scholarly journals The Effectiveness of the Squared Error and Higgins-Tsokos Loss Functions on the Bayesian Reliability Analysis of Software Failure Times under the Power Law Process

Engineering ◽  
2019 ◽  
Vol 11 (05) ◽  
pp. 272-299
Author(s):  
Freeh N. Alenezi ◽  
Christ P. Tsokos
Keyword(s):  
Reliability Analysis ◽  
Power Law ◽  
Loss Functions ◽  
Power Law Process ◽  
Software Failure ◽  
Failure Times ◽  
Squared Error

Reliability analysis of the cable system of drum shearer using the power law process model

2012 ◽  
Vol 26 (4) ◽  
pp. 309-323 ◽  
Author(s):  
Seyed Hadi Hoseinie ◽  
Mohammad Ataei ◽  
Reza Khalokakaie ◽  
Behzad Ghodrati ◽  
Uday Kumar
Keyword(s):  
Reliability Analysis ◽  
Power Law ◽  
Process Model ◽  
Cable System ◽  
Power Law Process ◽  
Drum Shearer

INFERENCES ON THE PARAMETERS AND SYSTEM RELIABILITY FOR A FAILURE-TRUNCATED POWER LAW PROCESS: A BAYESIAN APPROACH USING A CHANGE-POINT

2004 ◽  
Vol 11 (02) ◽  
pp. 175-185 ◽  
Author(s):  
M. G. RICHARDSON ◽  
A. P. BASU
Keyword(s):  
Power Law ◽  
Change Point ◽  
Repairable System ◽  
Repairable Systems ◽  
Process Change ◽  
Power Law Process ◽  
System Failures ◽  
Failure Times ◽  
Age Dependent ◽  
Change Point Model

The reliability of a repairable system that is either improving or deteriorating depends on the system's chronological age. If such a system undergoes "minimal repair" at the occurrence of each failure so that the rate of system failures is not disturbed by the repair, then a nonhomogeneous Poisson process (NHPP) may be used to model the "age-dependent" reliability of the system. The power law process (PLP) is a model within the class of NHPP models and is commonly used as a model for describing the failure times of a repairable system. We introduce a new model that is an extension of the PLP model: the power law process change-point model. This model is capable of describing the failure times of particular types of repairable systems that experience a single change in their rates of occurrence of failures. Bayesian inference procedures for this model are developed.

scholarly journals Bayesian Estimation of the Parameter of the p-Dimensional Size-Biased Rayleigh Distribution

2017 ◽  
Vol 56 (1) ◽  
pp. 88-91
Author(s):  
Arun Kumar Rao ◽  
Himanshu Pandey ◽  
Kusum Lata Singh
Keyword(s):  
Probability Density Function ◽  
Probability Density ◽  
Bayesian Estimation ◽  
Density Function ◽  
Rayleigh Distribution ◽  
Survival Model ◽  
Loss Functions ◽  
Bayes Estimators ◽  
Hazard Functions ◽  
Squared Error

In this paper, we have derived the probability density function of the size-biased p-dimensional Rayleigh distribution and studied its properties. Its suitability as a survival model has been discussed by obtaining its survival and hazard functions. We also discussed Bayesian estimation of the parameter of the size-biased p-dimensional Rayleigh distribution. Bayes estimators have been obtained by taking quasi-prior. The loss functions used are squared error and precautionary.

Optimization of Leased Equipment Maintenance Policy Based on History Failure Data

2021 ◽  
pp. 2150030
Author(s):  
Ke Dong ◽  
Kehong Chen
Keyword(s):  
Power Law ◽  
Cost Model ◽  
Maintenance Strategy ◽  
Maintenance Policy ◽  
Power Law Process ◽  
Total Cost ◽  
Cost Rate ◽  
Failure Data ◽  
Expected Total Cost ◽  
The Cost

We propose a maintenance policy for new equipment on a repair-refund maintenance strategy in this paper and derive the optimal lease period from the lessor’s perspective based on independent and identical distribution of historical failure data which obey power law process. The cost model of a full refund and a proportional refund is studied, and the corresponding optimal leasing period is determined by reducing the expected total cost rate to the largest extent. We use a numerical example to illustrate the proposed cost model and analyze the sensitivity of related parameters. Furthermore, we show that the proportional refund policy is preferable than a full refund to the lessor. Finally, according to the simulation outcome, the proposed methods are effective and instructions for lessor in regard to equipment lease are provided.

scholarly journals A Bayesian Approach for Estimating Parameter of Rayleigh Distribution

2019 ◽  
Vol 11 (1) ◽  
pp. 23-39
Author(s):  
J. Mahanta ◽  
M. B. A. Talukdar
Keyword(s):  
Weibull Distribution ◽  
Loss Function ◽  
Bayesian Approach ◽  
Rayleigh Distribution ◽  
Loss Functions ◽  
Bayes Risk ◽  
Squared Error ◽  
Different Types ◽  
Two Parameters ◽  
Special Case

This paper is concerned with estimating the parameter of Rayleigh distribution (special case of two parameters Weibull distribution) by adopting Bayesian approach under squared error (SE), LINEX, MLINEX loss function. The performances of the obtained estimators for different types of loss functions are then compared. Better result is found in Bayesian approach under MLINEX loss function. Bayes risk of the estimators are also computed and presented in graphs.

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