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Reliability and Sensitivity Analysis of an Insured System with Conditional Warranty Duration Lengthier than Insurance Duration
Abstract
The terms reliability, warranty and insurance are interwoven in some ways. The warranty of system and insurance coverage offered by the manufacturer or third party reflects its potential reliability. In certain situations, the insurance may expire before the warranty time. To address this issue, the reliability and sensitivity analysis of a single-unit insured system has been carried out. The system may functions in warranty period with or without insurance cover whereas no insurance cover is given during nonwarranty period. If faults are covered under warranty or the insurance terms, the manufacturer or insurance company is liable to pay all the repair/replacement costs; otherwise, the user must pay the entire cost. The reliability metrics of the system and factors impacting system profitability are derived using Markov and regenerative processes. Profit equations and sensitivity functions are established for all stakeholders. The sensitivity function for system availability is also derived for all the possible considered periods. Exponential distribution is used to illustrate the developed model numerically.
... Markovian processes are employed which are well-suited for analyzing systems with probabilistic state transitions that adhere to the memoryless property, where future states are influenced solely by the current state. The effectiveness of the model based on the Markovian process has been proven in various reliability applications [19], making them a preferred tool for systems with state-based transitions, the analysis provides a detailed examination of the system's stochastic behavior over time. Key reliability metrics, including system availability are obtained to evaluate the system's performance, utilizing real transformer data on failures and repairs. ...
This paper presents a multi-source preventive maintenance (MPM) based precision sensitivity optimization method for parallel robotic systems. Taking a parallel mechanism as an example, the input error can be divided into finite mutually independent uncertain error sources, and the probabilistic error model is established by the Monte Carlo stochastic method. Considering that several times of maintenance can lead to an increase of the accuracy degradation factor, a generalized hierarchy maintenance yield model is established, where the cost of preventive maintenance and failure replacement maintenance are distinguished between the independent error source and the overall error source. The nonlinear relationship between the maintenance yield per unit cost and influencing factors, including the error threshold and the maintenance times is obtained, which allows to develop an optimal maintenance strategy. Preventive maintenance is introduced to avoid unintended failure of the mechanism while extending the lifetime. The high-precision parallel mechanism has demonstrated promising applications in medical, industrial and other fields, and its economic benefits can be effectively improved by incorporating the MPM method. The experiment of manufacturing human lung models using a parallel 3D printing device demonstrates that the MPM method can improve the long-term precision and reliability of the parallel device, and the optimized human lung contour tracking precision can be improved by up to 55.56%.
Facilitated by advanced digital technologies, reliability managers can monitor system working cycles during the whole life cycle. Such a technological realization can help reliability managers ensure system reliability in real time by monitoring working cycles. In this paper, by incorporating a limited random working cycle, rebate and charge into warranty theory, a random free repair warranty with rebate and charge (RFRW-RC) is devised to ensure system reliability during the warranty stage. Under RFRW-RC, the rebate removes manufacturers’ responsibility for continuing to ensure system reliability, while the charge is a support where manufacturers continue to ensure system reliability. The warranty cost of RFRW-RC is derived, and a random discrete free repair warranty (RDFRW) is presented by simplifying RFRW-RC. By mixing random age replacement last (RARL) and classic age replacement (CAR), a random hybrid age replacement (RHAR) is designed in order to ensure system reliability during the post-warranty stage. In such an RHAR, RARL is applied to extend the replacement time during the post-warranty stage in order to maximize the remaining life of the system through warranty, and CAR is used to lower the maintenance cost of the system through warranty. The cost rate of RHAR is modeled, and the cost rate of RDFRW is offered as well by discussing parameter values. The decision variable is optimized by minimizing the cost rate model. The properties of the presented models are explored from numerical perspectives.
The purpose of this study is to analyze the behavior of some industrial systems in light of the cost-free warranty policy. According to this policy, we assume that the repairman is not always present in the system. When the active unit fails, the repairman will be called to visit the system; however, administrative procedures may delay the visit for some time. Once on the system, the repairman first inspects whether the fault is caused by the user or not and whether it is repairable or not. According to product warranty laws, the repairman carries out the repair or replacement of the faulty unit. The failure time, administrative delay time, inspection time, and repair time are assumed taken as a negative exponential distribution. The system model is analyzed by the supplementary variable technique and Laplace transform, as various performance metrics of system efficiency have been obtained. The sensitivity and relative sensitivity analyses for the system parameters have also been performed. Finally, an illustrative example is taken to illustrate the efficiency of the system.
