USE OF THE MILITARY STANDARD PLANS FOR HAZARD RATE UNDER THE WEIBULL DISTRIBUTION

1961 ◽  
Author(s):  
HENRY P. GOODE ◽  
JOHN H. KAO
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
The Military

scholarly journals A New Flexible Bathtub-Shaped Modification of the Weibull Model: Properties and Applications

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
Qinghu Liao ◽  
Zubair Ahmad ◽  
Eisa Mahmoudi ◽  
G. G. Hamedani
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate ◽  
Likelihood Estimation ◽  
Estimation Procedure ◽  
Weibull Model ◽  
Rate Function ◽  
Model Parameters ◽  
Hazard Functions ◽  
Practical Applications ◽  
Nonnested Models

Many studies have suggested the modifications and generalizations of the Weibull distribution to model the nonmonotone hazards. In this paper, we combine the logarithms of two cumulative hazard rate functions and propose a new modified form of the Weibull distribution. The newly proposed distribution may be called a new flexible extended Weibull distribution. Corresponding hazard rate function of the proposed distribution shows flexible (monotone and nonmonotone) shapes. Three different characterizations along with some mathematical properties are provided. We also consider the maximum likelihood estimation procedure to estimate the model parameters. For the illustrative purposes, two real applications from reliability engineering with bathtub-shaped hazard functions are analyzed. The practical applications show that the proposed model provides better fits than the other nonnested models.

GENERAL SEQUENTIAL IMPERFECT PREVENTIVE MAINTENANCE MODELS

2000 ◽  
Vol 07 (03) ◽  
pp. 253-266 ◽  
Author(s):  
DAMING LIN ◽  
MING J. ZUO ◽  
RICHARD C. M. YAM
Keyword(s):  
Weibull Distribution ◽  
Preventive Maintenance ◽  
Hazard Rate ◽  
Numerical Examples ◽  
Cost Rate ◽  
Effective Age ◽  
Rate Adjustment ◽  
The Mean ◽  
Mean Cost

This paper presents new sequential imperfect preventive maintenance (PM) models incorporating adjustment/improvement factors in hazard rate and effective age. The models are hybrid in the sense that they are combinations of the age reduction PM model and the hazard rate adjustment PM model. It is assumed that PM is imperfect: It not only reduces the effective age but also changes the hazard rate, while the hazard rate increases with the number of PMs. PM is performed in a sequence of intervals. The objective is to determine the optimal PM schedule to minimize the mean cost rate. Numerical examples for a Weibull distribution are given.

scholarly journals On a Special Weighted Version of the Odd Weibull-Generated Class of Distributions

2021 ◽  
Vol 26 (3) ◽  
pp. 62
Author(s):  
Zichuan Mi ◽  
Saddam Hussain ◽  
Christophe Chesneau
Keyword(s):  
Distribution Function ◽  
Weibull Distribution ◽  
Probability Density ◽  
Hazard Rate ◽  
Cumulative Distribution Function ◽  
Data Fitting ◽  
Environmental Data ◽  
Cumulative Distribution ◽  
Model Parameters ◽  
New Class

In recent advances in distribution theory, the Weibull distribution has often been used to generate new classes of univariate continuous distributions. They find many applications in important disciplines such as medicine, biology, engineering, economics, informatics, and finance; their usefulness is synonymous with success. In this study, a new Weibull-generated-type class is presented, called the weighted odd Weibull generated class. Its definition is based on a cumulative distribution function, which combines a specific weighted odd function with the cumulative distribution function of the Weibull distribution. This weighted function was chosen to make the new class a real alternative in the first-order stochastic sense to two of the most famous existing Weibull generated classes: the Weibull-G and Weibull-H classes. Its mathematical properties are provided, leading to the study of various probabilistic functions and measures of interest. In a consequent part of the study, the focus is on a special three-parameter survival distribution of the new class defined with the standard exponential distribution as a reference. The exploratory analysis reveals a high level of adaptability of the corresponding probability density and hazard rate functions; the curves of the probability density function can be decreasing, reversed N shaped, and unimodal with heterogeneous skewness and tail weight properties, and the curves of the hazard rate function demonstrate increasing, decreasing, almost constant, and bathtub shapes. These qualities are often required for diverse data fitting purposes. In light of the above, the corresponding data fitting methodology has been developed; we estimate the model parameters via the likelihood function maximization method, the efficiency of which is proven by a detailed simulation study. Then, the new model is applied to engineering and environmental data, surpassing several generalizations or extensions of the exponential model, including some derived from established Weibull-generated classes; the Weibull-G and Weibull-H classes are considered. Standard criteria give credit to the proposed model; for the considered data, it is considered the best.

scholarly journals Statistical Analysis of Data From Electronic Component Lifetests (A Tutorial Paper)

1987 ◽  
Vol 12 (4) ◽  
pp. 259-279 ◽  
Author(s):  
J. Møltoft
Keyword(s):  
Statistical Analysis ◽  
Weibull Distribution ◽  
Exponential Distribution ◽  
Hazard Rate ◽  
Failure Mechanisms ◽  
Electronic Component ◽  
Cmos Circuit ◽  
Analysis Techniques ◽  
Graph Paper ◽  
Circuit Components

Methods of statistically analysing data from electronic component lifetests are discussed. Particular emphasis is given to analysis techniques using the assumptions of constant hazard rate (Exponential distribution), the Weibull distribution and mixed Weibull distributions. The methods used for analysing Weibull data when the data itself is non-uniform due to both removal of test samples during test and also the non-continuance of surveillance of components under test are discussed. Attention is finally given to the effect of two or more failure mechanisms which can produce S-shaped patterns when data is plotted on Weibull Graph paper.Numerous examples are given, mainly from the field of analysis of CMOS circuit components.

scholarly journals The Marshall-Olkin Additive Weibull Distribution with Variable Shapes for the Hazard Rate

2016 ◽  
Vol 46 (126) ◽  
pp. 1-1 ◽  
Author(s):  
Ahmed Z. Afify ◽  
Gauss M. Cordeiro ◽  
Haitham M. Yousof ◽  
Abdus Saboor ◽  
Edwin M.M. Ortega
Keyword(s):  
Weibull Distribution ◽  
Hazard Rate
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