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Article Linear Two-Dimensional Consecutive K-Type Systems in Multi-State Case(Elsevier Sci Ltd, 2026) Yi, He; Balakrishnan, Narayanaswamy; Li, XiangIn the context of consecutive k-type systems, multi-state system models are only considered in the onedimensional 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 1-connected-(k, r)-out-of-(m, n): G systems without/with overlapping, and multi-state linear 1-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.Article Social Determinants of Health and Risk of Lower Extremity Amputation in Patients with Peripheral Artery Disease in Canada: Protocol for a Systematic Review and Meta-Analysis(BMJ Publishing Group, 2026) Chowdhury, Abhiroop; Sheikh, Fatima; Azab, Sandi M.; De Souza, Russell J.; Banfield, Laura; Balakrishnan, Narayanaswamy; Anand, Sonia S.Introduction Peripheral artery disease (PAD) affected approximately 800 000 Canadians aged 25 years or older in 2015 and it poses a substantial risk of lower extremity amputation (LEA). While clinical risk factors for amputation are well-established, the impact of social determinants of health (SDoH) on amputation risk remains unclear, particularly in a Canadian context.Objectives This systematic review aims to: (1) synthesise evidence on the associations between multilevel SDoH domains and LEA (both major and/or minor) risk in Canadian PAD patients including intersectional effects of race and ethnicity with another SDoH domain, and (2) evaluate the statistical methodologies used in the researched literature to inform future study design and analysis approaches.Methods and analysis We will systematically search MEDLINE, Embase, EmCare, Global Health, Cumulative Index to Nursing and Allied Health Literature and Web of Science for studies examining SDoH and LEA in Canadian patients with PAD (including chronic limb-threatening ischaemia which is a severe form of PAD). Date limits for each database will be from inception through December 2025. SDoH will be categorised using a modified Healthy People 2030 SDoH framework under six domains: economic stability, education, food, neighbourhood and physical environment, healthcare system and community and social context. Two reviewers will independently screen titles, abstracts and full texts, with discrepancies resolved by a third reviewer. Data will be extracted on study characteristics, SDoH measures, outcomes and statistical methods. Risk of bias will be assessed using RoB 2 for randomised trials, ROBINS-I for non-randomised studies of interventions and ROBINS-E for studies investigating exposures. A narrative synthesis, and where data permit, a Bayesian hierarchical meta-analysis using both effect size and contingency table approaches will be conducted. Statistical heterogeneity will be explored through subgroup analyses and meta-regression, examining study design, SDoH measurement approaches and population characteristics.Ethics and dissemination As a systematic review and meta-analysis, ethics approval is not required. For institutional oversight, we provide the contact of Dr Sonia Anand (Associate Vice-President, Global Health, McMaster University; anands@mcmaster.ca). Results will be reported following PRISMA guidelines and disseminated through a peer-reviewed publication.PROSPERO registration number CRD420251115759.Article Nonparametric Tests for Comparing Reliabilities of Coherent Systems at Specific Mission Time(IEEE-Inst Electrical Electronics Engineers Inc, 2026) Xu, Xuan; Zhu, Xiaojun; Balakrishnan, Narayanaswamy; Ng, Hon Keung TonyReliability analysis of coherent systems is critical for evaluating the performance of systems whose functionality depends on the reliability of their components. Traditional parametric methods for comparing reliabilities of coherent systems assume a specific probability distribution for component lifetimes, which may result in inaccurate results when these model assumptions are violated. This article introduces nonparametric procedures using system-level data with known signatures to compare the reliabilities of systems. The proposed methodology avoids parametric distributional assumptions for component lifetimes while relying on the standard assumption in signature-based reliability analysis. Specifically, a two-sample likelihood ratio test procedure is proposed to demonstrate a component or system with superior reliability. Monte Carlo simulations are performed to evaluate the performance of the proposed methods. Furthermore, we examine the effect of system structure on test power and determine favourable structures to enhance the power performance of the test. Practical examples are used to illustrate the proposed test procedures.
