scholarly journals Determination of Optimal Warranty Period with Preventive Maintenance Actions for Items from Heterogeneous Populations

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Minjae Park
Keyword(s):  
Repair Time ◽  
Minimal Repair ◽  
Optimal Length ◽  
Repair Service ◽  
Expected Cost ◽  
Heterogeneous Populations ◽  
Cost Rate ◽  
Warranty Period ◽  
Optimal Maintenance ◽  
Warranty Length

In this study, we develop an optimal maintenance policy with replacement service and minimal repair service for items from heterogeneous populations and determine the optimal warranty length and repair time threshold. We consider the information-based repair-replacement policy model and develop the formula to evaluate the expected cost rate during the product life cycle. A general formulation is derived for the expected cost rate under a warranty policy for items of heterogeneous populations. When a replacement service and minimal repair service are provided for a failed item, then an item from a weak population has the property of an item from a weak population after service. Similarly, an item from a strong population has the property of an item from a strong population after service. We define the optimal maintenance strategies to minimize the expected cost rate with failure time and repair time for items with heterogeneous reliability characteristics. The effects of parameters of the intensity function for the failure times on the optimal length of the warranty period are studied numerically. Assuming that the product deteriorates, we illustrate the proposed approach using numerical applications and observe the impacts of relevant parameters on the optimal length of the warranty period.

A modified block replacement policy with two variables and general random minimal repair cost

1996 ◽  
Vol 33 (2) ◽  
pp. 557-572 ◽  
Author(s):  
Shey-Huei Sheu
Keyword(s):  
Operating System ◽  
Replacement Policy ◽  
Repair Cost ◽  
Minimal Repair ◽  
Expected Cost ◽  
Cost Rate ◽  
Age Dependent ◽  
Modified Block ◽  
The Cost ◽  
Random Part

This paper considers a modified block replacement with two variables and general random minimal repair cost. Under such a policy, an operating system is preventively replaced by new ones at times kT (k= 1, 2, ···) independently of its failure history. If the system fails in [(k − 1)T, (k − 1)T+ T0) it is either replaced by a new one or minimally repaired, and if in [(k − 1) T + T0, kT) it is either minimally repaired or remains inactive until the next planned replacement. The choice of these two possible actions is based on some random mechanism which is age-dependent. The cost of the ith minimal repair of the system at age y depends on the random part C(y) and the deterministic part ci (y). The expected cost rate is obtained, using the results of renewal reward theory. The model with two variables is transformed into a model with one variable and the optimum policy is discussed.

Determination of optimal post-warranty variable maintenance period for repairable second-hand product based on mean residual life

2021 ◽  
pp. 1748006X2110629
Author(s):  
Jae-Hak Lim ◽  
Dae Kyung Kim ◽  
Dong Ho Park
Keyword(s):  
Life Cycle ◽  
Preventive Maintenance ◽  
Residual Life ◽  
Mean Residual Life ◽  
Maintenance Period ◽  
Life Distribution ◽  
Expected Cost ◽  
Cost Rate ◽  
Warranty Period ◽  
Significant Difference

Due to the increased transactions of second-hand products in the market, the optimization of maintenance strategy for the second-hand product has become very important issue to attract a great attention from many researchers of late. This paper proposes a new post-warranty strategy with a variable self-maintenance period for the second-hand product, assuming that the product is replaced by another one on the first failure following a fixed length of post-warranty self-maintenance period. During the non-renewing warranty period, the product is subject to preventive maintenance periodically at a prorated cost while only minimal repair is implemented at each failure by the dealer. The main goal of this study is to determine an optimal length of post-warranty self-maintenance period which minimizes the expected cost rate per unit time during the product’s life cycle from the user’s perspective. This approach considers not only the periodic preventive maintenance during the warranty period, but also the remaining life distribution of the product after the warranty expires, which is the significant difference of this work from many existing maintenance policies. For this purpose, we formulate the expected length of life cycle and evaluate the expected total cost incurred during the life cycle of the second-had product which is purchased at the age of [Formula: see text] The existence of the optimal self-maintenance period is proved analytically under mild conditions and the proposed maintenance model is compared with an existing model with regard to the expected cost rate. Finally, assuming that the life distribution of the product follows a Weibull distribution, the effect of relevant parameters on the optimal self-maintenance period is analyzed numerically.

