Statistical inference for component lifetime distribution from coherent system lifetimes under a proportional reversed hazard model

2020 ◽  
pp. 1-25
Author(s):  
Adeleh Fallah ◽  
Akbar Asgharzadeh ◽  
Hon Keung Tony Ng
Keyword(s):  
Statistical Inference ◽  
Hazard Model ◽  
Lifetime Distribution ◽  
Coherent System ◽  
Proportional Reversed Hazard Model

Some results involving generalized proportional reversed hazard model

2018 ◽  
Vol 12 (32) ◽  
pp. 1635-1643
Author(s):  
Nassr Al-Maflehi ◽  
Mohammedelameen Eissa Qurashi
Keyword(s):  
Hazard Model ◽  
Proportional Reversed Hazard Model

On unimodality of the lifetime distribution of coherent systems with failure-dependent component lifetimes

2018 ◽  
Vol 55 (2) ◽  
pp. 473-487 ◽  
Author(s):  
M. Bieniek ◽  
M. Burkschat
Keyword(s):  
Standard Deviation ◽  
Upper Bound ◽  
Lifetime Distribution ◽  
Coherent System ◽  
Density Functions ◽  
Coherent Systems ◽  
Underlying Distribution ◽  
Dependent Component ◽  
Different Types ◽  
The Mean

Abstract We study the conditions for unimodality of the lifetime distribution of a coherent system when the ordered component lifetimes in the system are described by generalized order statistics. Results for systems with independent and identically distributed lifetimes of components are included in this setting. The findings are illustrated with some examples for different types of systems. In particular, coherent systems with strictly bimodal density functions are presented in the case of independent standard uniform distributed lifetimes of components. Furthermore, we use the results to derive a sharp upper bound on the expected system lifetime in terms of the mean and the standard deviation of the underlying distribution.

Identifiability problems in coherent systems

1990 ◽  
Vol 27 (04) ◽  
pp. 862-872 ◽  
Author(s):  
Shmuel Nowik
Keyword(s):  
Lifetime Distribution ◽  
Coherent System ◽  
Necessary And Sufficient Condition ◽  
Absolutely Continuous ◽  
Lifetime Distributions ◽  
Single Positive ◽  
Continuity Assumption ◽  
Identifiability Problems ◽  
The Common ◽  
Necessary And Sufficient

Given a coherent system, let Z be the age of the machine at breakdown, and I the set of parts failed by time Z. Assume that the component lifetimes are independent. Assume further that the lifetime distributions are mutually absolutely continuous and that each possesses a single positive atom at the common essential infimum. We prove that the joint distribution of (Z, I) identifies the lifetime distribution of each part if and only if there is at most one component belonging to all cut sets. If we relax the mutual absolute continuity assumption by allowing isolated intervals of constancy, then a necessary and sufficient condition for identifiability is that no two parts be in parallel.

Identifiability problems in coherent systems

1990 ◽  
Vol 27 (4) ◽  
pp. 862-872 ◽  
Author(s):  
Shmuel Nowik
Keyword(s):  
Lifetime Distribution ◽  
Coherent System ◽  
Necessary And Sufficient Condition ◽  
Absolutely Continuous ◽  
Lifetime Distributions ◽  
Single Positive ◽  
Continuity Assumption ◽  
Identifiability Problems ◽  
The Common ◽  
Necessary And Sufficient

Given a coherent system, let Z be the age of the machine at breakdown, and I the set of parts failed by time Z. Assume that the component lifetimes are independent. Assume further that the lifetime distributions are mutually absolutely continuous and that each possesses a single positive atom at the common essential infimum. We prove that the joint distribution of (Z, I) identifies the lifetime distribution of each part if and only if there is at most one component belonging to all cut sets. If we relax the mutual absolute continuity assumption by allowing isolated intervals of constancy, then a necessary and sufficient condition for identifiability is that no two parts be in parallel.

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