Ki Mun Jung

System maintenance cost dependent on life cycle under renewing warranty policy

A number of optimal maintenance policies have been proposed and studied based on several types of warranty policies. As the criteria for optimality, the expected cost rate per unit time during the life cycle of the system is quite often used by many authors. However, the expected cost rate may depend on the length of life cycle and so the definition of life cycle plays a significant role in optimizing the maintenance policy. This paper considers a system maintenance policy during the post-warranty period under the renewing warranty policy and the life cycle is defined from the users perspective. The life cycle starts with the installment of a new system and ends when the system is replaced by a new one at the expense of the user. In many renewing warranty models, the life cycle is defined as the lifelength of the new system installed initially, which is quite different from our definition. The expected cost rate per unit time is evaluated based on the life cycle newly defined and is compared with the existing results.

Optimal post-warranty maintenance policy with repair time threshold for minimal repair

Abstract In this paper, we consider a renewable minimal repair–replacement warranty policy and propose an optimal maintenance model after the warranty is expired. Such model adopts the repair time threshold during the warranty period and follows with a certain type of system maintenance policy during the post-warranty period. As for the criteria for optimality, we utilize the expected cost rate per unit time during the life cycle of the system, which has been frequently used in many existing maintenance models. Based on the cost structure defined for each failure of the system, we formulate the expected cost rate during the life cycle of the system, assuming that a renewable minimal repair–replacement warranty policy with the repair time threshold is provided to the user during the warranty period. Once the warranty is expired, the maintenance of the system is the users sole responsibility. The life cycle of the system is defined on the perspective of the user and the expected cost rate per unit time is derived in this context. We obtain the optimal maintenance policy during the maintenance period following the expiration of the warranty period by minimizing such a cost rate. Numerical examples using actual failure data are presented to exemplify the applicability of the methodologies proposed in this paper.

Optimization of cost and downtime for replacement model following the expiration of warranty

Abstract This paper deals with the optimal replacement policies following the expiration of warranty: renewing warranty and non-renewing warranty. If the system fails during its warranty period, it is replaced with a new one and if the system fails after the warranty period is expired, then it is minimally repaired at each failure. The criterion used to determine the optimality of the replacement period is the overall value function, which is established based on the expected downtime and the expected cost rate combined. Firstly, we develop the expected downtime per unit time and the expected cost rate per unit time for our replacement model when the cost and downtime structures of maintaining the system are given. The overall value function suggested by Jiang and Ji [Age replacement policy: a multi-attribute value model. Reliab Eng Syst Saf 2002;76:311–8] is then utilized to determine the optimal maintenance period based on the expected downtime and the expected cost rate. Numerical examples are presented for illustrative purpose.

Modeling consumer acceptance probabilities

This paper investigates how to estimate the likelihood of a customer accepting a loan offer as a function of the offer parameters and how to choose the optimal set of parameters for the offer to the applicant in real time. There is no publicly available data set on whether customers accept the offer of a financial product, whose features are changing from offer to offer. Thus, we develop our own data set using a fantasy student current account. In this paper, we suggest three approaches to determine the probability that an applicant with characteristics will accept offer characteristics using the fantasy student current account data. Firstly, a logistic regression model is applied to obtain the acceptance probability. Secondly, linear programming is adapted to obtain the acceptance probability model in the case where there is a dominant offer characteristic, whose attractiveness increases (or decreases) monotonically as the characteristics value increases. Finally, an accelerated life model is applied to obtain the probability of acceptance in the case where there is a dominant offer characteristic.

Cost optimization model following extended renewing two-phase warranty☆

Abstract In this paper, we study an extended warranty model under which the customer is offered an additional warranty period after the original two-phase warranty expires. Under the original two-phase warranty, the warranty period is divided into two non-overlapping subintervals, one of which is for replacement warranty, and the other is for minimal repair warranty. If the system failure occurs during the original warranty period, the failed system is either replaced or minimally repaired by the manufacturer, and if the failure occurs during the extended warranty period, only the minimal repair is conducted. For the system failure during the replacement warranty period, the failed system is replaced by a new one, and the warranty term is renewed anew. Following the expiration of extended warranty, the customer is solely responsible for maintaining the system for a fixed length of time period and replaces the system at the end of such a maintenance period. During the maintenance period, only the minimal repair is given for each system failure. Such a maintenance model can be considered as a generalization of several existing maintenance models which can be obtained as special cases. The main purpose of this article is to determine, from the customer’s perspective, the optimal length of maintenance period after the extended warranty expires. As the criterion to determine the optimal replacement strategy, we adopt the expected cost rate per unit time during the life cycle of the system. Given the cost structures incurred during the life cycle of the system, we formulate the expected cost and the expected length of life cycle to obtain the expected cost rate. The uniqueness of optimal solution for the decision variable is verified when the life distribution of the system shows an increasing failure rate. Numerical examples are provided to illustrate the proposed optimal replacement strategy.

