Modelling and Optimization of Inspection and Preventive Replacement for Renewable Warranty Products with Residual Warranty Time Threshold
Preventive maintenance actions are performed before failures of products and they aim at reducing the risk of failure.With the development of monitoring technology and information technology,a new type of preven-tive maintenance action,condition based maintenance(CBM),has emerged.The decision-making of CBM is mainly based on the"diagnostic"information of products.Compared to the traditional periodic maintenance actions,condition based maintenance actions have been proven to be more economical and more effective in improving system availability and security.The modeling and optimization of CBM have become a research focus in the field of reliability and maintenance.Motivated by the aforementioned engineering practice,this paper links the modelling and optimization of CBM with warranty decision-making.It is assumed that products can take three states:normal,defective and failure.Based on the concept of two-stage failure process,the modelling and optimization of periodic inspection and preventive replacement of renewable warranty products with residual warranty time threshold are carried out.The warranty period is divided into two stages:the inspection and replacement period and the minimal maintenance period.The inspection and replacement period begins when a new product starts to operate and ends when the residual warranty period equals a threshold.The minimal maintenance period starts when the residual warranty periods equals the threshold and ends when the warranty expires.During the inspection and replacement period,the manufacturer shall carry out periodic inspections at equal intervals.If the product is identified to be in a defective state or fails,the product will be replaced immediately.To reduce the service cost,during the minimal maintenance period,the manufacturer does not implement inspections or replacements,but only carries out minimal maintenanceson failures.For comparison,another two renewable warranty models,named A.1 and A.2,are built.Under Model A.1,neither inspections nor preventive replacements are carried over the whole warranty period.For Model A.2,inspections and preventive replacements are implemented during the whole warranty period and no residual warranty time is set.By using the probability analysis method,the average warranty costs per unit time for the aforementioned three models are given.From the manufacturer's perspective,the average warranty cost per unit time is minimized by optimizing threshold of the residual warranty time and the inspection interval.A numerical example is given to illustrate the superiority of setting inspections,preventive replacements and residual warranty time.The results of the numerical example show that the optimal inspection interval increases with the increase in the cost for one inspection and decreases with the increasein the cost for a minimal repair action.As for the optimal remaining warranty time,it is insensitive to the cost of one inspection and increases with the cost of a minimal repair action.The time for which the product stays in normal and defective states is assumed to fit Weibull distributions in the numerical example.Effects of shape and scale parameters of these Weibull distributions on the optimal inspection interval and remaining warranty time are also discussed in the numerical example.The above-mentioned conclusions can be valuable to the warranty policy decisions.In the current model,preventive replacements and minimal repair actions are considered during the warranty period.In the industrial engineering,imperfect maintenance activities are common and the warranty of a product may be non-renewable.Hence,imperfect maintenance activity optimization of products with non-renewable warranty terms is worth discussing.
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