## FAQ

What is the aim of every 7Epsilon penalty matrix study?

What is product specific process knowledge?

What are main effects and interactions in 7Epsilon?

Why do we need to look at interactions?

How do we link design parameters with alloy chemistry and sand/mould or process parameters?

What is a penalty matrix? What is its principle?

What is a Main Effects Bubble Diagram?

What is an optimal and avoid factor region in terms of penalty values or bubble diagrams?

How is a penalty matrix populated?

Is there a software tool that uses the 7Epsilon penalty matrix approach?

How do we believe that answers from p-matrix software are logical?

What is a Confirmation Trial Plan?

What is tolerance limit optimisation?

How do I choose factor settings for a Confirmation Trial Plan?

How does the Penalty Matrix Approach facilitate Knowledge Retention and Reuse?

How to reduce defects in steps as you collect in-process data?

What data do we need for a 7Epsilon penalty matrix study?

What are steps in performing a 7Epsilon penalty matrix study?

7Epsilon's goal is not to use statistical tools for conducting design of experiments. The objective is to create a confirmation trial plan by analysing in-process data using penalty matrices, reviewing literature along with the domain knowledge.

Penalty matrices give you a list of top 15-20 parameters from potential combinations that could run into thousands. These parameters confine to their tolerance limits as they come from your own data sets. These simple yet innovative matrices help you visualize your in-process data and categorise optimal, avoid and no effect factor regions to reduce the variation in response values. You can then select optimal levels of combination of several factors to design a Confirmation Trial to validate the findings.

Implementation of a Confirmation Trial means simultaneous adjustment of multiple factor settings called as 'tweaking the process' or 'tolerance optimisation'. Foundry experts do this all the time. New process knowledge is gained after the confirmation trial shows reduction in variation of response.

7Epsilon gives a formal evidence based structure to this process so that the entire process improvement team benefits by gaining new knowledge that has potential to save money.

**What is the aim of every 7Epsilon penalty matrix study?**

The aim of every 7Epsilon penalty matrix study is to reduce your rejection rate further down by 1-2% from your existing levels of rejection and not coming down to zero percent in your first go.

**What is product specific process knowledge?**

In a manufacturing setup, Product Specific Process knowledge – is defined as

- The actionable information
- In the form of an optimal list of measurable factors and their ranges (e.g. Niobium: 0.77% – 0.827%; Aluminium: 3.24% - 3.306% Zirconium: 0.026% – 0.05%; Carbon: 0.095% – 0.113%; )
- in order to meet desired business goals that are process responses

e.g. to minimize defect rates, porosity scores or rework time etc. and maximize mechanical properties

**What are main effects and interactions in 7Epsilon?**

Main effect means a particular factor on its own will show reduction of variation in process response.

Interaction means a particular 'factor A' on its own is NOT STRONG ENOUGH to show reduction of variation in process response. However, if 'factor A' is maintained in its particular range and 'factor B' is maintained in its own particular range, then their joint effect has an ability to reduce the variation in process response.

**Why do we need to look at interactions?**

Two or more factors that are NOT STRONG ENOUGH on their own can still contribute to the reduction in variation of process response as their joint effect can be STRONG ENOUGH to reduce the variation in the process response.

**How do we link design parameters with alloy chemistry and sand/mould or process parameters?**

This is an advanced analysis and can be done once you undertake number of simple 7Epsilon projects.

**What is a penalty matrix? What is its principle?**

Penalty matrix is a data visualization method that helps you visualize your in-process data in a unique matrix format to discover trends in your data set.

Penalty matrix is based on a simple but innovative concept of penalising the variation in response values depending upon severity.

Penalty function is developed depending upon response types and threshold values chosen by users that categorize desired and undesired response for the corresponding response type.

The penalty function assigns 0 penalty value to good process output (ie. desired response), 100 penalty value to unacceptable process output (i.e. undesired response) and scales penalty values linearly from 1 to 99 for the remaining data or observations.

These penalty values are then transferred onto corresponding factor values to discover optimal, avoid and no effect regions of your process parameter.

Example scatter and penalty function for response % Shrinkage

**What are response types?**

Response types could be Lower the Better (LB), Higher the Better (HB) and Nominal the Best (NB).

Lower the Better response type is applied to rejection data. Here, good process output or desired response lies at the lower end of the spectrum below a threshold value. Unacceptable process output is at the higher end of the spectrum above a threshold value.