The aim of this paper is to analyze a system, which consists of two components, working under a cost-free warranty policy. Past literature reflects that till now the focus of researchers is those systems which work without taking rest. But here authors emphasized on an industrial system which takes rest after working for a specific amount of time. This strategy helps the system to run for a long time with less failure. After taking rest, the system starts its working again. During the mathematical modeling of the system various state of the same are critically analyzed. Reliability of the considered system has been obtained for the different combinations of failure and repair rates. Also, the various parameters which affect the system performance have been evaluated.
This paper considers a maintenance scheduling model by using the concepts of failure free warranty policy. In this model, all the repairs during warranty are cost-free to the users, provided failures are not due to the negligence of the users. However, the users will have to repair the failed unit at their own expenses beyond warranty. During their formulation, the failure rate of the system is considered to be negative exponential distribution while the preventive maintenance (PM), repair and replacement time distributions are taken to be arbitrary with different probability density functions. Under these assumptions, using the supplementary variable technique, the various expressions which depict the behavior of the system such as reliability of the system, Mean Time to System Failure (MTSF), availability and profit function have been derived. Further, steady-state behavior of the system has also been derived. To substantiate the proposed approach, the effect of the parameters of the system has been analyzed through the system reliability, and expected profit through an illustrative example.
Th is paper examines the recent experience with insurance and other risk-fi nancing instruments in developing countries in order to gain insights into their eff ectiveness in reducing economic insecuri-ty. Insurance and other risk fi nancing strategies are viewed as eff orts to recover from negative income shocks through risk pooling and transfer. Specifi c examples of public-private insurance programs for households, business-fi rms, and governments are described, highlighting their limitations, especially in light of the post-Katrina experience in the United States. It examines arguments both in support of and in opposition to donor and public involvement in provision of subsidized insurance in devel-oping countries.
Manufacturers of consumer products, such as automobiles, usually offer warranties guarantee- ing the product or its parts, for example, for five years or 50,000 miles, whichever comes first. There are at least two issues of interest to applied mathematicians,and statisticians that arise from warranty considerations. The first is the specification of an optimum price-warranty combination, and the second is the forecast of a reserve fund to meet warranty,claims against the product. The former involves a consideration,of the item's reliability, its rate of usage, the consumer's attitude toward a specific warranty, and the competitor's actions, all of which lead towards a game,theoretic formulation,of the problem. The latter involves the analysis of a special kind of time series in two-dimensions, for which the use of dynamic linear models appears to be natu- ral. This is an expository paper. Due to the timeliness of the topic, the focus here is on problem definition, its scope, and its formulation in a manner that facilitates analysis. Imbedded in the discussion are strategies for addressing some,of the ensuing issues. The overall goal is tb enlighten the reader about an area of research in the mathematical,sciences that has an impact on industrial competitiveness,and the manufacturing,sciences. Keywords. forecasting, Kalman filtering, optimization, point processes, quality, reliability, renewal theory,
Warranty and insurance are equally essential for a technological system to cover repair/replacement costs of all types of losses, i.e., natural wear/tear or unexpected external force/accidents. This paper examines the sensitivity and profitability of a stochastic model whose defects may cover under conditional warranty/insurance. The system user may extend the warranty period by paying an additional price. As a result, the system functions in normal warranty, extended warranty, and during non-warranty periods. If a system fault occurred is covered under warranty conditions, the manufacturer is responsible for all repair/replacement costs during normal/extended warranty which otherwise are paid by the insurance provider if covered under an insurance claim, or else, the user is responsible for the entire cost when coverage of fault neither falls in warranty conditions nor under the insurance policy. Using Markov and the regenerative process, various measures of system effectiveness associated with the profit of the user and the manufacturer are examined. Relative sensitivity analysis of the profit function and availability has been performed for all periods.
In the business world, product warranty and insurance plays an important role by increasing the demand of the product to maximizing the average profit or minimizing the average cost in a manufacturing system. Also, the customers’ demand depends on several factors, viz. quality, selling price, payment strategies, warranty and insurance of the product. This paper develops an imperfect production inventory model with preventive machine maintenance, rework, warranty and insurance coverage on the accidentally damaged part(s) of the product. The concerned production system can randomly shift from an in-control state to an out-of-control state at any time during a production run, and the time elapsed while the production process stays in the in-control state is assumed to be exponentially distributed. The rates of producing reworkable defective items in the in-control state and out-control states are different. The demand rate of the customers is considered as the product’s selling price and warranty period dependent. To attract customers and increase the demand for the product, the manufacturer offers an insurance policy on the damageable part(s) of the product within the warranty period. The main aim of this study is to find the optimal production time, selling price for the different warranty periods of the product, which maximizes the profit per unit business period. To examine the validity of the proposed model, two numerical examples are considered and solved with the help of MATHEMATICA software. Finally, the effects of warranty and insurance policies on the products are analyzed, based on the numerical examples.