A Generalized Age Replacement Policy for Systems Under Renewing Repair-Replacement Warranty

This paper presents a warranty cost model for repairable products when an age replacement policy is adopted in conjunction with the renewal of a minimal repair-replacement warranty. A study of the optimal choice of the preventive replacement age is also presented. When renewing a minimal repair-replacement warranty, either minimal repair is carried out or the product is replaced, depending on the length of repair time when the product failures occur during the warranty period. In this study, we develop mathematical formulas to evaluate the long-run expected cost rates during the life cycle of the product under the proposed cost models and determine the optimal preventive replacement ages by minimizing the objective functions. Furthermore, the effects of the renewing warranty on the optimal preventive replacement age and its corresponding expected cost rate are investigated for various situations regarding the warranty policy. This study extends the existing results on the age replacement policy by considering situations that are more practical, where both minimal repair and replacement are considered simultaneously upon product failure. Assuming that the product deteriorates with age, we illustrate our proposed cost model and its optimization using numerical examples and observe the impact of relevant parameters on the optimal solutions regarding the preventive replacement age.

Optimal warranty policies considering repair service and replacement service under the manufacturer’s perspective

In this paper, under the manufacturer’s point of view, a warranty cost model is proposed in consideration of both repair service and replacement service simultaneously upon the system failure to find the optimized warranty period in terms of an expected cost rate during the warranty cycle. If a failed system can’t be repaired by the threshold warranty servicing time in the warranty service center, the replacement service is provided for the failed system instead of continuing to provide the repair service. Under such circumstance, new warranty cost models are developed and the renewable warranty policy is investigated for free and pro-rata two-dimensional warranty dependent on both failure time and warranty servicing time. From the manufacturer’s point of view, the warranty period is newly defined starting from the system’s purchasing time and ending at the expiration time of the warranty. This paper determines the optimal warranty period by applying Nelder–Mead downhill simplex method to minimize the expected cost rate during the warranty period. The real application is discussed adopting the proposed approach based on the actual field data and numerical examples are presented to exemplify the applicability of the methodologies derived in this paper.

When to Rebuild or When to Adjust Scorecards

Data-based scorecards, such as those used in credit scoring, age with time and need to be rebuilt or readjusted. Unlike the huge literature on modelling the replacement and maintenance of equipment there have been hardly any models that deal with this problem for scorecards. This paper identifies an effective way of describing the predictive ability of the scorecard and from this describes a simple model for how its predictive ability will develop. Using a dynamic programming approach one is then able to find when it is optimal to rebuild and when to readjust a scorecard. Failing to readjust or rebuild a scorecard when they aged was one of the defects in credit scoring identified in the investigations into the sub-prime mortgage crisis.

Optimization of periodic preventive maintenance policy following the expiration of two-dimensional warranty

Abstract This paper considers an optimal periodic preventive maintenance policy after the expiration of two-dimensional warranty. During the two-dimensional warranty period, both renewal warranty and nonrenewal warranty are considered and a repair time threshold is pre-specified so that the failed system is either minimally repaired or is replaced depending on whether the length of repair time exceeds the repair time threshold or not. After the warranty expires, the system undergoes the preventive maintenance periodically a fixed number of times by the user to prolong the life of the system and then the system is replaced preventively by a new one. In this study, we develop an optimal post-warranty periodic preventive maintenance strategy by minimizing the expected cost rate incurred during the life cycle of the system. From the users perspective, the system is maintained free of charge or with prorated charge on the failed system during the warranty period. Once the warranty expires, the maintenance cost of the system is entirely charged to the user. Subject to such a cost structure, we derive the formula to evaluate the expected cost rate, which is used as an objective function for the optimality. The main goal of this paper is to determine an optimal preventive maintenance cycle after the warranty expires and thus to propose an optimal post-warranty strategy for the user. The effect of several parameters on the optimal strategy is also investigated numerically in this study. For the purpose of illustration of our proposed model, we present and discuss some numerical examples.

Notice of Retraction Optimized maintenance policies subject to the preventive maintenance before warranty expires

In this paper, two-factor warranty policy is investigated considering the preventive maintenance (PM) services in the warranty period using failure times and warranty servicing times from the manufacturers perspective. Under the warranty, the replacement service is considered as well as the repair service for a failed product as warranty services and the PM service is scheduled for systems quality and reliability in the warranty period. If a failed product could not be repaired by the threshold time limit in the warranty service center, the replacement service is provided instead of continuing to provide repair service in the model and using Jung and Parks maintenance model, the maintenance policy is investigated with a preventive replacement service during the warranty period [1]. In this study, an optimal maintenance policy is proposed considering two-factor warranty to find the optimized preventive maintenance interval in terms of an expected cost rate. Free replacement/repair warranty and pro-rata warranty are also considered in the paper. The real application is implemented using the proposed approach by field data and numerical examples are discussed to exemplify the applicability of the methodologies derived in this paper.