Nonlinear Inference Procedures for Location-Scale Families in Ordered Sequential Reliability Structure
Keywords:
Sequential order statistics; k-out-of-n systems; Minimum risk equivariant estimator; Location-scale families; Reliability theory; Reliability function; Mission planning; Monte Carlo simulationAbstract
This paper extends the framework of sequential order statistics from (1,3) and (2,3) systems to four-component systems, specifically (1,4) and (2,4) configurations. We derive the joint probability density functions for sequential order statistics under gamma-exponential mixture distributions and develop minimum risk equivariant estimators (MREE) for location-scale parameters under squared error loss.For the (2,4) system, the mean time betweenfailure (MTBF) is shown to be , while for the (1,4) system it is , representing 12% and 4% improvements over three-component (2,3) and (1,3) systems, respectively. Reliability functions are derived, exhibiting monotonic exponential decay with time, and provide practical guidance for mission planning and maintenance scheduling. Explicit closed-form expressions are provided for MREE of location parameter , scale parameter , and general percentiles . Monte Carlo simulations demonstrate that the proposed estimators achieve 15–45% lower mean squared error compared to naive moment-based estimators across various sample sizes. Application to simulated electronic component reliability data validates the practical utility of the methodology.
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