OPTIMAL AGE REPLACEMENT AND INSPECTION POLICIES WITH RANDOM FAILURE AND REPLACEMENT TIMES

2011 ◽  
Vol 18 (05) ◽  
pp. 405-416 ◽  
Author(s):  
TOSHIO NAKAGAWA ◽  
XUFENG ZHAO ◽  
WON YOUNG YUN
Keyword(s):  
Finite Time ◽  
Failure Time ◽  
Replacement Policy ◽  
Inspection Cost ◽  
Preventive Replacement ◽  
Optimal Policies ◽  
Excess Costs ◽  
Random Failure ◽  
Age Replacement ◽  
Replacement Time

It is well-known in the standard age replacement policy that a finite preventive replacement time does not exist when the failure time is exponential and the optimal preventive replacement time is nonrandom. It is shown that when the failure time is exponential, a finite time exists by introducing the shortage and excess costs. In addition, the random age replacement is proposed and similar discussions are made. Furthermore, the periodic and random inspection policies are taken up, and their optimal policies are shown to correspond theoretically to those of the age replacement ones. It is shown finally that when the random inspection cost is the half of the periodic one, two expected costs are almost the same.

AN OPPORTUNITY-BASED AGE REPLACEMENT POLICY CONSIDERING WARRANTY

1999 ◽  
Vol 06 (03) ◽  
pp. 229-236 ◽  
Author(s):  
BERMAWI P. ISKANDAR ◽  
HIROAKI SANDOH
Keyword(s):  
Time Distribution ◽  
Failure Time ◽  
Sufficient Conditions ◽  
Replacement Policy ◽  
Minimal Repair ◽  
Failure Time Distribution ◽  
Warranty Period ◽  
Preventive Replacement ◽  
Long Run ◽  
Age Replacement

This study discusses an opportunity-based age replacement policy for a system which has a warranty period (0, S]. When the system fails at its age x≤S, a minimal repair is performed. If an opportunity occurs to the system at its age x for S<x<T, we take the opportunity with probability p to preventively replace the system, while we conduct a corrective replacement when it fails on (S, T). Finally if its age reaches T, we execute a preventive replacement. Under this replacement policy, the design variable is T. For the case where opportunities occur according to a Poisson process, a long-run average cost of this policy is formulated under a general failure time distribution. It is, then, shown that one of the sufficient conditions where a unique finite optimal T* exists is that the failure time distribution is IFR (Increasing Failure Rate). Numerical examples are also presented for the Weibull failure time distribution.

Age-replacement policy and optimal work size

2002 ◽  
Vol 39 (2) ◽  
pp. 296-311 ◽  
Author(s):  
Jie Mi
Keyword(s):  
Time Distribution ◽  
Failure Time ◽  
Repair Time ◽  
Replacement Policy ◽  
Average Amount ◽  
Failure Time Distribution ◽  
Long Run ◽  
Random Failure ◽  
Age Replacement ◽  
Work Size

Suppose that there is a sequence of programs or jobs that are scheduled to be executed one after another on a computer. A program may terminate its execution because of the failure of the computer, which will obliterate all work the computer has accomplished, and the program has to be run all over again. Hence, it is common to save the work just completed after the computer has been working for a certain amount of time, say y units. It is assumed that it takes a certain time to perform a save. During the saving process, the computer is still subject to random failure. No matter when the computer failure occurs, it is assumed that the computer will be repaired completely and the repair time will be negligible. If saving is successful, then the computer will continue working from the end of the last saved work; if the computer fails during the saving process, then only unsaved work needs to be repeated. This paper discusses the optimal work size y under which the long-run average amount of work saved is maximized. In particular, the case of an exponential failure time distribution is studied in detail. The properties of the optimal age-replacement policy are also derived when the work size y is fixed.

