Optimal replacement under a minimal repair strategy—a general failure model

In this paper we generalize the minimal repair replacement model introduced by Barlow and Hunter (1960). We assume that there is available information about the underlying condition of the system, for instance through measurements of wear characteristics and damage inflicted on the system. We assume furthermore that the system failure rate and the expected cost of a repair/replacement at any point of time are adapted to this information. At time t = 0 a new system is installed. At a stopping time T, based on the information about the condition of the system, the system is replaced by a new and identical one, and the process is repeated. Failures that occur before replacement are rectified through minimal repair. We assume that a minimal repair changes neither the age of the system nor the information about the condition of the system. The problem is to find a T which minimizes the total expected discounted cost. Under appropriate conditions an optimal T is found. Some generalizations and special cases are given.

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Burn-in procedures for a generalized model

Journal of Applied Probability ◽

10.1017/s0021900200020027 ◽

2001 ◽

Vol 38 (02) ◽

pp. 542-553 ◽

Cited By ~ 25

Author(s):

Ji Hwan Cha

Keyword(s):

The Other ◽

Replacement Policy ◽

Type I ◽

Type Ii ◽

Failure Model ◽

Minimal Repair ◽

Optimal Replacement ◽

Complete Repair ◽

Optimal Replacement Policy ◽

Type Of Failure

In this paper two burn-in procedures for a general failure model are considered. There are two types of failure in the general failure model. One is Type I failure (minor failure) which can be removed by a minimal repair or a complete repair and the other is Type II failure (catastrophic failure) which can be removed only by a complete repair. During a burn-in process, with burn-in Procedure I, the failed component is repaired completely regardless of the type of failure, whereas, with burn-in Procedure II, only minimal repair is done for the Type I failure and a complete repair is performed for the Type II failure. In field use, the component is replaced by a new burned-in component at the ‘field use age’ T or at the time of the first Type II failure, whichever occurs first. Under the model, the problems of determining optimal burn-in time and optimal replacement policy are considered. The two burn-in procedures are compared in cases when both the procedures are applicable.

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A Generalized Age Replacement Model in the Presence of Inventory Constraints

International Journal of Reliability Quality and Safety Engineering ◽

10.1142/s0218539397000291 ◽

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.

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Burn-in procedures for a generalized model

Journal of Applied Probability ◽

10.1239/jap/996986761 ◽

2001 ◽

Vol 38 (2) ◽

pp. 542-553 ◽

Cited By ~ 38

Author(s):

Ji Hwan Cha

Keyword(s):

The Other ◽

Replacement Policy ◽

Type I ◽

Type Ii ◽

Failure Model ◽

Minimal Repair ◽

Optimal Replacement ◽

Complete Repair ◽

Optimal Replacement Policy ◽

Type Of Failure

In this paper two burn-in procedures for a general failure model are considered. There are two types of failure in the general failure model. One is Type I failure (minor failure) which can be removed by a minimal repair or a complete repair and the other is Type II failure (catastrophic failure) which can be removed only by a complete repair. During a burn-in process, with burn-in Procedure I, the failed component is repaired completely regardless of the type of failure, whereas, with burn-in Procedure II, only minimal repair is done for the Type I failure and a complete repair is performed for the Type II failure. In field use, the component is replaced by a new burned-in component at the ‘field use age’ T or at the time of the first Type II failure, whichever occurs first. Under the model, the problems of determining optimal burn-in time and optimal replacement policy are considered. The two burn-in procedures are compared in cases when both the procedures are applicable.

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SOME RESULTS ON A NEW CLASS OF SHOCK MODELS

Asia Pacific Journal of Operational Research ◽

10.1142/s021759591000282x ◽

2010 ◽

Vol 27 (04) ◽

pp. 503-515

Author(s):

ALAGAR RANGAN ◽

AYŞE TANSU

Keyword(s):

Failure Time ◽

System Failure ◽

First Passage ◽

New Class ◽

Optimal Replacement ◽

Random Threshold ◽

Shock Models ◽

Special Cases ◽

Replacement Problem ◽

First Passage Problem

Traditional shock models view system failure time as a first passage problem. Yeh Lam proposed a new class of models called δ-shock models in which failure was dependent on the frequency of shocks. The present work generalizes Yeh Lam's results for renewal shock arrivals and random threshold. Several special cases and an optimal replacement problem are also discussed.

