Handle Sigma problems with variation and centering problems

There are two types of problems that arise within a process: problems with variation and problems with centering. The goal is to have a process that targets a target with minimal variation. Continuous decision tools are used to describe the nature and extent of these two types of problems when studying a continuous CT characteristic. With variation problems, we draw conclusions about the standard deviation or the variance of the population based on sample data. With centering problems, we draw conclusions based on the average or median of the population based on sample data.

Confidence intervals allow us to estimate population parameters (mean, standard deviation, etc.) within a range of values ​​set to a pre-assigned probability called “confidence level”.

The One Sample t-Test and Z-Test are used to compare the population mean with a value like the target. The t-Test is normally used for small samples (30). However, as the sample size increases, the results of the t-Test approach the Z-Test.

When we want to determine the influence of factors such as procedures, material type, mounting sequence, temperature, etc. during our process, we can use the Two-Sample t-Test to determine if the mean of a CT characteristic changes significantly under two different conditions. For 2 or more conditions, we can use the One-Way ANOVA Test (analysis of variance).

The homogeneity of variance tests is used to determine whether the variances of a CT characteristic change significantly under two or more different conditions introduced by one factor.

With the Two-Way ANOVA we can analyze the effect of two factors on a CT characteristic. An interaction effect between the two factors means that they have a combined effect on the CT trait.

The correlation coefficient is used to calculate the strength of the linear relationship between a continuously dependent variable (Y) and a continuously independent variable (X). If the relationship is strong, an equation describing this relationship can be obtained by linear regression analysis. With an appropriate line plot we can visualize the comparison with prediction bands. Most continuous decision-making tools assume that the data comes from a normal population. If it is not possible to characterize the population distribution or if the distribution is not normal, non-parametric tests can be used. Instead of studying the mean, these tests use the median because it is a more appropriate measure of the central tendency for data from non-symmetric distributions.

Source by Thomas Edwards