Median Inactivity Time Function and its Reliability Properties
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Abd El-Fattah Mohamed Kandil
,
Mohamed Kayid
Abstract
Let the non-negative random variable X denote the life time of a unit, then the random variable X(t) = t – X for X ≤ t for a fixed t ∈ {x : FX (x) > 0}, is known as inactivity time or reversed residual life time. In this paper, we define a new non-parametric class of life distributions based on the median of the random variable X(t) and study its reliability properties. Some new results concerning the proposed class are given including some closure properties and characterizations. We also introduce and study a new stochastic ordering based on the median of X(t) and find its relationship with other well-known order relations. Finally, we provide the median inactivity time function of some well-known life time distributions.
© de Gruyter 2010
Articles in the same Issue
- Editorial
- Acceptance Sampling Plans from Truncated Life Tests Based on the Log-Logistic Distributions for Percentiles
- Book Review: Generalized Gaussian Error Calculus by Dr. rer. nat. Michael Grabe
- On the Robustness of Reliability Characteristic of Alpha-Distributed Lifetimes
- Binomial Poisson Distribution Revisited
- Empirical Evaluation of Stochastikon Magister
- Selection of Bayesian Double Sampling Inspection Plans by Attributes with Small Acceptance Numbers
- Analysis of a Complex System Modelled by a Marked Point Process and Assuming Vacations for a Repairman
- Optimal Replacement Policy Based on the Number of Down Times with Priority in Use
- Median Inactivity Time Function and its Reliability Properties
- Statistical Inference on Software Reliability Assuming Exponential Fault Correction Time
- On Testing Exponentiality Against DMRL Alternatives
- Designing Single Sampling Plans by Variables Using Predictive Distribution
Articles in the same Issue
- Editorial
- Acceptance Sampling Plans from Truncated Life Tests Based on the Log-Logistic Distributions for Percentiles
- Book Review: Generalized Gaussian Error Calculus by Dr. rer. nat. Michael Grabe
- On the Robustness of Reliability Characteristic of Alpha-Distributed Lifetimes
- Binomial Poisson Distribution Revisited
- Empirical Evaluation of Stochastikon Magister
- Selection of Bayesian Double Sampling Inspection Plans by Attributes with Small Acceptance Numbers
- Analysis of a Complex System Modelled by a Marked Point Process and Assuming Vacations for a Repairman
- Optimal Replacement Policy Based on the Number of Down Times with Priority in Use
- Median Inactivity Time Function and its Reliability Properties
- Statistical Inference on Software Reliability Assuming Exponential Fault Correction Time
- On Testing Exponentiality Against DMRL Alternatives
- Designing Single Sampling Plans by Variables Using Predictive Distribution