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Extended optimal replacement model with random minimal repair costs

European Journal of Operational Research ◽

10.1016/0377-2217(93)e0364-4 ◽

1995 ◽

Vol 85 (3) ◽

pp. 636-649 ◽

Cited By ~ 93

Author(s):

Shey-Huei Sheu ◽

William S. Griffith ◽

Toshio Nakagawa

Keyword(s):

Minimal Repair ◽

Optimal Replacement ◽

Repair Costs ◽

Replacement Model

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When to Substitute a Missing Upper Lateral With a Canine: A Simplified Approach

The Journal of Indian Orthodontic Society ◽

10.1177/0301574220980540 ◽

2021 ◽

pp. 030157422098054

Author(s):

Renu Datta

Keyword(s):

Anterior Segment ◽

Specific Treatment ◽

Simplified Approach ◽

Special Cases ◽

Randomized Control ◽

The One ◽

Individual Presentation ◽

Available Information ◽

Missing Tooth ◽

Made In

Introduction: The upper lateral incisor is the most commonly missing tooth in the anterior segment. It leads to esthetic and functional imbalance for the patients. The ideal solution is the one that is most conservative and which fulfills the functional and esthetic needs of the concerned individual. Canine substitution is evolving to be the treatment of choice in most of the cases, because of its various advantages. These are special cases that need more time and effort from the clinicians due to space discrepancy in the upper and lower arches, along with the presentation of individual malocclusion. Aims and Objectives: Malocclusion occurring due to missing laterals is more complex, needing more time and effort from the clinicians because of space discrepancy, esthetic compromise, and individual presentation of the malocclusion. An attempt has been made in this article to review, evaluate, and tabulate the important factors for the convenience of clinicians. Method: All articles related to canine substitution were searched in the electronic database PubMed, and the important factors influencing the decision were reviewed. After careful evaluation, the checklist was evolved. Result: The malocclusions in which canine substitution is the treatment of choice are indicated in the tabular form for the convenience of clinicians. Specific treatment-planning considerations and biomechanics that can lead to an efficient and long-lasting result are also discussed. Conclusion: The need of the hour is an evidence-based approach, along with a well-designed prospective randomized control trial to understand the importance of each factor influencing these cases. Until that time, giving the available information in a simplified way can be a quality approach to these cases.

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Replacement Model for Street Lighting Systems

Nigerian Journal of Technology ◽

10.4314/njt.v40i1.8 ◽

2021 ◽

Vol 40 (1) ◽

pp. 49-55

Author(s):

A.M. Usman ◽

Y.A. Adediran ◽

A.O. Otuoze ◽

O.O. Mohammed ◽

O.S. Zakariyya

Keyword(s):

Field Survey ◽

Optimal Time ◽

North Central ◽

Street Lighting ◽

Maintenance Costs ◽

Optimal Replacement ◽

Replacement Model ◽

Lighting Systems ◽

The University ◽

Replacement Time

Replacing failed bulbs of streetlights in a location can be very tasking and expensive if the optimal time for replacement is not determined. In this paper, a model has been developed that helps to establish the optimal time for the replacement of streetlight bulbs. Burnt-out bulbs are replaced individually when they fail, and group replacement is carried out on all bulbs after a specified time. The costs for both individual replacement and group replacement are determined. The developed model was applied to locally sourced data from a field survey of a streetlight installation at the University of Ilorin, Ilorin, North-central Nigeria. The model gave the optimum replacement time of burnt-out bulbs as the eighteenth week when applied to the data used in this work. The optimum replacement time will be dependent on the dataset used. This makes the developed model useful in establishing the optimal replacement time of any stochastically failing items that are in large quantities. The model will help to reduce maintenance costs for facility managers.

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A general shock model for a reliability system

Journal of Applied Probability ◽

10.1017/s002190020001812x ◽

2000 ◽

Vol 37 (04) ◽

pp. 925-935 ◽

Cited By ~ 5

Author(s):

Georgios Skoulakis

Keyword(s):

Distribution Function ◽

Point Process ◽

Renewal Process ◽

General System ◽

System Structure ◽

Random Numbers ◽

System Failure ◽

Shock Model ◽

Stieltjes Transform ◽

Special Cases

We study a reliability system subject to shocks generated by a renewal point process. When a shock occurs, components fail independently of each other with equal probabilities that are random numbers drawn from a distribution that may differ from shock to shock. We first consider the case of a parallel system and derive closed expressions for the Laplace-Stieltjes transform and the expectation of the time to system failure and for its density in the case that the distribution function of the renewal process possesses a density. We then treat a more general system structure, which has some very important special cases, such as k-out-of-n:F systems, and derive analogous formulae.

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Optimal replacement under a general failure model

Advances in Applied Probability ◽

10.2307/1426944 ◽

1978 ◽

Vol 10 (2) ◽

pp. 431-451 ◽

Cited By ~ 75

Author(s):

Bo Bergman

Keyword(s):

Threshold Value ◽

Rate Function ◽

The State ◽

Failure Rate Function ◽

State Variable ◽

Optimal Replacement ◽

State Dependent ◽

Long Run ◽

Special Cases ◽

Dependent Failure

Replacement policies based on measurements of some increasing state variable, e.g. wear, accumulated damage or accumulated stress, are studied in this paper. It is assumed that the state measurements may be regarded as realizations of some stochastic process and that the proneness to failure of an active unit may be described by an increasing state-dependent failure rate function. Average long-run cost per unit time is considered. The optimal replacement rule is shown to be a control limit rule, i.e. it is optimal to replace either at failure or when the state variable has reached some threshold value, whichever occurs first. The optimal rule is determined. Some generalizations and special cases are given.

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