Miscellaneous Notes

General Fix #4: Click the Start/Windows button, Type Go to Start (Start/Run) type the following in the search box: cmd /c “echo off | clip” (including the quotes) then hit Enter. Note that there is a space between "cmd" and "/" but nowhere else. I keep a copy of this command in my stickies on ClipX so I don't have to go back and find it every time this happens. If you prefer, you can create a desktop shortcut that does the same thing. Just right-click on any free space on the desktop and select New, Shortcut. Type the command into the location box. Click Next, name the shortcut and Finish.

DOE-based testing for leakage of fluid from a flange

·         This appears to use a pass/fail response variable in a DOE.  If so, then the QE would have needed to use Logistic Regression methods to analyze the DOE data.  There was no evidence that the QE used this statistical method.

·         Also, the sample sizes were far too small, and the levels for the factors might need reconsideration as this type of study needs to find and test the boundary between process settings that yield 'good' product and those that yield 'bad' product.  This type of DOE model has been used successfully.  It requires additional training and coaching.

·         There is a very good chance that if he had done the above things a bit differently, that the QE could have discovered how process inputs affect this response.



Statements about Ppk being "greater than" or "less than" a stated value

·         First, it is great that the QE was checking this with the DOE treatments.  It can give very useful clues as to how to balance 'optimized' process output (e.g. seal strengths) with statistical control and capability of the process at different settings.

·         However, to state that Ppk (or Cpk, etc.) is "greater than" or "less than" a particular value (here, 1.33) requires reporting the interval estimate of the PCI (Process Capability Index), which I did not find in the report. 

o   Think of this as a hypothesis test (similar to a one-sample t-test) with H0: Ppk = 1.33 (or >= 1.33; or <= 1.33). 

o   Then the alternate hypothesis is Ha: Ppk <> 1.33 (or < 1.33; or > 1.33).


Model diagnostics

·         Whenever we use a statistical method, we should know the assumptions behind the method/model and we need to test these assumptions.  Tests of these assumptions ("model diagnostics") need to be performed, and the results of these diagnostics should be included in the report.  Violations of model assumptions need to be addressed.

·         Oftentimes we find that violations of assumptions provide some useful and actionable process or product design knowledge that leads to improvement.



Other potentially useful considerations:

·         While the QE attended to this issue when the Ppk value was reported for each DOE treatment, it is often helpful to make a map of not only the expected mean response based on the DOE model, but also of the expected variance in the DOE design space. 

·         It is also useful to look at the "robustness" of the response, which the QE did to some extent.  This means that we want the response to be as "flat" as possible (small slope of the response variable) where we intend to set the process so that changes in process inputs (or materials) don't cause a rapid change in the process output.   This can - and has - allowed us to make tradeoffs; one example was when we made minor changes (a reduction) in process speed that justified and lead to more stable product reliability.

·         Knowing the slope of the process response can also help us assess the allowable fluctuations in process inputs (such as =/- 5 degrees or psi) vs. the controllable variation in process inputs (maybe we can only control temp within +/- 10 degrees).


PERT Project Schedule Estimates and the Beta Distribution



Table 3 illustrates the project with three time estimates for each activity. While m represents the most likely time for the activity, a suggests the optimistic estimate and b is the pessimistic estimate. The estimated time and or standard deviation for each activity ( E ) are calculated from the formula for the flexible beta distribution. With a reasonably large number of activities, summing the means tends to approximate a normal distribution, and statistical estimates of probability can be applied.

The mean is calculated as [( a + 4m + b ) ÷ 6 ], an average heavily weighted toward the most likely time, m. The standard deviation for an activity is [( b a ) ÷ 6 ], or one-sixth of the range. Managers with a basic understanding of statistics may relate this to the concept of the standard deviation in the normal distribution. Since ±3 standard deviations comprise almost the entire area under the normal curve, then there is an intuitive comparison between a beta standard deviation and the normal standard deviation.


Subpages (1): Box Dimensions