Modeling a sequentially inspected system prone to degradation and shocks

PurposeIn certain environments, the system may not fail completely, but undergoes degradation, and the system productivity might decrease. Meanwhile, at the same time, the system may be vulnerable to shocks. A single-unit system prone to degradation and shocks is proposed in this study, and emphasis is placed upon determining its availability and cost rate.Design/methodology/approachThe considered single-unit system is expected to have three states, namely, normal, degraded and failed. As the system enters the degraded state, it is said to be partially failed. The degraded state incurs higher degradation than the normal state and is more prone to shocks. Inspections are used to determine the state and failure type of the system. Inspections are predetermined to be carried out sequentially at time I, I+aI, I+aI+a2I,… where 0 < a ≤ 1, until the detection of degradation/failure. Perfect repairs are conducted instantly on spotting the partial/complete failure. Two cases have been considered of repair taking constant times and random times.FindingsExplicit results on the reliability, availability (both point and limiting availability) and long-run average cost rate (LRACR) of a sequentially inspected single-unit system prone to degradation and shocks under constant and random repair times are given. Numerical example of an oil pipeline system is taken to clarify the acquired results.Originality/valueA sequentially inspected single-unit system prone to degradation and shock is studied unlike done previously.

Calculating Cost Distributions of a Multiservice Loss System

Congestion pricing has received lots of attention in the scientific discussion. Congestion pricing means that the operator increases prices at the time of congestion and the traffic demand is expected to decrease. In a certain sense, shadow prices are an optimal way of congestion pricing: users are charged shadow prices, i.e., the expectations of future losses because of blocked connections. The shadow prices can be calculated exactly from Howard&rsquo;s equation, but this method is difficult. The paper presents simple approximations to the solution of Howard&rsquo;s equation and a way to derive more exact approximations. If users do not react by lowering their demand, they will receive higher bills to pay. Many users do not react to increased prices but would want to know how the congestion pricing mechanism affects the bills. The distribution of the price of a connection follows from knowing the shadow prices and the probability of a congestion state. There is another interesting distribution. The network produces profit to the operator, or equivalently, blocked connections produce a cost to the operator. The average cost rate can be calculated from Howard&rsquo;s equation, but the costs have some distribution. The distribution gives the risk that the actual costs exceed the average costs, and the operator should include this risk to the prices. The main result of this paper shows how to calculate the distribution of the costs in the future for congestion pricing by shadow prices and for congestion pricing with a more simple pricing scheme that produces the same average costs.

Reliability modelling and maintenance policy optimization for a repairable parallel system

This paper proposes an integrated approach for reliability modelling and maintenance scheduling of repairable parallel systems subject to hidden failures. The system consists of heterogeneous redundant subsystems whose failures are revealed only by inspections. Inspections at periodic times reveal the components state and repair actions are decided by the excursion of a basic state process describing the total number of failed components in each subsystem. Using the standard renewal arguments, the paper aims at minimizing the average cost rate by the joint determination of the optimal inspection interval, the partial repair threshold and the preventive replacement threshold. We illustrate the procedure for the case as the components' lifetimes conform to the Weibull distribution. Numerical examples are used to illustrate the proposed model and the response of the optimal solutions to the model's parameters.

Reliability modelling and maintenance policy optimization for a repairable parallel system

This paper proposes an integrated approach for reliability modelling and maintenance scheduling of repairable parallel systems subject to hidden failures. The system consists of heterogeneous redundant subsystems whose failures are revealed only by inspections. Inspections at periodic times reveal the components state and repair actions are decided by the excursion of a basic state process describing the total number of failed components in each subsystem. Using the standard renewal arguments, the paper aims at minimizing the average cost rate by the joint determination of the optimal inspection interval, the partial repair threshold and the preventive replacement threshold. We illustrate the procedure for the case as the components' lifetimes conform to the Weibull distribution. Numerical examples are used to illustrate the proposed model and the response of the optimal solutions to the model's parameters.

Availability and cost assessment of systems with dormant failure undergoing sequential inspections

PurposeThe system encountering dormant failure subject to sequential inspections is modeled and the emphasis is made on determining the availability and long-run average cost rate for the model. The derived results are then utilized to obtain the optimal inspection period minimizing the cost.Design/methodology/approachExplicitly, a system with a functional and a failed state is taken into account. Inspections are performed to reveal the dormant failures and are assumed to be carried out at time T, T + aT, T + aT+a2 T, … where 0 < a = 1 in each cycle. Perfect repairs taking random times are performed if the system is found in a failed state during any inspection.FindingsSome theorems on the point availability, limiting availability and long-run average cost rate are obtained in the study. An illustration is shown to explain the results obtained in the proposed work. The effect of inspection time on the availability and cost rate is also analyzed graphically.Originality/valueThe availability and cost rate for a system with dormant failure under a sequential inspection policy are figured out unlike previous research.

