Optimal stopping in a semi-Markov shock model

1978 ◽  
Vol 15 (03) ◽  
pp. 629-634 ◽  
Author(s):  
Dror Zuckerman
Keyword(s):  
Failure Time ◽  
Stopping Time ◽  
Shock Model ◽  
Failure Model ◽  
Accumulated Damage ◽  
Shock Process ◽  
Long Run ◽  
Semi Markov Process ◽  
Failure Cost ◽  
Damage Process

We examine a failure model for a system existing in a random environment. The system accumulates damage through a shock process and the failure time depends on the accumulated damage in the system. The cumulative damage process is assumed to be a semi-Markov process. Upon failure the system must be replaced by a new identical one and a failure cost is incurred. If the system is replaced before failure, a smaller cost is incurred. We allow a controller to replace the system at any stopping time before failure time. We consider the problem of specifying a replacement rule which minimizes the total long-run average cost per unit time.

Optimal stopping in a semi-Markov shock model

1978 ◽  
Vol 15 (3) ◽  
pp. 629-634 ◽  
Author(s):  
Dror Zuckerman
Keyword(s):  
Failure Time ◽  
Stopping Time ◽  
Shock Model ◽  
Failure Model ◽  
Accumulated Damage ◽  
Shock Process ◽  
Long Run ◽  
Semi Markov Process ◽  
Failure Cost ◽  
Damage Process

We examine a failure model for a system existing in a random environment. The system accumulates damage through a shock process and the failure time depends on the accumulated damage in the system. The cumulative damage process is assumed to be a semi-Markov process. Upon failure the system must be replaced by a new identical one and a failure cost is incurred. If the system is replaced before failure, a smaller cost is incurred. We allow a controller to replace the system at any stopping time before failure time. We consider the problem of specifying a replacement rule which minimizes the total long-run average cost per unit time.

FAILURE TIME DISTRIBUTION UNDER A δ-SHOCK MODEL AND ITS APPLICATION TO ECONOMIC DESIGN OF SYSTEMS

1999 ◽  
Vol 06 (03) ◽  
pp. 237-247 ◽  
Author(s):  
ZEHUI LI ◽  
LING-YAU CHAN ◽  
ZHIXIN YUAN
Keyword(s):  
Poisson Distribution ◽  
Time Distribution ◽  
Failure Time ◽  
Time Lag ◽  
Economic Design ◽  
Point Of View ◽  
Shock Model ◽  
Failure Model ◽  
Failure Time Distribution ◽  
As If

Suppose that shocks arrive and act on a system according to a Poisson distribution with mean rate of arrival equal to λ shock(s) per unit time. A δ-shock failure model is proposed in this paper, which assumes that when a system is acted on by a shock, it will recover fully in time δ(>0), and after that it will function as if no shock had occurred before. If the time lag between two successive shocks is less than δ, the second shock will cause failure of the system. Theoretical expressions related to the distribution of the failure time of the system are derived. These results can be used to optimize the design of a system from a costing point of view.

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.

A stochastic covariate failure model for assessing system reliability

2001 ◽  
Vol 38 (03) ◽  
pp. 761-767 ◽  
Author(s):  
Nader Ebrahimi
Keyword(s):  
System Reliability ◽  
Alternative Model ◽  
Failure Time ◽  
Failure Mechanisms ◽  
Failure Model ◽  
Proposed Model ◽  
Deterioration Process

Many failure mechanisms can be traced to an underlying deterioration process, and stochastically changing covariates may influence this process. In this paper we propose an alternative model for assessing a system's reliability. The proposed model expresses the failure time of a system in terms of a deterioration process and covariates. When it is possible to measure deterioration as well as covariates, our model provides more information than failure time for the purpose of assessing and improving system reliability. We give several properties of our proposed model and also provide an example.

Failure distributions of shock models

1980 ◽  
Vol 17 (03) ◽  
pp. 745-752 ◽  
Author(s):  
Gary Gottlieb
Keyword(s):  
Failure Rate ◽  
Sufficient Conditions ◽  
Cumulative Damage ◽  
Shock Model ◽  
Life Distribution ◽  
Increasing Failure Rate ◽  
Shock Models ◽  
Damage Process

A single device shock model is studied. The device is subject to some damage process. Under the assumption that as the cumulative damage increases, the probability that any additional damage will cause failure increases, we find sufficient conditions on the shocking process so that the life distribution will be increasing failure rate.

