In this paper, we present a Bayesian analysis of a data set selected from a Brazilian food company. This data set represents the times taken for different quality control analysts to test manufactured products arriving at the company’s quality control department. The samples selected from each batch contain mixtures of different products, which may be submitted to quality testing taking different times. From preliminary analysis of the data, it was observed that the histograms presented two clusters, indicating a mixture of distributions. A mixture of parametrical distributions was thus assumed in the presence of a covariate in order to analyze the data set and to establish standards to be used by the company for the times taken by the analysts. Inferences and predictions are obtained using a Bayesian approach with standard existing Markov Chain Monte Carlo (MCMC) methods.

The present work deals with the cutting forces and cutting temperature produced during turning of titanium alloy Ti-6Al-4V with PVD TiN coated tungsten carbide inserts under dry environment. The 1st order mathematical models are developed using multiple regression analysis and optimized the process parameters using contour plots. The model presented high determination coefficient (R2 = 0.964 and 0.989 explaining 96.4 % and 98.9 % of the variability in the cutting force and cutting temperature, which indicates the goodness of fit for the model and high significance of the model. The developed mathematical model correlates the relationship of the cutting force and temperature with the process parameters with good degree of approximation. From the contour plots, the optimal parametric combination for lowest cutting force is v 3 (75 m/min) – f 1 (0.25 mm/rev). Similarly, the optimal parametric combination for minimum temperature is v 1 (45 m/min) – f 1 (0.25 mm/rev). Cutting speed is found to be the most significance parameter on cutting forces followed by feed. Similarly, for cutting temperature, feed is found to be the most influencing parameter followed by cutting speed.

Ti-6Al-4V Extra Low Interstitial (ELI) exhibits superior properties because of controlled interstitial element of iron and oxygen. The effects of four cutting parameters namely cutting speed, feed, depth of cut and tool nose radius on responses like cutting force, average cutting temperature and surface roughness have been investigated for turning of Ti-6Al-4V (ELI). Total 81 experiments have been performed in dry environment. Grey Relational Analysis has been used for multi-objective optimization. Analysis of Variance test has been carried out to investigate contribution of input parameters. The model was found fit with R-Square value of 88.74%. Regression and ANN models are developed for prediction and compared. From the Grey relational analysis, it is clear that optimum parameters to minimize cutting force, cutting temperature and surface roughness while turning Ti-6Al-4V (ELI), are cutting speed as 140 rpm, Nose radius 1.2mm, Feed 0.051mm/rev and depth of cut is 0.5mm. In comparison of regression model, the ANN model is found to be more accurate with average error of 3.57%.