statrefs home‎ > ‎Main‎ > ‎Fundamentals‎ > ‎Sampling and Randomization‎ > ‎

Sampling from Multicavity Molds



(Example files are attached at the bottom of this page.)

This section discusses methods for selecting subsets of cavities from a multi-cavity mold for mold qualification studies. This might also include multi-lane processes or process steps that use several sets of the same tooling.  The approach uses a preliminary study (prior to mold OQ-PQ) to explore potential similarities and differences in responses across all cavities.
  • These notes only describe possible approaches for selecting subsets of cavities from a multi-cavity mold.
  • CAUTION:  These notes do not offer any judgment regarding the potential risks vs. benefits from using this approach.


The cavities (lanes, tools, etc.) selected to represent all cavities in subsequent studies (including process validation Operational Qualification and Performance Qualification) have been referred to as "ambassador cavities".


Assumptions include:
  • The performance in each cavity is stable over time (statistically in control).



The steps include:

  • A preliminary ANOVA-based study across all elements (cavities, lanes, tools, etc.) which also preserves time-order of data
  • From this preliminary data:
    • identify and eliminate sources of variation
    • explain and address any differences between cavities, lanes, tools, etc.
  • if enough samples are collected from each cavity (lane, tool, etc.) with the time-order preserved, look for gross signs of instability
  • collect specimens from each cavity (lane, tool, etc.) at the same time so that methods can be used to look for similarities and differences in behavior.  scatterplot matrices are one example of how this can be studied.
    • possibly also recenter the process if needed.
  • Once excess variation and unanticipated/unwanted differences have been addressed, select a subset of the elements of the process (homogeneous cavities, lanes, tools, etc.) and conduct Phase 1 SPC studies









Test Method based on variables (continuous) data.


Collect specimens from each cavity.

If the number of shots chosen for testing is a subset of the total number of shots (by cavity), then consider using a random number generator to select the specific shots whose specimens will be tested.  This will help avoid missing any cyclical / periodic issues.

Look for cavities with similar (homogeneous) behavior.
  • Perform One-Way ANOVA.
  • Look for groups of cavities with similar performance in (1) means and (2) variances.

Other considerations for selection of subsets of cavities may include:
  • Normality of data from cavities.
  • Residual analysis from ANOVA diagnostics, noting cavities with unusual observations (outliers).
  • Preliminary assessment of potential Ppk based on cavity means and standard deviations.  This assumes that future SPC studies will demonstrate that the cavities are statistically in control.
  • Geographic location of cavities chosen, avoiding choosing cavities entirely from one region of the mold leaving other regions of cavities unrepresented.



Test Method based on survival/reliability data, potentially including censoring.


Similar to method for variables data.
Collect specimens from each cavity.

Look for cavities with similar (homogeneous) behavior.
  • Use survival analysis methods to find groups of cavities with similar responses.
  • Consider non-parametric comparisons (Wilcoxon, Log Rank), as well as multiple comparison method (SAS macro similar to Scheffe).

Other considerations for selection of subsets of cavities may include:
  • Geographic location of cavities chosen, avoiding choosing cavities entirely from one region of the mold leaving other regions of cavities unrepresented.



Test Method based on attribute (categorical) data.


Collect specimens from each cavity.
May need to collect a larger sample size from each cavity than for tests based on variables (continuous) data.

Look for cavities with similar (homogeneous) behavior.
  • Use tests for equivalence of proportions or methods based on cross-tab tables and the Chi-square statistic.
  • Odds Ratios and Logistic Regression can also be useful in certain situations.


Other considerations for selection of subsets of cavities may include:
  • Geographic location of cavities chosen, avoiding choosing cavities entirely from one region of the mold leaving other regions of cavities unrepresented.



 
Comments