A modified block replacement policy with two variables and general random minimal repair cost

1996 ◽  
Vol 33 (02) ◽  
pp. 557-572 ◽  
Author(s):  
Shey-Huei Sheu
Keyword(s):  
Operating System ◽  
Replacement Policy ◽  
Repair Cost ◽  
Minimal Repair ◽  
Expected Cost ◽  
Cost Rate ◽  
Age Dependent ◽  
Modified Block ◽  
The Cost ◽  
Random Part

This paper considers a modified block replacement with two variables and general random minimal repair cost. Under such a policy, an operating system is preventively replaced by new ones at timeskT(k=1, 2, ···) independently of its failure history. If the system fails in [(k − 1)T,(k− 1)T+T0) it is either replaced by a new one or minimally repaired, and if in [(k− 1)T+T0, kT) it is either minimally repaired or remains inactive until the next planned replacement. The choice of these two possible actions is based on some random mechanism which is age-dependent. The cost of theith minimal repair of the system at ageydepends on the random partC(y) and the deterministic partci(y). The expected cost rate is obtained, using the results of renewal reward theory. The model with two variables is transformed into a model with one variable and the optimum policy is discussed.

Optimal design of sales and maintenance under the renewable warranty

2018 ◽  
Vol 52 (2) ◽  
pp. 529-542 ◽  
Author(s):  
Can Jiao ◽  
Xiaoyan Zhu
Keyword(s):  
New Product ◽  
Repair Time ◽  
Replacement Policy ◽  
Sales Growth ◽  
Minimal Repair ◽  
Profit Model ◽  
Sales Price ◽  
Warranty Period ◽  
Total Profit ◽  
Warranty Cost

This paper presents an integrated model to determine the optimal sales price, preventive maintenance (PM) interval and warranty period with the objective of maximizing the total profit. It is assumed that the sales growth can be featured by NHPP-Bass model over the time. Production cost, R&D cost and warranty cost involving product reliability are considered in this integrated profit model. Then, we consider a periodic PM policy, minimal repair and replacement policy in this paper and the product is deteriorated with the time goes. We also consider effects of the repair time of the repairable product. During the warranty period, manufacturer conducts the PM periodically, and if the repair time is beyond the limited repair time, the failure is replaced with a new product attached renewed warranty period. If not, the failed product is conducted with only minimal repair. Moreover, we give the numerical example and the sensitive analysis to provide insights into the influence of sales price, warranty period and PM interval.

WARRANTY SERVICING WITH A BROWN–PROSCHAN REPAIR OPTION

2012 ◽  
Vol 29 (03) ◽  
pp. 1240023 ◽  
Author(s):  
RUDRANI BANERJEE ◽  
MANISH C. BHATTACHARJEE
Keyword(s):  
Two Dimensional ◽  
Failure Model ◽  
Remedial Action ◽  
Minimal Repair ◽  
Numerical Illustration ◽  
Expected Cost ◽  
Warranty Period ◽  
The Cost

Reducing warranty servicing costs are of great interest to product manufacturers or sellers who are contractually bound to provide post-sales support, up to a specified warranty period, usually in the form of some remedial action that restores a failed item to a functioning condition. Here, in the spirit of Jack et al. (2009) strategy based on partitioning the effective warranty period into three intervals, we consider and analyze the cost of a new two-dimensional warranty servicing strategy, that probabilistically exercises a choice between a replacement and a minimal repair to rectify the first failure if any, in the middle interval. The behavior of the expected cost is numerical illustration with Weibull failure model.

The Optimal Maintenance Period for Repairable Product after Warranty Expiration under Renewing Warranty

2010 ◽  
Vol 118-120 ◽  
pp. 860-865 ◽  
Author(s):  
Z.Y. Hu ◽  
Li Yang Xie
Keyword(s):  
Life Cycle ◽  
Failure Rate ◽  
Maintenance Period ◽  
Cost Rate ◽  
Numerical Example ◽  
Warranty Period ◽  
Optimal Maintenance ◽  
The Cost ◽  
Cost Factors ◽  
Increasing Function

A model of the optimal maintenance period for repairable product after warranty expiration under renewing warranty is proposed. In the process to fulfilling warranty, the failures of product within warranty period happen randomly, the replacements of products successively failed with warranty period form a renewing process. Given failure rate of product, the period of fulfilling warranty is function of warranty period. User purchasing a product is considered an investment; the period of fulfilling warranty and the maintenance period after warranty make up the life cycle of product investment. Taking various cost factors into account, making model of the cost rate in life cycle of product investment under renewing warranty, the cost rate is function of maintenance period. Give the failure rate of product is an increasing function, it is derived that there is unique optimal maintenance period minimizing the cost rate. Finally, numerical example is given for illustration.

