Minimax Multivariate Control Chart Using a Polynomial Function

Minimax control chart uses the joint probability distribution of the maximum and minimum standardized sample means to obtain the control limits for monitoring purpose. However, the derivation of the joint probability distribution needed to obtain the minimax control limits is complex. In this paper the multivariate normal distribution is integrated numerically using Simpson’s one third rule to obtain a non-linear polynomial (NLP) function. This NLP function is then substituted and solved numerically using Newton Raphson method to obtain the control limits for the minimax control chart. The approach helps to overcome the problem of obtaining the joint probability distribution needed for estimating the control limits of both the maximum and the minimum statistic for monitoring multivariate process.

Statistical Analyses of the Effects of Welding Processes on Load, Extension and Hardness Properties of Welded Mild Steel Plates

Mild steel plates of thicknesses 0.5 mm,0.6 mm,0.7 mm,0.8 mm,0.9 mm and 1.0 mm were prepared as test samples.After welding with the developed welding robot and manual electric arc welding machine these test samples were subjected to Tensile Strength and Hardness tests.All data obtained including hardness,load and extension were analyzed and the data produced from electric arc welding operations,the robot welding operations and un-welded plates(control)were compared with one another.The statistical analyses of hardness,load and extension tests for developed welding robot,manual electric arc welding and un-welded(control)mild steel plates of different thicknesses were carried out.The results revealed that for hardness,the developed robot welding has the highest mean value of 115.30,standard deviation value of 14.32 and variance value of 205.06.The descriptive statistics of the load showed that the developed robot welding samples collectively have the lowest mean value of 2,536.85,standard deviation value of 704.21 and variance value of 495,911.72.The descriptive statistics of the extension in which the developed robot welding samples collectively have the lowest mean value of 1.29,standard deviation value of 0.43 and variance value of 0.18 were also determined.The result for hardness showed homogeneity of variance among hardness tests of the samples,which implies variation in the hardness test among the tests of the samples since p-value is 0.038.While the result for loads shows homogeneity of variance among loads of the samples in which the result reveals that there is no variation in the loads among the tests of the samples since p-value is 0.322.The result for extension shows homogeneity of variance among extensions of the samples in which it revealed that there is variation in the extensions among the tests of the samples since p-value is 0.011.The analysis of variance(ANOVA)test result revealed that there is a significant difference in the hardness of the samples in which developed robot welding operation gave the highest hardness compared with electric arc welding and un-welded(CONTROL)since p-value is 0.028.The ANOVA test result for load revealed that there is no significant difference in the loads of the samples since p-value is 0.51.The ANOVA test result of the extension shows that there is a significant difference in the extension of the samples in which developed robot welding operation gave the lowest extension compared with electric arc welding and un-welded(CONTROL)since p-value is 0.001.The results of hardness also showed the mean difference of 16.48 between developed robot welding and un-welded(CONTROL)samples and 7.26 between developed robot welding and electric arc welding samples.Finally,for extension the mean difference of-5.28 between developed robot welding and un-welded(CONTROL)samples and-1.22 between developed robot welding and electric arc welding samples were established.