A generalized age-dependent minimal repair with random working times

2021 ◽  
Vol 156 ◽  
pp. 107248
Author(s):  
Shey-Huei Sheu ◽  
Tzu-Hsin Liu ◽  
Zhe-George Zhang ◽  
Xufeng Zhao ◽  
Yu-Hung Chien
Keyword(s):  
Minimal Repair ◽  
Age Dependent

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.

Age-dependent minimal repair

1985 ◽  
Vol 22 (02) ◽  
pp. 370-385 ◽  
Author(s):  
Henry W. Block ◽  
Wagner S. Borges ◽  
Thomas H. Savits
Keyword(s):  
Continuous Function ◽  
Stochastic Model ◽  
Renewal Process ◽  
Failure Time ◽  
Minimal Repair ◽  
Life Distribution ◽  
Complete Repair ◽  
Age Dependent ◽  
Image Position

A stochastic model is developed to describe the operation in time of the following maintained system setting. A piece of equipment is put in operation at time 0. Each time it fails, a maintenance action is taken which, with probability p(t), is a complete repair or, with probability q(t)=1– p(t), is a minimal repair, where t is the age of the equipment in use at the failure time. It is assumed that complete repair restores the equipment to its good as new condition, that minimal repair restores the equipment to its condition just prior to failure and that both maintenance actions take negligible time. If the equipment's life distribution F is a continuous function, the successive complete repair times are shown to be a renewal process with interarrival distribution for t ≧ 0. Preservation and monotone properties of the model extending the results of Brown and Proschan (1983) are obtained.

OPTIMAL PREVENTIVE-MAINTENANCE WARRANTY POLICIES FOR REPAIRABLE PRODUCTS WITH AGE-DEPENDENT MAINTENANCE COSTS

2005 ◽  
Vol 12 (02) ◽  
pp. 111-125 ◽  
Author(s):  
RUEY HUEI YEH ◽  
MING-YUH CHEN
Keyword(s):  
Optimal Policy ◽  
Preventive Maintenance ◽  
Life Time ◽  
Optimal Number ◽  
Closed Form Expression ◽  
Minimal Repair ◽  
Maintenance Costs ◽  
Special Cases ◽  
Age Dependent ◽  
The Impact

This paper develops a mathematical model to derive the optimal preventive maintenance warranty (PMW) policy for repairable products with age-dependent maintenance costs. Under a PMW, any product failures are rectified by minimal repair, and additional preventive maintenance actions are carried out within the warranty period. When the costs for preventive maintenance and minimal repair are age-dependent, the optimal number of preventive maintenance actions, corresponding maintenance degrees, and the maintenance schedule for designing a PMW policy are derived here such that the expected total warranty cost is minimized. Under some reasonable conditions, we show that there exists a unique optimal PMW policy in which the product is maintained periodically with the same preventive maintenance degree. Using this property, an efficient algorithm is provided to search for the optimal policy. Some related models developed in the literature are discussed and these models are in fact special cases of the model proposed in this paper. Furthermore, when the life-time distribution of a product is Weibull, a closed-form expression of the optimal policy is obtained. Finally, the impact of providing preventive maintenance is evaluated through numerical examples.

A Generalized Age Replacement Model in the Presence of Inventory Constraints

1997 ◽  
Vol 04 (04) ◽  
pp. 395-412
Author(s):  
Shey-Huei Sheu
Keyword(s):  
Inventory Model ◽  
Minimal Repair ◽  
Special Cases ◽  
Replacement Model ◽  
Inventory Constraints ◽  
Realistic Assumption ◽  
Age Dependent ◽  
Unlimited Supply ◽  
Age Replacement ◽  
Replacement Problem

Many authors in the literature have studied the age replacement problem and its various modifications. One, generally, is asked to assume that at any time there is an unlimited supply of items available for replacement. This is often not a very realistic assumption. In this article we will examine a generalized age replacement model with age-dependent minimal repair when replacements are constrained by two simple inventory model. Various special cases are included. A numerical example is given to illustrate the method.

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.

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