Analysis of medians under two-way model with and without interaction for Birnbaum–Saunders distributed response

The Birnbaum–Saunders (BS) distribution, well-known as the fatigue-life has been used in numerous disciplines ranging from engineering to medical sciences. In this article, we develop a test for analysis of medians BS distributed response assess impact two interacting factors on median, where no is presently available. proposed integrated likelihood ratio (ILRT) eliminates nuisance shape parameters by integrating them out. second-order accurate asymptotic chi-square distribution ILRT derived. An in-depth simulation study strongly supports its excellent performance even under small group sizes. Furthermore, developed one-way model found uniformly superior over peers, straightway extendable general multiway setup, and potential be extended other non-normal variables. Its genuine need industry, responses are commonly encountered, highlighted through three real data sets: picked out deposition time influential factor epitaxial layer experiment, revealed significant spools fiber life failure times Kevlar 49 data, gave more parameter estimates delivery assessed various adequacy tools, competitors failed deliver desired results.