Random Age Replacement Policies with Periodic Planning Times

2019 ◽  
Vol 26 (05) ◽  
pp. 1950023 ◽  
Author(s):  
Satoshi Mizutani ◽  
Xufeng Zhao ◽  
Toshio Nakagawa
Keyword(s):  
Weibull Distribution ◽  
Failure Time ◽  
Optimal Solutions ◽  
Expected Cost ◽  
Numerical Examples ◽  
Cost Rate ◽  
Modeling Approaches ◽  
Maintenance Policies ◽  
Age Replacement

The random age replacement policies discussed in literatures are helpful to complete the nonstopping works with random working cycles, however, maintenance policies are more easily performed at periodic times in real applications. For such a viewpoint, this paper proposes that age replacement policies are planned at periodic times while considering the random working cycles. Using the modeling approaches of replacement first and last policies, we discuss two models such that the unit is replaced at periodic times [Formula: see text] and working cycles [Formula: see text], whichever occurs first and whichever occurs last. The expected cost rate models are obtained and their optimal solutions for [Formula: see text] and [Formula: see text] are discussed. The comparisons between the policies of [Formula: see text] and [Formula: see text], and replacement first and last are made from the point of cost. Numerical examples are illustrated when the failure time has a Weibull distribution.

NOTE ON MTTF OF A PARALLEL SYSTEM

2011 ◽  
Vol 18 (01) ◽  
pp. 43-50 ◽  
Author(s):  
TOSHIO NAKAGAWA ◽  
WON YOUNG YUN
Keyword(s):  
Weibull Distribution ◽  
Asymptotic Method ◽  
Failure Time ◽  
Asymptotic Methods ◽  
Parallel System ◽  
Optimal Number ◽  
System Failure ◽  
Expected Cost ◽  
Cost Rate ◽  
Mean Time

A parallel system with n identical units is considered, and its mean time to system failure (MTTF) is obtained when the failure time is exponential. A simple asymptotic method of computing MTTF is proposed and its approximal values are compared with the exact MTTFs when the failure time has a Weibull distribution. It is of great interest that such asymptotic methods give good approximations to exact MTTFs. Furthermore, when the number of units is random, the MTTF and an optimal number of units to minimize the expected cost rate are derived.

GENERAL SEQUENTIAL IMPERFECT PREVENTIVE MAINTENANCE MODELS

2000 ◽  
Vol 07 (03) ◽  
pp. 253-266 ◽  
Author(s):  
DAMING LIN ◽  
MING J. ZUO ◽  
RICHARD C. M. YAM
Keyword(s):  
Weibull Distribution ◽  
Preventive Maintenance ◽  
Hazard Rate ◽  
Numerical Examples ◽  
Cost Rate ◽  
Effective Age ◽  
Rate Adjustment ◽  
The Mean ◽  
Mean Cost

This paper presents new sequential imperfect preventive maintenance (PM) models incorporating adjustment/improvement factors in hazard rate and effective age. The models are hybrid in the sense that they are combinations of the age reduction PM model and the hazard rate adjustment PM model. It is assumed that PM is imperfect: It not only reduces the effective age but also changes the hazard rate, while the hazard rate increases with the number of PMs. PM is performed in a sequence of intervals. The objective is to determine the optimal PM schedule to minimize the mean cost rate. Numerical examples for a Weibull distribution are given.

TWO COMMODITY COORDINATED INVENTORY SYSTEM WITH MARKOVIAN DEMAND

2006 ◽  
Vol 23 (04) ◽  
pp. 497-508 ◽  
Author(s):  
V. S. S. YADAVALLI ◽  
G. ARIVARIGNAN ◽  
N. ANBAZHAGAN
Keyword(s):  
Probability Distribution ◽  
Inventory System ◽  
Poisson Processes ◽  
Expected Cost ◽  
Numerical Examples ◽  
Cost Rate ◽  
Continuous Review ◽  
Long Run ◽  
Operational Characteristics ◽  
The One

This paper considers a two commodity continuous review inventory system. The demand points for each commodity are assumed to form Poisson processes. It is further assumed that the demand for the first commodity require the one unit of second commodity in addition to the first commodity with probability p1. Similarly, the demand for the second commodity require the one unit of first commodity in addition to the second commodity with probability p2. This assumption model the situation in which a buyer who intends to buy one particular commodity may also go for another commodity. The limiting probability distribution for the joint inventory levels is computed. Various operational characteristics, expression for the long run total expected cost rate is derived. The results are illustrated with numerical examples.

