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On the Generalized Decreasing Mean Time to Failure or Replaced Ordering.

Haiyan Wang1, Diantong Kang2, Lei Yan1

  • 1Business School, Zhejiang Wanli University, Ningbo, Zhejiang 315100, China.

Computational Intelligence and Neuroscience
|November 25, 2021
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This study introduces two new stochastic orders: decreasing mean time to failure or replaced (DMTFR) and generalized decreasing mean time to failure or replaced (GDMTFR). The research focuses on characterizing GDMTFR properties and their relationships with DMTFR.

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Area of Science:

  • Reliability Engineering
  • Stochastic Processes
  • Probability Theory

Background:

  • Stochastic orders are crucial for comparing random variables in reliability and risk analysis.
  • Existing orders may not fully capture complex failure/replacement patterns.
  • There is a need for new stochastic orders to enhance reliability comparisons.

Purpose of the Study:

  • To introduce and define two novel stochastic orders: DMTFR and GDMTFR.
  • To investigate the fundamental properties and characterizations of the GDMTFR order.
  • To explore the relationships and implications between the newly defined DMTFR and GDMTFR orders.

Main Methods:

  • Definition of new stochastic orders: decreasing mean time to failure or replaced (DMTFR) and generalized decreasing mean time to failure or replaced (GDMTFR).
  • Mathematical derivation of characterizations for the GDMTFR order.
  • Analysis of implication relationships, closure, and reversed closure properties for GDMTFR.

Main Results:

  • Establishment of the DMTFR and GDMTFR stochastic orders.
  • Characterization of the GDMTFR order, providing criteria for its application.
  • Identification of implication relationships between DMTFR and GDMTFR.
  • Investigation of closure and reversed closure properties of GDMTFR.

Conclusions:

  • The new GDMTFR order offers a more generalized framework for reliability analysis.
  • The established properties and relationships provide a foundation for future research in stochastic ordering.
  • Illustrative examples demonstrate the practical applicability of the GDMTFR order in reliability contexts.