ProSensus calculates multivariate specification regions to ensure that the right balance of properties is achieved.
Specification ranges on individual properties are often misleading because the measured quality properties are seldom truly independent of each other. The figure illustrates this problem using just two correlated properties.
The problem is compounded the more properties and/or materials there are. By contrast, multivariate methods provide a way to formulate specification regions that specifically address the observed relationships (correlations) among all the measured properties.
These types of specification problems are present in many industries. ProSensus has helped formulate multivariate specifications in several industries. Three examples will be shown in some detail here:
- Chemical Industry – Blown Film Process
- Pharmaceutical Industry – API Specifications
- Food Industry – Multiple Raw Materials
The ProSensus Approach
1) Blown Film Process
There are 10 properties measured on the resin used to create the blown film in this process.
A multivariate latent variable model showed that these 10 properties can be summarized via two multivariate combinations that can clearly separate acceptable and unacceptable lots of product. Specifications were set in this two-dimensional projected space to avoid the use of resins with properties that would result in an off-spec product being produced at the facility.
2) Pharmaceutical Industry – API specifications
Several bad batches were being produced at this pharmaceutical facility, with each bad batch costing upwards of $ 1 million. Better raw material specifications were clearly required to avoid such an occurrence. Seven measured properties are available for the Active Pharmaceutical Ingredient (API) used in this process. Multivariate models were built, and there was a clear separation of batches that would result in good product (conditions A and C) versus bad product (condition B).
Each new lot of material is run through this model (made accessible through a web portal) to determine if it will result in acceptable product. Depending on the specific balance of properties leading to an off-spec result (as captured in the contribution plot), a rejected lot can sometimes be diverted to another process where an acceptable quality outcome is still achievable.
3) Food Industry – Multiple Raw Materials
This example with Mondelez International in the food industry is quite challenging because there are 9 different raw materials from different suppliers, each with several measured properties. In order to set specifications, ProSensus needed to first determine which properties of the raw materials impact the product quality.
A multivariate model was built to predict product quality from raw material properties and processing conditions. Statistically insignificant variables were removed. The result was that properties of 8 of the 9 raw materials were significant for the prediction of quality, as well as many of the processing conditions. This is shown in the coefficient plot below.
When a new lot of one of the 8 key raw materials is being sent to the plant, the food manufacturer needs to be able to evaluate whether it will produce good product. However, it cannot be considered on its own. The manufacturer must consider the measured properties of the specific lot of this raw material in combination with all possible other lots of the other materials that it may be combined with.
ProSensus developed an advanced method for performing these calculations, where each new lot is combined with thousands of other combinations of raw material lots in a Monte Carlo simulation. If out-of-spec product is predicted with any other possible balance of properties of other materials, the material can be rejected. The figure below shows a new raw material that is expected to result in out-of-spec product with 7% of the possible combinations of lots of the other raw materials.
- C. Duchesne, J.F. MacGregor, “Establishing multivariate specification regions for incoming raw materials”, Journal of Quality Technology, 36(1), 78-94, 2004.
- 2. J.F. MacGregor, T. Kourti, “Statistical process control of multivariate processes”, Control Engineering Practice, 3, 403-414, 1995.
- 3. Z. Liu, M-J. Bruwer, J.F. MacGregor (ProSensus), B. Polsky, G. Visscher (Mondelez International), “Setting up simultaneous specifications on multiple raw materials to ensure product quality and minimize risk,” Presented at IFPAC-2013, Baltimore, USA, January 2013. (Slides available from ProSensus on request.)