Systems Statistical Engineering – Hierarchical Fuzzy Constraint Propagation

Driven by the growing need in the 21st century for integrating rigorous statistical analysis into engineering research, there is a movement to develop an integrated statistical engineering science within statistics and quality communities (Hoerl & Snee, 2010; Anderson-Cook et al., 2012). Systems Statistical Engineering research seeks to integrate the Causal Bayesian hierarchical modeling (Pearl, 2009) and cybernetic control theory within Beer’s Viable System Model (1972, 1979, 1985) and the Complex Systems Governance framework (Keating, 2014; Keating & Katina, 2015, 2016) to produce multivariate systemic models for robust dynamic systems mission performance. Cotter & Quigley (2018) set forth the Bayesian systemic hierarchical constraint propagation theoretical basis for modeling the amplification and attenuation effects of environmental constraints propagated into systemic variability and variety. In their conceptual development, they simplified the analysis to only deterministic constraints, which model only the impact of statistical risks of failure. Imprecision and uncertainty in the assessment of qualitative product constraints will induce additional variance components in systemic variability and variety. To make causal Bayesian hierarchical modeling more capable of capturing and representing the imprecise and uncertain nature of environments, we must incorporate rough or fuzzy boundaries to model imprecision and grey boundaries to model uncertainty in constraint propagation at each system level to measure the overall impact of qualitative requirements on the organizational productive variability and variety. This research sets forth a proposed method to incorporate fuzzy set theory into Systems Statistical Engineering causal Bayesian hierarchical qualitative constraints modeling.