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Product quality and reliability characteristics are important considerations for all manufacturers in the product and process design. Industrial experiments may include both quality and reliability characteristics with the goal to obtain a compromise optimization of the two responses. In many cases, such experiments do not use a completely randomized design. Instead, they involve a more complicated experimental protocol, for example, subsampling, blocking, and split-plot structure. This paper presents a framework for the simultaneous optimization of quality and reliability characteristics with random effects. The paper provides a linear mixed model for quality characteristic and a nonlinear mixed model for Type I censored lifetime to incorporate random effects in the analysis. Subsequently, the desirability function approach is used to obtain a trade-off between the quality and reliability characteristics. The mixed models in this paper can incorporate information from all censored test stands and random effects. The proposed framework provides engineers with an appropriate approach to simultaneously optimize the quality and reliability characteristics with random effects. The paper used a case study to illustrate the proposed framework. A simulation study is also considered to present the necessary of incorporating random effects in the modelling stage.

Simultaneous optimization of quality and censored reliability characteristics with constrained randomization experiment