Analysis of two components parallel repairable degenerate system with vacation

<abstract><p>This article studies a parallel repairable degradation system with two similar components and a repairman who can take a single vacation. Suppose that the system consists of two components that cannot be repaired "as good as new" after failures; when the repairman has a single vacation, the fault component of system may not be repaired immediately, namely, if a component fails and the repairman is on vacation, the repair of the component will be delayed, if a component fails and the repairman is on duty, the fault component can be repaired immediately. Under these assumptions, a replacement policy $ N $ based on the failed times of component 1 is studied. The explicit expression of the system average cost rate $ C(N) $ and the optimal replacement policy $ N^{\ast} $ by minimizing the $ C(N) $ are obtained, which means the two components of the system will be replaced at the same time if the failures of component 1 reach $ N^{\ast} $. To show the advantage of a parallel system, a replacement policy $ N $ of the cold standby system consisting of the two similar components is also considered. The numerical results of both systems are given by the numerical analysis. The optimal replacement policy $ N^* $ for both systems are obtained. Finally, the comparison of numerical results shows the advantages of the parallel system.</p></abstract>

A study on an optimal replacement policy for a degenerative system under partial product process

In this paper, we study a degenerative reparable system with two types of failure states.Any system after repair can not be as good as new. A general monotone process model for adegenerative system under partial product process is used. We use a replacement policy N based on the failure number of the system and to determine an optimal replacement policy N* such that the average cost rate is minimized.

Cost of Illness Analysis and Quality of Life in Ischemic Stroke Patients In Usu Medan Hospital

Objective: aims to evaluate the COI INA-CBG BPJS patients hospitalized for ischemic stroke BPJS (n = 33) at USU Medan Hospital in February 2019-August 2019 period. Design: this study was conducted used a prospective cohort study method in patients with ischemic stroke (n = 33) in USU Hospital. Interventions: the intervened variable were the cost of patient therapy and calculating the difference in claims of INA-CBGs with the cost of patient therapy. Main outcome measures: the main measurement in this study was quality of life with European Quality of Life - 5 Dimensions Three Level (EQ5D3L). Results: the results of this study indicate the total average cost of ischemic stroke inpatient therapy at the In patient Installation of USU Hospital in Medan obtained Rp 2,284,854 The average cost / rate incurred by the Hospital for ischemic stroke patients (n = 33) is still below the INA-CBGs claim rate. There was a relationship between the quality of life of ischemic stroke patients with diagnosis and comorbidities of patients (p = 0.004). The average quality of life (QoL) of ischemic stroke patients was obtained 0.7324 ± 0.2118. Conclusion: it could be concluded that the quality of life of ischemic stroke patients is classified as good 32 patients (96.96%).

A new δ-shock model for systems subject to multiple failure types and its optimal order-replacement policy

In this article, a generalized δ-shock model with multi-failure thresholds is studied. For the new model, the system fails depending on the interval times between two consecutive shocks which arrive according to a Poisson process. The shorter interval times may cause more serious failures and thus result in longer down times and more costs for repair. Assuming that the repair is imperfect, an order-replacement policy N is adopted. Explicitly, the spare system for replacement is ordered at the end of ( N – 1)th repair and the aging system is replaced at the Nth failure or at an unrepairable failure, whichever occurs first. In addition, the system must meet the requirement of availability, that is, the long-run average operating time per unit time should not be lower than a certain level. The average cost rate C( N) and the stationary availability A( N) are derived analytically. Some convergence properties of A( N) and C( N) are also investigated. The optimal order-replacement policy N* can be obtained numerically with the constraint of availability. Finally, an illustrative example is given and some sensitivity analyses are conducted to demonstrate the proposed shock model.

A bivariate replacement policy for an imperfect repair system based on geometric processes

A repair replacement model for a deteriorating system with delayed repair is studied, in which the successive working times after repair and the consecutive repair times of the system are described by geometric processes. The instantaneous availability is studied in the case of general distributions for the working time, repair time and delayed repair time. A bivariate replacement policy is considered, that is, the system is replaced whenever the working age of the system reaches T or at the first hitting time of the working time after repair with respect to the working time threshold τ, whichever occurs first. The explicit expression of the long-run average cost rate under the replacement policies is derived. The corresponding optimal replacement policy can be determined numerically, and numerical examples are presented to demonstrate the application of the developed model and approach. It is shown that the optimal solution and optimal value are sensitive to the tiny change in the ratios of the Geometric processes and the expectation of the delayed repair time.