What a transformation really does is getting the median of the actual data set become the mean and the median in the new domain where data now closely follows a normal distribution. Therefore, transforming back the value of the mean does not produce a value matching the mean on the original data set but its median.

Although transformations do work in making a non-normal distribution appear normal, at the shop floor level they are of little use. If you don’t believe that, try explaining an operator he should be plotting data and making decision on the square root of seconds or the log of inches…

I do not agree with your statement that “When data is not normally distributed, the cause for non-normality should be determined and appropriate remedial actions should be taken.”

There is nothing wrong with data not following a normal distribution. There is nothing to be fixed. The word “normal” somehow may be misleading to imply that all data must be normal. The term really comes from observation of many processes in nature and manufacturing where the bell-shaped curve naturally or normally occurs.

As you correctly pointed out on the purchase order-generation process example, data are stable, but you would have been able to draw the same conclusion applying non-parametric methods such as a Minitab run-chart that proves the series of original data points to analyze four types of instability. Most likely, all four would come out with high p-Values, indicating a stable process. ]]>

Thank you for your article! I thought this was a great example and something I will be able to apply to a project in which I’ve been involved.

Eric

]]>I agree with the author that the lower limit is useless – the boundary conditions puts this at zero. Cycle time can’t be negative. Context has to override the calculated value of -2.7

Interpreting ALL the data in relation to the upper Limit of 9.12, the process is at least approximately, or reasonably, predictable. (Interpreting 50 data in one go is different to interpreting a new value, or a few new values, in a sequential Approach.)

The Green Belt team could then monitor future data after this baseline period using the upper Limit of 9.12.

The explanations of data transformation are easy to read and understand. This clarity, however, doesn’t mean the original data in this case should be transformed. For me, unnecessary and unjustified. ]]>

Please read Dr Wheeler “Normality and the Process Behavior Chart”

]]>Its because the belt wants to continue to monitor the process by analysing the data in a control chart. We all know control limits in a control chart assume Normal data. However his data is not normal, as demonstrated. So by carrying out the transformation, and determining the correct limits, these can now be applied to the actual, non-normal, data. Now going forward the only apparent out of control points will be ‘real’ out of control points. This will need to be performed each time data is added to the distribution as this could change the distribution shape, however the process stability can be assessed statistically with this transformation.

Nizamuddin Siddiqui,

Take for example the UCL: in the transformed data UCL is = 3.442. To represent as untransformed you just square it (3.442)^2 = 11.847. This is the reverse of the original transformation for Lambda 0.5

]]>Can you please tell me when the back-transformation is used the control limits are not matching with the original data control limits but how?

I am waiting for your response.

Thanks

]]>So why bother?

Because the individual values of the transformed data have no practical meaning, the Green Belt had to re-create a control chart for the original data, but this time with the correct control limits (Figure 10). To do this, the Belt used the upper and lower CLs from the control chart of the transformed data and transformed them back into their original values

]]>which statistical analysis software you have used? please named me.. ]]>