Availability analysis and maintenance optimization for multiple failure mode systems considering imperfect repair

2021 ◽  
pp. 1748006X2110127
Author(s):  
Qingan Qiu ◽  
Baoliang Liu ◽  
Cong Lin ◽  
Jingjing Wang
Keyword(s):  
Failure Modes ◽  
Maintenance Cost ◽  
Imperfect Maintenance ◽  
Maintenance Policy ◽  
Cost Rate ◽  
Availability Analysis ◽  
Long Run ◽  
Optimal Maintenance ◽  
Maintenance Policies ◽  
Periodic Inspections

This paper studies the availability and optimal maintenance policies for systems subject to competing failure modes under continuous and periodic inspections. The repair time distribution and maintenance cost are both dependent on the failure modes. We investigate the instantaneous availability and the steady state availability of the system maintained through several imperfect repairs before a replacement is allowed. Analytical expressions for system availability under continuous and periodic inspections are derived respectively. The availability models are then utilized to obtain the optimal inspection and imperfect maintenance policy that minimizes the average long-run cost rate. A numerical example for Remote Power Feeding System is presented to demonstrate the application of the developed approach.

Optimization of equal-cycle maintenance strategy considering imperfect preventive maintenance

2021 ◽  
pp. 095440892110638
Author(s):  
Xinlong Li ◽  
Yan Ran ◽  
Genbao Zhang
Keyword(s):  
Decision Making ◽  
Preventive Maintenance ◽  
Maintenance Cost ◽  
Maintenance Strategy ◽  
Action Unit ◽  
Cost Rate ◽  
Equipment Reliability ◽  
Optimal Maintenance ◽  
Important Means ◽  
Maintenance Decision

Preventive maintenance is an important means to extend equipment life and improve equipment reliability. Traditional preventive maintenance decision-making is often based on components or the entire system, the granularity is too large and the decision-making is not accurate enough. The meta-action unit is more refined than the component or system, so the maintenance decision-making based on the meta-action unit is more accurate. Therefore, this paper takes the meta-action unit as the research carrier, considers the imperfect preventive maintenance, based on the hybrid hazard rate model, established the imperfect preventive maintenance optimization model of the meta-action unit, and the optimization solution algorithm was given for the maintenance strategy. Finally, through numerical analysis, the validity of the model is verified, and the influence of different maintenance costs on the optimal maintenance strategy and optimal maintenance cost rate is analyzed.

Sequential imperfect preventive maintenance policy with random maintenance quality under reliability limit

2011 ◽  
Vol 225 (8) ◽  
pp. 1926-1935 ◽  
Author(s):  
Z Wang ◽  
J Yang ◽  
G Wang ◽  
G Zhang
Keyword(s):  
Failure Rate ◽  
Preventive Maintenance ◽  
Average Cost ◽  
Numerical Control ◽  
Maintenance Policy ◽  
Cost Rate ◽  
Proposed Model ◽  
Optimal Maintenance ◽  
Average Cost Rate ◽  
Optimal Maintenance Policy

To determine the optimal maintenance number for a system with random maintenance quality in infinite time horizon, a sequential imperfect preventive maintenance model considering reliability limit is proposed. The proposed model is derived from the combination of the Kijima type virtual age model and the failure rate adjustment model. Maintenance intervals of the proposed model are obtained through an iteration method when both failure rate increase factor and maintenance restoration factor are random variables with a uniform distribution. The optimal maintenance policy is presented by minimizing the long-run average cost rate. A real numerical example for the failures of numerical control equipment is given to demonstrate the proposed model. Finally, a discussion is presented to show how the optimal average cost rate depends on the different cost parameters. The results show that in order to satisfy the practical requirements of high reliability, it is necessary and worthwhile to consider the system's reliability limit in preventive maintenance practice.

An optimal inspection–repair–replacement policy for standby systems

1995 ◽  
Vol 32 (1) ◽  
pp. 212-223 ◽  
Author(s):  
Lam Yeh
Keyword(s):  
Geometric Model ◽  
Optimal Solution ◽  
Simple Algorithm ◽  
Replacement Policy ◽  
System State ◽  
Expected Cost ◽  
Long Run ◽  
Optimal Maintenance ◽  
Maintenance Model

In this paper, an optimal maintenance model for standby systems is studied. An inspection–repair–replacement policy is employed. Assume that the state of the system can only be determined through an inspection which may incorrectly identify the system state. After each inspection, if the system is identified as in the down state, a repair action will be taken. It will be replaced some time later by a new and identical one. The problem is to determine an optimal policy so that the availability of the system is high enough at any time and the long-run expected cost per unit time is minimized. An explicit expression for the long-run expected cost per unit time is derived. For a geometric model, a simple algorithm for the determination of an optimal solution is suggested.

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