A hybrid preventive maintenance model for systems with partially observable degradation

2020 ◽  
Vol 31 (3) ◽  
pp. 345-365 ◽  
Author(s):  
Maxim Finkelstein ◽  
Ji Hwan Cha ◽  
Gregory Levitin
Keyword(s):  
Preventive Maintenance ◽  
Replacement Policy ◽  
Hybrid Strategy ◽  
Cost Rate ◽  
Shot Noise Process ◽  
Shock Process ◽  
Long Run ◽  
Age Replacement ◽  
Partially Observable ◽  
Maintenance Model

Abstract A new model of hybrid preventive maintenance of systems with partially observable degradation is developed. This model combines condition-based maintenance with age replacement maintenance in the proposed, specific way. A system, subject to a shock process, is replaced on failure or at some time ${T}_S$ if the number of shocks experienced by this time is greater than or equal to m or at time $T>{T}_S$ otherwise, whichever occurs first. Each shock increases the failure rate of the system at the random time of its occurrence, thus forming a corresponding shot-noise process. The real deterioration of the system is partially observed via observation of the shock process at time ${T}_S$. The corresponding optimization problem is solved and a detailed numerical example demonstrates that the long-run cost rate for the proposed optimal hybrid strategy is smaller than that for the standard optimal age replacement policy.

RELIABILITY MEASURES OF A COLD STANDBY SYSTEM WITH PREVENTIVE MAINTENANCE AND REPAIR

2013 ◽  
Vol 20 (06) ◽  
pp. 1350022 ◽  
Author(s):  
S. C. MALIK ◽  
SUDESH K. BARAK
Keyword(s):  
Preventive Maintenance ◽  
Failure Time ◽  
Reliability Measures ◽  
Maintenance And Repair ◽  
Regenerative Point ◽  
Cold Standby ◽  
Semi Markov Process ◽  
Standby System ◽  
Regenerative Point Technique ◽  
Negative Exponential

The purpose of the present study is to determine reliability measures of a two-unit cold standby system with preventive maintenance and repair. The units are identical in nature subject to constant failure from normal mode. Preventive maintenance of the operative unit is carried out after a pre-specific time "t" up to which no failure occurs. However, repair of the unit is done at its failure. The unit works as new after repair and preventive maintenance. The switch devices are perfect. The distributions of failure time and the time by which unit undergoes for preventive maintenance are taken as negative exponential while that of preventive maintenance and repair times are assumed as arbitrary with different probability density functions. The random variables associated with failure, preventive maintenance and repair times are statistically independent. The semi-Markov process and regenerative point technique are adopted to derive the expressions for system performance measures in steady state. The graphical behavior of MTSF, availability and profit function have been observed with respect to preventive maintenance rate for particular values of other parameters and costs.

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.

Long-run dynamics between cost of quality and quality performance

2019 ◽  
Vol 36 (8) ◽  
pp. 1438-1453 ◽  
Author(s):  
Sebastian Sturm ◽  
Gernot Kaiser ◽  
Evi Hartmann
Keyword(s):  
Scale Effect ◽  
Cost Reduction ◽  
Secondary Data ◽  
Quality Performance ◽  
Data Set ◽  
Quality Cost ◽  
Content Type ◽  
Cost Of Quality ◽  
Long Run ◽  
Failure Cost

Purpose The dynamics of quality performance and quality cost are gaining renewed interest in quality management literature. Using large sample secondary data, the purpose of this paper is to build up empirical evidence for increasing quality performance in manufacturing in the long-run. The authors then examine whether it is possible to reduce internal and external failure cost over time without increasing prevention and appraisal expenditures in return. Finally, a scale effect in reducing quality cost is measured to clarify the long-run dynamics between quality cost and quality performance. Design/methodology/approach The authors conduct statistical analysis on a large sample secondary data set to reveal relationships between total cost of quality, its components and overall quality performance. Findings Significantly higher quality performance and lower quality cost are observed in the long-run. Quality costs grow less than half as fast as sales volume, pointing to a significant scale effect in quality cost reduction. Practical implications Businesses can use these implications for targeting failure costs and budgeting appraisal and prevention costs. Based on company-specific historical learning behavior through prevention and appraisal activities, an increasingly reliable prognosis of failure cost shall be possible. Originality/value For the first time, quality performance and cost dynamics are assessed using a secondary data set with more than 400 observations. A scale effect for quality cost reduction is measured. The results are of great importance to quality management practice and research.

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