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 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.

AVAILABILITY OF WEAPON SYSTEMS WITH LOGISTIC DELAYS: A SIMULATION APPROACH

2003 ◽  
Vol 10 (04) ◽  
pp. 429-443 ◽  
Author(s):  
K. SADANANDA UPADHYA ◽  
N. K. SRINIVASAN
Keyword(s):  
Time Distribution ◽  
Failure Time ◽  
Discrete Event ◽  
Repair Process ◽  
Fighter Aircraft ◽  
Failure Time Distribution ◽  
Weapon Systems ◽  
Monte Carlo Techniques ◽  
Event Simulation ◽  
Transient Solutions

The availability of weapon systems such as fighter aircraft, battle tanks and warships during high intensity conflicts becomes low. In this paper the availability of fighter aircraft with five major subsystems (structures, engine, avionics, electrical and environmental) are considered. This depends mainly on attrition factors (failure due to unreliability and failure due to battle damage) and logistic delays, which affect repair process. We develop a simulation model considering the fighter aircraft as the weapon system for arriving at transient solutions for availability with logistic delays. The methodology is based on discrete event simulation using Monte Carlo techniques. The failure time distribution (Weibull) for different subsystems, repair time distribution (exponential) and logistic delay time distribution (lognormal) were chosen with suitable parameters. The results indicate the pronounced decrease in availability (to as low as 20% in some cases) due to logistic delays. The results are however sensitive to the reliability, maintainability and logistic delay parameters.

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.

scholarly journals Profit Analysis of Non Identical Repairable Units Subject to Two Phase Repair of System

2019 ◽  
pp. 1-6
Author(s):  
Raeesa Bashir ◽  
Nafeesa Bashir ◽  
Shakeel A. Mir
Keyword(s):  
Time Distribution ◽  
Failure Time ◽  
Two Phase ◽  
Failure Time Distribution ◽  
Profit Analysis

The paper deals with the profit analysis of three non-identical units A, B, and C in which either Unit A or one of the units B and C should work for the successful functioning of the system. Two types of repairman are available in the system viz. Ordinary and Expert repairman. The expert repairman is called only when the system breaks down. Unit A gets priority for repair and is repaired by expert repairman while as Unit B and C is repaired by ordinary repairman if the system doesn’t fail totally. The failure time distribution of unit-A, B and C are taken as exponential. The distribution of time to repair of units is assumed to be general.

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