A COMPARISON STUDY OF REPLACEMENT POLICIES FOR A CUMULATIVE DAMAGE MODEL

2014 ◽  
Vol 21 (04) ◽  
pp. 1450021
Author(s):  
ALFONSUS JULANTO ENDHARTA ◽  
WON YOUNG YUN
Keyword(s):  
Damage Model ◽  
Cumulative Damage ◽  
Replacement Policy ◽  
Model Parameters ◽  
Comparison Study ◽  
Expected Cost ◽  
Numerical Examples ◽  
Cost Rate ◽  
Periodic Inspection ◽  
Cumulative Damage Model

A comparison study in basic preventive replacement (PR) policies based on a cumulative damage model is done. Three well-known PR policies (time-based, shock number-based, cumulative damage-based policies) are considered and the expected cost rate is used as the objective function to determine the optimal policy. Each policy requires certain information in the cumulative damage model. We evaluate the expected values of information by numerical examples and investigate the effect of model parameters and cost terms on the optimal expected cost rate. A damage-based replacement policy with periodic inspection is also proposed and compared with the three PR policies by numerical examples.

RANDOM AND AGE REPLACEMENT POLICIES

2010 ◽  
Vol 17 (01) ◽  
pp. 27-39 ◽  
Author(s):  
MINGCHIH CHEN ◽  
SATOSHI MIZUTANI ◽  
TOSHIO NAKAGAWA
Keyword(s):  
Damage Model ◽  
Working Time ◽  
Replacement Policy ◽  
Extended Model ◽  
Expected Cost ◽  
Cost Rate ◽  
Cumulative Damage Model ◽  
Age Replacement ◽  
Random Times ◽  
Operating Unit

This paper proposes a random and age replacement policy for an operating unit which works at random times. First, the unit is replaced before failure at a planned time T or at the completion of a working time, whichever occurs first. The expected cost rate is obtained. Next, as one extended model, the unit is replaced before failure at a number N of working times or at a planned time T. An optimal policy which minimizes the expected cost rate is discussed analytically, and its numerical example is given. Two modified models, where the unit is replaced at the first completion of the working time over time T or at number N, and it is replaced at time T or number N, whichever occurs last, are considered. Furthermore, we show that this corresponds to a cumulative damage model by replacing shock with work. Finally, one optimization problem of how much time to preset for scheduling the completion of N works is proposed.

On optimal life extension for degrading systems

2020 ◽  
Vol 234 (3) ◽  
pp. 487-495
Author(s):  
Ji Hwan Cha ◽  
Maxim Finkelstein
Keyword(s):  
Complex Systems ◽  
Preventive Maintenance ◽  
Life Extension ◽  
Optimal Solutions ◽  
Numerical Examples ◽  
Cost Rate ◽  
Noticeable Increase ◽  
Novel Approach ◽  
Long Run ◽  
Useful Life

We consider life extension models for critical, complex systems with relatively long lifecycles. In contrast to traditional optimal preventive maintenance that usually minimizes the corresponding long run cost rate, a finite number of preventive maintenances are performed to increase the expected lifetime of these systems in an optimal way. The cases of periodic and aperiodic preventive maintenance actions are discussed. The proposed novel approach to life extension allows for simple sensitivity analysis with respect to parameters of the model. The obtained optimal solutions can result in a noticeable increase in the useful life of complex systems. Our findings are illustrated by numerical examples.

