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Article Linear Two-Dimensional Consecutive K-Type Systems in Multi-State Case(Elsevier Ltd, 2026) Yi, H.; Balakrishnan, N.; Li, X.In the context of consecutive k -type systems, multi-state system models are only considered in the one-dimensional case and not in the two-dimensional case due to the complexity involved. In this paper, we consider several linear two-dimensional consecutive k -type systems in the multi-state case for the first time, as generalization of consecutive k -out-of- n systems and l -consecutive- k -out-of- n systems without/with overlapping. These systems include multi-state linear connected-(k , r)-out-of-(m, n): G systems, multi-state linear connected-(k , r)-or-(r , k)-out-of-(m, n): G systems, multi-state linear l -connected-(k , r)-out-of-(m, n): G systems without/with overlapping, and multi-state linear l -connected-(k , r)-or-(r , k)-out-of-(m, n): G systems without/with overlapping. We then derive their reliability functions by using the finite Markov chain imbedding approach (FMCIA) in a new way. We also present several examples to illustrate all the results developed here. © 2026 Elsevier Ltd.Article Distance-Based Estimation Under Progressive Type-I Interval Censoring(Taylor & Francis Ltd, 2026) Balakrishnan, N.; Castilla, E.Monte Carlo simulation is used to demonstrate improved estimation performance of proposed distance-type estimators for lifetime models under progressive Type-I interval censoring. We propose novel distance-based estimators for lifetime models under progressive Type-I interval censoring. These estimators minimize the discrepancy between observed and model-based conditional failure probabilities using either quadratic or Mahalanobis distances, providing natural alternatives to maximum likelihood estimators (MLEs). Through extensive Monte Carlo simulations, we demonstrate that the Mahalanobis estimator outperforms MLE, particularly under heavy censoring or sparse data. The quadratic estimator also yields competitive results, especially under model misspecification. Two real data examples illustrate the practical advantages of the proposed approach.
