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<p>Quasi-renewal process (QRP) was introduced by Wang and Pham in 1996. After a brief introduction to QRP, we compare ordinary renewal processes, trend renewal processes and QRPs with respect to stochastic ordering between the generating inter-arrival/failure-time random variables, the trend function and the QRP parameter. The results give sufficient, and in some cases necessary and sufficient, conditions under which one model produces stochastically more arrivals than another. The comparisons are useful in reliability growth, imperfect maintenance and warranty settings, where the ordering of the counting variables provides a direct comparison of expected failure or repair burden. Illustrative examples and a numerical comparison are given.</p>

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On Stochastic Ordering Comparisons of Renewal, Trend Renewal and Quasi-renewal Processes

  • 期刊论文

  • 发表日期：

    2026年6月15日

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  • Suman Kalyan Ghosh,
  • Sreenivasan Ravi

摘要

Quasi-renewal process (QRP) was introduced by Wang and Pham in 1996. After a brief introduction to QRP, we compare ordinary renewal processes, trend renewal processes and QRPs with respect to stochastic ordering between the generating inter-arrival/failure-time random variables, the trend function and the QRP parameter. The results give sufficient, and in some cases necessary and sufficient, conditions under which one model produces stochastically more arrivals than another. The comparisons are useful in reliability growth, imperfect maintenance and warranty settings, where the ordering of the counting variables provides a direct comparison of expected failure or repair burden. Illustrative examples and a numerical comparison are given.