BOOTSTRAP CONFIDENCE INTERVAL OF OPTIMAL AGE REPLACEMENT POLICY

2014 ◽  
Vol 21 (04) ◽  
pp. 1450018 ◽  
Author(s):  
SHUNSUKE TOKUMOTO ◽  
TADASHI DOHI ◽  
WON YOUNG YUN
Keyword(s):  
Confidence Interval ◽  
Failure Time ◽  
Interval Estimation ◽  
Parametric Bootstrap ◽  
Replacement Policy ◽  
Time Data ◽  
Age Replacement ◽  
Replacement Problem ◽  
Two Parameter ◽  
Replacement Time

In this paper, we consider an interval estimation of the age replacement problem, where the underlying failure time probability is given by the two-parameter Weibull distribution. The parametric bootstrap is used to obtain the probability distribution of an estimator for the optimal age replacement time minimizing the expected cost per unit time in the steady state. We focus on both cases with complete and incomplete samples of failure time data, and calculate not only the higher moments of an estimator for the optimal age replacement time but also the confidence interval.

Age-replacement policy and optimal work size

2002 ◽  
Vol 39 (02) ◽  
pp. 296-311 ◽  
Author(s):  
Jie Mi
Keyword(s):  
Time Distribution ◽  
Failure Time ◽  
Repair Time ◽  
Replacement Policy ◽  
Average Amount ◽  
Failure Time Distribution ◽  
Long Run ◽  
Random Failure ◽  
Age Replacement ◽  
Work Size

Suppose that there is a sequence of programs or jobs that are scheduled to be executed one after another on a computer. A program may terminate its execution because of the failure of the computer, which will obliterate all work the computer has accomplished, and the program has to be run all over again. Hence, it is common to save the work just completed after the computer has been working for a certain amount of time, say y units. It is assumed that it takes a certain time to perform a save. During the saving process, the computer is still subject to random failure. No matter when the computer failure occurs, it is assumed that the computer will be repaired completely and the repair time will be negligible. If saving is successful, then the computer will continue working from the end of the last saved work; if the computer fails during the saving process, then only unsaved work needs to be repeated. This paper discusses the optimal work size y under which the long-run average amount of work saved is maximized. In particular, the case of an exponential failure time distribution is studied in detail. The properties of the optimal age-replacement policy are also derived when the work size y is fixed.

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.

GRAPHICAL APPROACH TO REPLACEMENT POLICY OF A K-OUT-OF-N SYSTEM SUBJECT TO SHOCKS

2003 ◽  
Vol 10 (01) ◽  
pp. 55-68 ◽  
Author(s):  
MUH-GUEY JUANG ◽  
SHEY-HUEI SHEU
Keyword(s):  
Real Data ◽  
Solution Procedure ◽  
Replacement Policy ◽  
Minimal Repair ◽  
Statistical Solution ◽  
Graphical Approach ◽  
Optimal Replacement ◽  
Optimal Policies ◽  
Age Replacement ◽  
Replacement Time

This paper deals with the problem of determining an optimal age replacement by incorporating minimal repair, planned replacement, and unplanned replacement into a k-out-of-n system subject to shocks. In particular, two kinds of solution procedures are discussed to obtain the optimal replacement age, one is a straightforward procedure, and the other is a graphical approach based on the Total Time on Test (TTT) concept. A statistical solution procedure for estimating the optimal replacement time is proposed, and the optimal policies are obtained directly from real data.

A weak derivative approach to optimization of threshold parameters in a multicomponent maintenance system

2001 ◽  
Vol 38 (02) ◽  
pp. 386-406 ◽  
Author(s):  
Bernd Heidergott
Keyword(s):  
Optimization Problems ◽  
Estimation Algorithm ◽  
Replacement Policy ◽  
Cost Performance ◽  
Weak Derivative ◽  
Preventive Replacement ◽  
Maintenance System ◽  
Threshold Optimization ◽  
Age Replacement ◽  
The Cost

We consider a multicomponent maintenance system controlled by an age replacement policy: when one of the components fails, it is immediately replaced; all components older than a threshold age θ are preventively replaced. Costs are associated with each maintenance action, such as replacement after failure or preventive replacement. We derive a weak derivative estimator for the derivative of the cost performance with respect to θ. The technique is quite general and can be applied to many other threshold optimization problems in maintenance. The estimator is easy to implement and considerably increases the efficiency of a Robbins-Monro type of stochastic approximation algorithm. The paper is self-contained in the sense that it includes a proof of the correctness of the weak derivative estimation algorithm.

