scholarly journals Bayes estimation of the reliability function and hazard rate of a weibull failure time distribution

1986 ◽  
Vol 1 (2) ◽  
pp. 47-56 ◽  
Author(s):  
S. K. Sinha
Keyword(s):  
Time Distribution ◽  
Hazard Rate ◽  
Failure Time ◽  
Reliability Function ◽  
Bayes Estimation ◽  
Failure Time Distribution

Bayesian Nonparametric Estimation of Failure Rates with Censored Data

1983 ◽  
Vol 32 (1-2) ◽  
pp. 79-90 ◽  
Author(s):  
J. S. Rao ◽  
R. C. Tiwari
Keyword(s):  
Failure Time ◽  
Dirichlet Distribution ◽  
Survival Function ◽  
Fixed Time ◽  
Bayes Estimation ◽  
Time Interval ◽  
Failure Rates ◽  
Failure Time Distribution ◽  
Accelerated Life ◽  
Bayesian Nonparametric Estimation

The failure time distribution is estimated in the nonparametric context when some of tbe observations arc censored. The time interval is partitioned into fixed class intervals, and number of failures and number censored in each of these intervals are observed. Using a Dirichlet distribution as the prior, the resulting estimates of the survival function and the failure rate have a nice and simple form. If instead of the fixed time intervals, one uses the “natural” intervals formed by the observed failure times, this gives essentially the same results as in Ferauson IUld Phadia (1977), Susarla and Van Ryzin (1976), but in a much simpler way. Bayes estimation under the increasins and decreasing failure rates is also considered, and applications to accelerated life testing are discussed.

scholarly journals A new dynamic model to optimize the reliability of the series-parallel systems under warm standby components

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Amir Mohammad Fakoor Saghih ◽  
Azam Modares
Keyword(s):  
Dynamic Models ◽  
Failure Time ◽  
Recursive Formula ◽  
Reliability Function ◽  
Mode Analysis ◽  
Redundancy Allocation ◽  
Failure Time Distribution ◽  
Before And After ◽  
Common Technique ◽  
Warm Standby

<p style='text-indent:20px;'>Redundancy allocation problem (RAP) is a common technique for increasing the reliability of systems. In this paper, a new model for the RAP is introduced that takes into account the warm standby and mixed strategy, the model dynamics, and the type of the strategy in redundancy allocation problems. A recursive formula is first obtained for the reliability function in the dynamic warm standby and mixed redundancy strategies that leverages the success mode analysis and works for any arbitrary failure-time distribution. Failure rates for warm standby units change before and after their replacement with a damaged unit, and, therefore, the reliability function in warm standby varies with time (i.e., the model is dynamic). Although dynamic models are commonplace in practice, they are more challenging to assess than static models, which have been mainly considered in the literature. An optimization problem is then formulated to select the best redundancy strategy and redundancy levels. Genetic algorithm and particle swarm optimization are leveraged to solve the problem. Finally, the efficiency of the presented method is verified through a numerical example. The experimental results verify that the proposed model for RAP significantly improves the system reliability, which can be of vital importance for system designers.</p>

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.

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.

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