In this paper, we consider an equipment leased with a warranty contract with the possibility to extend the warranty at a given price that depends on its duration. During the warranty period, the lessor (who possesses the equipment) performs and pays for repairs at failure and for preventive maintenance (PM) actions whenever the equipment reliability reaches a specific limit. After the warranty ends, repairs and PM actions are still performed by the lessor, but they are billed to the lessee (who rents the equipment). Furthermore, in case the total average equipment downtime due to repair and PM actions during the lease period surpasses a certain pre-specified limit agreed on in the lease contract, a penalty is supported by the lessor. A mathematical model and numerical procedure are proposed to determine the PM intervals durations that maximise the lessor’s expected total profit during the lease period. The optimal solution is obtained by determining the combination between the optimal equipment reliability threshold that triggers a PM action and the optimal extended warranty period. A numerical example is given to illustrate the use of the proposed model and a sensitivity analysis is performed.
The success of a new product depends on both engineering decisions (product reliability) and marketing decisions (price, warranty). A higher reliability results in a higher manufacturing cost and higher sale price. Consumers are willing to pay a higher price only if they can be assured about product reliability. Product warranty is one such tool to signal reliability with a longer warranty period indicating better reliability. Better warranty terms result in increased sales and also higher expected warranty servicing costs. Warranty costs are reduced by improvements in product reliability. Learning effects result in the unit manufacturing cost decreasing with total sales volume and this in turn impacts on the sale price. As such, reliability, price and warranty decisions need to be considered jointly. The paper develops a model to determine the optimal product reliability, price and warranty strategy that achieve the biggest total integrated profit for a general repairable product sold under a free replacement-repair warranty strategy in a market and looks at two scenarios for the pricing and warranty of the product. The model assumes that the sale rate increases as the warranty period increases and decreases as the price increases. The maximum principle method is used to obtain optimal solutions for dynamic price and warranty situations. Finally, numerical examples are given to illustrate the proposed model.
Some of the risks associated with manufacturing may be managed by establishing appropriate manufacturing quality levels and assuring them by appropriate inspection and quality control plans. In addition, by providing warranties or post-sales servicing contracts, consumers may be protected from risks of purchasing nonconforming items. The purpose of this paper is to devise a framework whereby management can simultaneously determine the appropriate manufacturing quality, inspection, and post-sales servicing plans. Using a renewal theoretic approach, the framework developed allows the substitution effects of these managerial decision variables to be explored, thereby providing joint policy choices regarding quality control and servicing.Handled by the Applied Probability : Stochastic Processes Department.
This paper presents a novel warranty policy named ‘full-service warranty’ (FSW) for repairable multi-component systems under which the failed component(s) or subsystem(s) will be replaced, in addition, a (perfect) maintenance action will be performed to reduce the chance of future system failure, both free of charge to consumers. Such a policy is desirable for both consumers and manufacturers since consumers receive better warranty service compared to the traditional free repair policy, at the same time, manufacturers may enjoy increase in sale as well as cost-saving due to improved product reliability by the maintenance action. Under the renewable FSW policy, from manufacturers’ point of view, cost models for complex systems with series, parallel, series–parallel (s–p) and parallel–series (p–s) structure are developed. Exact expressions for the first and second centered moments of warranty cost per product sold are obtained. Sensitivity analysis is performed based on a numerical example.
Effective management of product warranty requires proper evaluation of alternative warranty policies. Many different types of warranty policies are in common use. Still others are discussed in the literature on product warranty. In this paper we formulate a taxonomy for warranty to assist the manager responsible for product warranty in choosing appropriate alternatives for evaluation before a final choice is made.
Warranty is an important element of marketing new products. The servicing of warranty results in additional costs to the manufacturer. Warranty logistics deals with various issues relating to the servicing of warranty. Proper management of warranty logistics is needed not only to reduce the warranty servicing cost but also to ensure customer satisfaction as customer dissatisfaction has a negative impact on sales and revenue. Unfortunately, warranty logistics has received very little attention. The paper links the literature on warranty and on logistics and then discusses the different issues in warranty logistics. It highlights the challenges and identifies some research topics of potential interest to operational researchers.
In the present investigation, we propose a hybrid warranty model for the renewing pro-rata warranty (RPRW), in which the failure rate of units, cost of preventive maintenance and cost of replacement are assumed to be constant. The expected total discounted maintenance cost has been derived in explicit form for different life time distributions viz. exponential, Rayleigh and Weibull distributions. We determine the optimal number and optimal period for preventive maintenance after the expiry of the warranty. Numerical illustrations are provided to check the validity of the analytical results.
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