Hard-to-set factors lead to split-plot type designs and mixed models. Mixed models are used to analyze multi-stratum designs as each stratum may have random effects on the responses. It is usual to use residual maximum likelihood (REML) to estimate random effects and generalized least squares (GLS) to estimate fixed effects. But a typical property of REML-GLS estimation is that it gives highly undesirable and misleading conclusions in non-orthogonal split-plot designs with few main plots. To overcome the problem a Bayesian method considering informative priors for variance components and using Markov chain Monte Carlo (MCMC) sampling would be an alternative approach. In the current study we have implemented MCMC techniques in two industrial experiments. Mixed binary logit and mixed cumulative logit models were considered for binary and categorical responses respectively. Deviance information criterion (DIC) was used to choose the best models in different scenarios.