Where should the NOR be inside the design space? How close can the NOR be to the edge of design space?
Once the design space is established, there is often a desire to map out the area where one would operate routinely. Typically,
NOR is based on target settings considering variability in process parameters. The target settings could be based on the optimality
of quality, yield, throughput, cycle-time, cost, and so forth. The NOR around this target could be based as a function of
equipment and control-systems variability. However, how close the NOR can be from the edge of the design space depends on
how the design space is developed. For example:
- If the design space is constructed based on the predicted values, then historically, the normal operating range is developed
as a small interval around a set point. This NOR can move throughout the design space, but should include a buffer to keep
the NOR from the edge and allow the NOR to be sufficiently within the design space. The sources of variability to consider
in developing the buffer between the NOR and the design space edge are: variability associated with inputs such as raw/starting
materials; variability in process controls, including set point tolerances and set point drifts; any operator-to-operator
variability; measurement error (whether these are at-line or off-line); and any error associated with the modeling of the
surface (e.g., amount of data, the factors and levels chosen, scale-up uncertainty).
- If the design space description includes an interval-based approach which points to an area of higher assurance then, data
dependent, there may be no buffer between the NOR and the interval boundary. The interval boundary may need to be updated
as more manufacturing data become available. The design space boundary may stay constant. In any case, every company should
have sound quality systems in place to ensure appropriate oversight on any changes to NORs.
I didn't run experiments along my design space boundary. How do I demonstrate that the boundary is acceptable?
The design space will only be as good as the mathematical or scientific models used to develop the design space. These models
can be used to produce predictions with uncertainty bands at points of interest along the edge of the design space, which
is contained within the experimental region. If these values are well within the specifications and there is significant process
understanding in the models, then the prediction may be sufficient.
If I use production-size batches to confirm my design space, how should I choose the number of batches to run, and what strategy
should I apply to select the best points?
There is no single recipe to choose the points to run in order to verify the design space when developed subscale. Several
options are provided in the answer to Question 17 (see Part II of this article series (2)). Briefly, using either mechanistic
or empirical models along with performing replicates could provide some idea of the average response along with an estimate
of the magnitude of the variability. Alternatively, using existing models and running a few points at the most extreme predicted
values may be a reasonable approach if the design space truly provides assurance that the critical quality attribute requirements
will be met. Finally, a highly fractionated factorial (supersaturated) experiment of production size batches matched to the
subscale batches is another way to confirm the design space.