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Sampling and Randomization








General thoughts on randomization.

 
For experimental designs, proper randomization is critical to ensure that some unforeseen element isn't confounded with the experiment.
  • Randomizing the order of DOE treatments.
  • Randomization of the selection of specimens from the process
  • (For DGR&R studies) Randomization of the assignment of specimens to combinations of Operator-Sample.
  • Randomization of the order of testing of specimens after they are produced (and assigned).


From Searle page 8:
"The manner in which data are obtained always affects inferences that can be drawn from them."



Related articles



Considerations for the selection of specimens from a process.


If the process involves sampling across multiple cavities, or across the width of a web of film
  • Consider doing a One-Way ANOVA study to see if there are homogeneous groups (cavities, etc.).  
  • If there are homogenous groups or regions, then consider collecting specimens from a subset of groups that represent the variation of the population.  This can reduce the sample size while providing useful information.  
  • For DGR&R, cannot mix groups (e.g. cavities) in the "Trial" term, as we seek to make trial-to-trial variation within each sample as homogeneous as possible because the Trial term is confounded with the Gauge Repeatability variance component.
  • If collecting specimens to study a process or a measurement system, give consideration to collecting specimens that represent the width of process variation, and changes in process output over time and under whatever conditions influence the process.


Considerations for randomization.

 
Identify and account for any restrictions on randomization.
  • If a restriction on randomization is unavoidable, create a blocking variable to track it through the analysis. 
  • Also, if restrictions on randomization may lead to potential confounding, it is possible to design the experiment such that the confounding aligns with a less important variable.  See Block Confounding.

For experiments when specimens are produced over a period of time:
  • Consider assigning groups of specimens to blocks of time (morning, afternoon; day 1, day 2; etc.) and ensuring that the randomization plan for assigning specimens to testing in the protocol includes a provision to account for the blocking variable. 
  • Document and track the specimens by the blocking variable through the analysis to see if the blocking variable has a noteworthy impact on the outcome. 


Randomization of the order of testing of specimens.


How important is it that the order of testing is also randomized?  Very! 

Why?  Because there may be unanticipated factors that can influence the outcome of testing that might change in a non-random way during the course of the testing.  An example might be temperature changes in a room where testing is being done for a GR&R or DOE study.

If multiple operators / technicians / appraisers will be used in the study, efforts should be taken to avoid having each operator conduct all of their testing at one time.  The order of testing of operators should be mixed ... if it can be fully randomized, then do so; otherwise consider having each operator do testing on a subset of the specimens assigned to them, and create a blocking variable for these subsets.  This blocking variable can then be randomized (partial randomization) and tracked throughout the analysis.

An example where randomization of the order of testing might not be feasible could be where mold shrink can affect the results, in which case the specimens might need to be tested in the order that they were collected ... and within a specified time after production.

 

Tools and methods for randomization.


Several methods are available for randomization.  Random number generators in various packages can be used.  Different random number generators may have different properties. 

 

Lesson learned from study regarding the relationship between burst and seal strength:
> Keep the specimens that were tested - don't dispose of them until after the reports are complete.