Optimal repair/replacement policy for a general repair model

2001 ◽  
Vol 33 (1) ◽  
pp. 206-222 ◽  
Author(s):  
Xiaoyue Jiang ◽  
Viliam Makis ◽  
Andrew K. S. Jardine
Keyword(s):  
Average Cost ◽  
Failure Time ◽  
Operating Time ◽  
Replacement Policy ◽  
Repair Cost ◽  
Virtual Age ◽  
Preventive Replacement ◽  
Long Run ◽  
Special Cases ◽  
Cost Limit

In this paper, we study a maintenance model with general repair and two types of replacement: failure and preventive replacement. When the system fails a decision is made whether to replace or repair it. The repair degree that affects the virtual age of the system is assumed to be a random function of the repair-cost and the virtual age at failure time. The system can be preventively replaced at any time before failure. The objective is to find the repair/replacement policy minimizing the long-run expected average cost per unit time. It is shown that a generalized repair-cost-limit policy is optimal and the preventive replacement time depends on the virtual age of the system and on the length of the operating time since the last repair. Computational procedures for finding the optimal repair-cost limit and the optimal average cost are developed. This model includes many well-known models as special cases and the approach provides a unified treatment of a wide class of maintenance models.

scholarly journals Failure-Correlated Opportunity-based Age Replacement Models

2019 ◽  
Vol 27 (02) ◽  
pp. 2040008
Author(s):  
Tadashi Dohi ◽  
Hiroyuki Okamura
Keyword(s):  
Arrival Time ◽  
Failure Time ◽  
Unit System ◽  
Hazard Gradient ◽  
Age Replacement ◽  
The Cost ◽  
Bivariate Copula ◽  
Bivariate Probability ◽  
Vector Valued ◽  
Replacement Time

In this paper, we extend the existing opportunity-based age replacement policies by taking account of dependency between the failure time and the arrival time of a replacement opportunity for one-unit system. Based on the bivariate probability distribution function of the failure time and the arrival time of the opportunity, we focus on two opportunity-based age replacement problems and characterize the cost-optimal age replacement policies which minimize the relevant expected costs, with the hazard gradient, which is a vector-valued bivariate hazard rate. Through numerical examples with the Farlie–Gumbel–Morgenstern bivariate copula and the Gaussian bivariate copula having the general marginal distributions, we investigate the dependence of correlation between the failure time and the opportunistic replacement time on the age replacement policies.

scholarly journals Penentuan Interval Waktu Penggantian Komponen Kritis Pada Mesin Volpack Menggunakan Metode Age Replacement

2017 ◽  
Vol 16 (2) ◽  
pp. 92
Author(s):  
Yanuar Yuda Prawiro
Keyword(s):  
Cost Savings ◽  
Solenoid Valve ◽  
Time Interval ◽  
Preventive Replacement ◽  
Replacement Method ◽  
Schedule Interval ◽  
Age Replacement ◽  
Engine Components ◽  
A Company ◽  
Replacement Time

CV. Cool Clean is a company engaged in packing tissue. During this time the company only perform corrective action that causes disruption of the production process due to frequent damage of a sudden the engine components volpack. In this study used a model of preventive replacement that can reduce downtime and costs. The method used to obtain the schedule interval a critical component is age replacement method. Seal heater obtained replacement time interval of 30 days with a 22% reduction in downtime. Replacement interval for knife foil is 26 days with a 27% reduction in downtime. Replacement interval for solenoid valve is30 days with a 29% reduction in downtime. Replacement interval forOring seal is 18 days with a 29% reduction in downtime. Replacement interval for needle bearing is 62 days with a 25% reduction in downtime. Results of this study also showed that by applying age replacement can save costs for seal heater Rp. 974.000 or 23%. Knife foil cost savings of Rp. 1.251.409 or 22%. Solenoid valve cost savings of Rp.546.539 or 24%. Oring seal cost savings of Rp. 350.096 or 26%. And needle bearing cost savings of Rp. 196.712 or 26%.

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