dependent case and N-policy have been adopted to explore the optimality issues using phase type quasi-renewal process analytically. The numerical illustrations warrant that the maintenance policy proposed in this paper produces a considerably lower cost.

The paper considers a stochastic inventory control system consisting of a central store (CS) and several lower stores (LS). The demand at each of the lower stores forms a recurrent stochastic flow. To replenish the stock the LS's file orders of fixed quantity with the CS following a two‐level control policy. In its turn, the CS also orders replenishments, and all the lots are delivered to it with some fixed delay. The orders from an LS to the CS are fulfilled in a delivery time if the lot required is in stock at the CS, otherwise the CS must itself wait for replenishment before sending the lot to the LS. The main result obtained is an approximate formula for the probability of the smooth operation of such a system.

This chapter extends Panyagometh and Roberts (2008) by taking into account differences in costs of closure among countries and the effects of subordinated debt on moral hazard problems. Our results show that a mandatory subordinated debt policy (MSDP) can be used with contingent purchase and assumption policy to further reduce probability of future bank failure if the high level of uninsured debt can improve the effectiveness of monitoring. While a MSDP might be appropriate for some developed countries with effective informational and supervisory environments and developed financial markets, such as the U.S., extending a MSDP into developing countries is questionable.