I am trying to evaluate nutrients uniformity of a batch produced by mixing four ingredients in a mechanical mixer. Want to use full-factorial design with three factors at two levels each (ingredient types, mixing speed , amount of material used) with multiple responses (nutrients - iron, copper, etc.).
Full Factorial 2 * 2 * 2 design = 8 unique trials
Product from each trial is packaged into two bags and samples are drawn from multiple locations (top/middle/bottom) out of bags for testing. Total 18 samples are tested from each batch. How can I include this data into DOE ? Will have to make sample locations and bag # as factors ? or will have to average results from 18 sample testing to include in full factorial design? do I have to run separate ANOVA analysis for each batch results to assess batch uniformity?
A few questions to help clarify your request.
It sounds like your design is set. A lot of the solution depends on how you intend to model the effects on the response and what estimates you want. Some of your effects are fixed and others are random. The three factors contribute fixed effects. Batch contributes a random effect. What about Bag and Location? It seems that you sample three times from each location in each bag from each batch. If so, are three samples required because of the imprecision of the assay to determine the nutrient levels? If measure system error is a large portion of the variation, then you might want to separate it from the process variation that you want to characterize. I would use the mean estimate of the three measurements to reduce the measurement error component.
You can enter Batch, Bag, and Location as factors. JMP will model their effects as fixed by default, but you can change them to random in the Fit Model dialog box. Random effects produce variance component estimates. Fixed effects produce coefficient estimates.
Variance component estimates require much larger sample sizes than mean estimates for comparable confidence intervals. That is, the estimation of the mean is much more efficient than the estimation of the variance.
Thanks for the response.
Full factorial is presumably the best classic comprehensive design which include trials with all combinations. Actually two of my factors are categorical (typo mistake - mixing technique is the factor instead of mixing speed, mixing speed is constant), total three factors (mixing technique, material amount or fill level, ingredient types). Yes, response is measured in respective nutrient concentration.
The bags are almost cylindrical when full, almost 3 ft tall and a special sampler is used to draw samples which allows sample to be drawn from same height/depth for top/mid/bottom. Each batch results into two bags (bag 1 and 2). Out of each bag, I plan to take samples (T/M/B) at three locations. 9 samples per bag (total 9*2=18 samples per batch). As I am not going to fix horizontal locations of sample, three top samples from three locations per bag can be considered as replicates. I intend to use "sample vertical location" (top, mid, bottom) and bag # (1/2) as factors. What do you think? Yes, due to variabilities such as assay, etc. taking three samples for T/M/B.
The full factorial design method makes sense in this case because you want all combinations. Include Bag and Position as factors. Do not replicate the design. You want to model the average concentration so that the random variation is predominately from the process and not from assay. Instead, add three columns to the right of the response data column in your table. Enter the triplicate assays in these columns. Add a formula for the mean to the response data column. (Hint: select the replicate data columns, right-click on one of them, and select New Formula Column > Aggregate > Mean. Copy the formula from this column and paste it into the formula for the response data column. You don't need the new data column, so delete it. Or just create the formula directly in the response data column if you think that is faster.)
Click the green triangle next to the Model table script. Remove any cross terms that include Bag or Position. Select Bag and Position terms, click the red triangle next to Attributes, and select Random Effect. Now you will estimate the fixed effects of Mixing Technique, Material Amount, and Ingredient Type. The REML outline will display the estimates of the variance components for Bag, Location, and statistical error.
I forgot to add that another aspect of the analysis that is not captured in the design is the nesting of factor levels. For example, Location = Middle is not the same for each Bag. That is physically impossible. JMP design methods assume that all factor levels are crossed. The nested structure is another aspect that is added in the Fit Model launch dialog box.
You might need some help with specifying your model in Fit Model dialog box, so just ask away!