Connection of Generalized Failure Rate and Generalized Reversed Failure Rate with Inequality Curves

The purpose of this paper is to introduce some properties of generalized failure rate (GFR) and generalized reversed failure rate (GRFR), study their connection with inequality measures and then apply it to make comparisons of some reliability models. In the second part of our paper, we obtain the properties for the GRFR based on the properties of the GFR and weighted distributions. The importance of such a study lies in the usefulness of using. Finally, we present two examples to illustrate the applications of the relationships outlined in this paper. A real dataset is used for clarifying presented concepts.

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Dynamic reliability models of mechanical load-sharing parallel systems considering strength degradation of components

Proceedings of the Institution of Mechanical Engineers Part C Journal of Mechanical Engineering Science ◽

10.1177/0954406214560000 ◽

2014 ◽

Vol 229 (13) ◽

pp. 2484-2495 ◽

Cited By ~ 2

Author(s):

Peng Gao ◽

Liyang Xie

Keyword(s):

Failure Rate ◽

Mechanical Load ◽

Parallel Systems ◽

Load Sharing ◽

Strength Degradation ◽

Random Load ◽

Dynamic Reliability ◽

Reliability Models ◽

Load Redistribution ◽

Mechanical Components

Conventional reliability analysis of load-sharing parallel systems is mainly based on failure rate of components, in which failure dependence of components and load redistribution are also characterized by specified failure rates. However, the failure rate of mechanical components always varies with time, which is difficult to measure. Therefore, in this paper, quantitative dynamic reliability models of mechanical load-sharing parallel systems are developed in terms of stress parameters and strength parameters rather than failure rate of components, which consider the degradation mechanism of mechanical components. The proposed models take into account the strength degradation path dependence (SDPD) of a component, the strength degradation process dependence between different components in a system, and the random load redistribution. In addition, Monte Carlo simulation is carried out to verify the proposed models. The results show that SDPD and the load-sharing effect have considerable influences on dynamic reliability of mechanical load-sharing parallel systems.

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Some general characteristics of two-state reliability models for maintained systems

Journal of Applied Probability ◽

10.1017/s0021900200103225 ◽

1995 ◽

Vol 32 (03) ◽

pp. 805-820

Author(s):

Norman A. Marlow ◽

Michael Tortorella

Keyword(s):

Failure Rate ◽

General Class ◽

Point Processes ◽

Limiting Distribution ◽

Renewal Processes ◽

Reliability Models

Formulas for the asymptotic failure rate, long-term average availability, and the limiting distribution of the number of long ‘outages' are obtained for a general class of two-state reliability models for maintained systems. The results extend known formulas for alternating renewal processes to a wider class of point processes that includes sequences of dependent or non-identically distributed operating and repair times.

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4. Increasing failure rate software reliability models for agile projects: a comparative study

Systems Performance Modeling ◽

10.1515/9783110619058-004 ◽

2020 ◽

pp. 45-66

Keyword(s):

Comparative Study ◽

Failure Rate ◽

Software Reliability ◽

Increasing Failure Rate ◽

Reliability Models ◽

Software Reliability Models

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Reliability models of belt drive systems under slipping failure mode

Advances in Mechanical Engineering ◽

10.1177/1687814016687195 ◽

2017 ◽

Vol 9 (1) ◽

pp. 168781401668719 ◽

Cited By ~ 1

Author(s):

Peng Gao ◽

Liyang Xie

Keyword(s):

Failure Mode ◽

Failure Rate ◽

Dynamic Characteristics ◽

Interference Model ◽

Design Parameters ◽

Belt Drive ◽

Dynamic Reliability ◽

Reliability Models ◽

Sensitivity Functions ◽

Drive Systems

Conventional reliability assessment and reliability-based optimal design of belt drive are based on the stress–strength interference model. However, the stress–strength interference model is essentially a static model, and the sensitivity analysis of belt drive reliability with respect to design parameters needs further investigations. In this article, time-dependent factors that contribute the dynamic characteristics of reliability are pointed out. Moreover, dynamic reliability models and failure rate models of belt drive systems under the failure mode of slipping are developed. Furthermore, dynamic sensitivity models of belt drive reliability based on the proposed dynamic reliability models are proposed. In addition, numerical examples are given to illustrate the proposed models and analyze the influences of design parameters on dynamic characteristics of reliability, failure rate, and sensitivity functions. The results show that the statistical properties of design parameters have different influences on reliability and failure rate of belt drive in cases of different values of design parameters and different operational durations.

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Some general characteristics of two-state reliability models for maintained systems

Journal of Applied Probability ◽

10.2307/3215131 ◽

1995 ◽

Vol 32 (3) ◽

pp. 805-820 ◽

Cited By ~ 5

Author(s):

Norman A. Marlow ◽

Michael Tortorella

Keyword(s):

Failure Rate ◽

General Class ◽

Point Processes ◽

Limiting Distribution ◽

Renewal Processes ◽

Reliability Models

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Relationship between the weighted distributions and some inequality measures

Communication in Statistics- Theory and Methods ◽

10.1080/03610926.2017.1397171 ◽

2018 ◽

Vol 47 (22) ◽

pp. 5573-5589 ◽

Cited By ~ 1

Author(s):

Zahra Behdani ◽

Gholam Reza Mohtashami Borzadaran ◽

Bahram Sadeghpour Gildeh

Keyword(s):

Inequality Measures ◽

Weighted Distributions

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Reliability and Lifetime Distribution Analysis of Belt Drive Systems considering Time-Dependent Stiffness of Belts

Shock and Vibration ◽

10.1155/2018/8691967 ◽

2018 ◽

Vol 2018 ◽

pp. 1-9 ◽

Cited By ~ 1

Author(s):

Peng Gao ◽

Liyang Xie

Keyword(s):

Failure Rate ◽

Dynamic Properties ◽

Lifetime Distribution ◽

Time Dependent ◽

Stiffness Degradation ◽

Belt Drive ◽

Distribution Analysis ◽

Distribution Models ◽

Reliability Models ◽

Drive Systems

Time-dependent reliability models, failure rate models, and lifetime distribution models of belt drive systems are developed in this paper, which take geometric parameters, material parameters, and motion parameters as the input and consider the dynamic properties of the belt drive systems. Most of the reliability models of belt drive systems are static models. The proposed models can take into account the time-dependent statistical properties of dynamic stress process. Moreover, the stiffness degradation is considered in the established models, whose influences on reliability indices are analyzed in case study. The results show that stiffness degradation has significant impacts on reliability, failure rate, and lifetime distribution. In addition, sensitivity models of reliability with respect to input parameters are constructed, which can be used for the guidance of safe design of belt drive systems.

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