Stochastic Properties and Parameter Estimation of Standby Systems

Zhengcheng Zhang
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Zhengcheng Zhang: Hainan Normal University, School of Mathematics and Statistics

Chapter Chapter 6 in Conditional Order Statistics and Conditional Spacings, 2025, pp 143-187 from Springer

Abstract: Abstract This chapter mainly investigates a general load-sharing parallel systemLoad-Sharing Parallel System with two components. Some comparisons among different kinds of standby systemsStandby System|( are constructed. Under some specific conditions, that load-sharing parallel systemParallel Systems is better than any one of its two components under the full load conditionFull Load Condition in the usual stochastic orderUsual Stochastic Order, is shown. When the lifetimes of the components are exponential distributionsExponential Distribution, we prove that load-sharing parallel systemParallel Systems is better than the usual parallel systemParallel Systems with the same two components. Moreover, we discuss the stochastic comparison of the residual lifetimes between two load-sharingParallel Systems parallel systemsLoad-Sharing Parallel System|(. Finally, at the end of this chapter, we deal with the parameter estimation for the load-sharing parallel systemLoad-Sharing Parallel System|) when the underlying distribution of component lifetime is Exponential Pareto.

Date: 2025
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DOI: 10.1007/978-981-96-7151-9_6

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