Periodic and sequential preventive maintenance policies

1986 ◽  
Vol 23 (2) ◽  
pp. 536-542 ◽  
Author(s):  
Toshio Nakagawa
Keyword(s):  
Weibull Distribution ◽  
Preventive Maintenance ◽  
Minimal Repair ◽  
Expected Cost ◽  
Optimal Policies ◽  
Failure Distribution ◽  
Maintenance Policies

This paper considers periodic and sequential preventive maintenance (PM) policies for the system with minimal repair at failure: the PM is done (i) at periodic times kx and (ii) at constant intervals xk (k = 1, 2, ···, N). The system has a different failure distribution between PM'S and is replaced at the Nth PM. The optimal policies which minimize the expected cost rates are discussed. The optimal x and N of periodic PM and {xk} of sequential PM are easily computed in a Weibull distribution case.

The Optimal Lot Sizing for Unreliable Economic Manufacturing Model

1997 ◽  
Vol 04 (04) ◽  
pp. 413-426 ◽  
Author(s):  
Tadashi Dohi ◽  
Yasunori Yamada ◽  
Naoto Kaio ◽  
Shunji Osaki
Keyword(s):  
Cost Function ◽  
Production Process ◽  
Optimal Policy ◽  
Lot Sizing ◽  
Lot Size ◽  
Expected Cost ◽  
Numerical Examples ◽  
Machine Breakdown ◽  
Special Cases ◽  
Age Replacement

This paper considers the optimal policy for an economic manufacturing model with stochastic machine breakdown and repair. The expected cost function is formulated and the optimal age replacement-like policy which minimizes it is derived analytically. The detailed properties on the resulting optimal lot size are examined for some special cases. Finally, numerical examples are devoted to show that the effect of corrective maintenance operation in the production process is remarkable.

AN AGE-BASED MAINTENANCE STRATEGY FOR A DEGRADATION-THRESHOLD-SHOCK-MODEL FOR A SYSTEM SUBJECTED TO MULTIPLE DEFECTS

2013 ◽  
Vol 30 (05) ◽  
pp. 1350016 ◽  
Author(s):  
I. T. CASTRO
Keyword(s):  
Poisson Process ◽  
Shock Model ◽  
Maintenance Strategy ◽  
External Shocks ◽  
Internal Defects ◽  
Expected Cost ◽  
Numerical Examples ◽  
Cost Rate ◽  
Gamma Processes ◽  
Theoretical Results

A system subject to internal defects and external shocks is analyzed in this paper. Internal defects initiate following a nonhomogeneous Poisson process (NHPP) and they grow according to deterioration processes modeled as gamma processes. A corrective replacement is performed when the deterioration of a defect exceeds a failure threshold. The system is subject to external shocks. After an external shock, the system is replaced with probability 1 – p and is minimally repaired with probability p. The system is preventively replaced at the age of T. Costs are associated with the maintenance actions. The value of T that minimizes the expected cost rate is obtained analytically. Numerical examples are showed to illustrate the theoretical results.

Age Replacement Policies with Shortage and Excess Costs

2018 ◽  
Vol 25 (06) ◽  
pp. 1850026
Author(s):  
Mingchih Chen ◽  
Xufeng Zhao ◽  
Toshio Nakagawa
Keyword(s):  
Failure Time ◽  
Expected Cost ◽  
Shortage Cost ◽  
Excess Costs ◽  
Failure Cost ◽  
Age Replacement ◽  
Operation Cost ◽  
Replacement Time

It has been proposed in recent literatures that if replacement time is planned too early prior to failure time, a waste of operation cost, i.e., excess costs, would incur because the system might run for an additional period of time to complete critical operations; and if the replacement time is too late after failure, a great failure cost, i.e., shortage cost, is incurred due to the delay in time of the carelessly scheduled replacement. The above notion of shortage and excess costs are taken into consideration for the replacement first, replacement last and replacement overtime models in this paper. We obtain the expected cost rates and their optimum replacement times. Comparisons among these optimum times are made analytically and numerically.

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