Higher the Better response type is applied to properties such as strength of material, hardness etc. Here, good process output or desired response lies at the higher end of the spectrum above a threshold value. Unacceptable process output is at the lower end of the spectrum below a threshold value.

Nominal the Best response type is applied to properties such as hardness. Here, optimal range could be between two limits and deviation from both limits is unacceptable

**What is a Main Effects Bubble Diagram?**

The response penalty values are transferred onto corresponding factor values to discover patterns in data to differentiate between optimal and avoid regions. Every point on the scatter diagram of a factor is assigned a response penalty value between 0 and 100 represented by bubbles in the Main Effects Bubble Diagram.

Bubbles with smaller diameter correspond to 0 penalty value that corresponds to desired response, whereas bubbles with larger diameter corresponds to 100 penalty value for undesired response.

Main Effects Bubble diagram for %Zirconium for response %Shrinkage

**What is an optimal and avoid factor region in terms of penalty values or bubble diagrams?**

Optimal region for a factor is the region/quartile with more number of data points with zero penalty value given to desired response. In terms of bubble diagram, the optimal factor region is the region with more number of bubbles with smaller diameter that in turn correspond to lower penalty values given to desired response.

Avoid region for a factor is the region/quartile with more number of data points with hundred penalty value given to undesired response. In terms of bubble diagram, the avoid factor region is the region with more number of bubbles with larger diameter that in turn correspond to higher penalty values given to undesired response.

Example Main Effects Bubble diagram for %Zirconium for response %Shrinkage

**How is a penalty matrix populated?**

p-matrix software analyses your in-process data by checking whether top 25%, top 50%, bottom 25%, bottom 50% or middle 50% of the process parameter settings influence the output of the process i.e. process responses. These 5 factor regions are represented as quartiles in the penalty matrix.

Q1 forms bottom 25% data values, Q2 forms bottom 50% data values, Q4 forms top 25% data values, Q3 forms top 50% data values and Q2+Q3 forms middle 50% region of process parameter.

Each cell in the penalty matrix shows number of data points within the factor region / quartile with the corresponding response penalty value. Response penalty values are continuous values from 0 to 100 but are shown as bins of 0-20, 20-40, 40-60, 60-80 and 80-100 for ease of readability.

Example Penalty Matrix for %Zirconium for response %Shrinkage

**Is there a software tool that uses the 7Epsilon penalty matrix approach?**

The penalty matrix approach is complemented by proven software tool to facilitate knowledge discovery so that foundries can reduce the rejection rate within three months.

The advantage of p-matrix software is that it analyses hundreds and thousands of penalty matrices or pivot tables for factors, responses and interactions among factors and ranks them in order of importance to discover the ones that you need to know.

In other words, at the end of p-matrix analysis, a process engineer would get a list of top 15-20 penalty matrices or pivot tables that he/she needs to look at from potential combinations that can run into thousands. This saves you time and money.

p-matrix software can discover Main Effects and Interactions from up to 40 process responses and 200 factors. You can input data in a very simple Excel format. The software outputs penalty matrices and a checklist on factor settings as Optimal, Avoid or No Effect.

**How do we believe that answers from p-matrix software are logical?**

Refer peer reviewed published literature in foundry conferences, journals, books or research thesis along with your own foundry experience coupled with p-matrix reports to make a final decision on parameters and their ranges for the confirmation trial.

E.g. if the middle 50% range of Niobium and Top 25% range for Aluminum is considered as an option in the confirmation trial to further reduce Shrinkage – not only because the trend was discovered by the p-matrix software but also it is reported in the peer reviewed literature.

- Kantor, B et. al. (2009), Influence of Al and Nb on castability of a Ni-based superalloy, IN713LC,
*International journal of cast metals research*, 22 (1-4), pp 62-65

...Increased Al and Nb additions result in decreased inter-dendritic shrinkage porosity...

**If we are analysing a defect e.g. surface finish and the answers from the p-matrix software are not logical. How do we move forward?**

p-matrix does not recognise the semantics behind the process parameter and response names. You may anonymize response and factor names for a p-matrix study by simply numbering them as response1, response2,…so on and factor1, factor2… so on etc. The software only looks for patterns in your data to discover optimal or avoid factor settings that will minimize the variation in process response. Domain knowledge is necessary to interpret the results.

If the results from the software do not seem logical then there may be additional factors that you may need to look for and collect data for. Data on relevant factors with proper traceability with response values will ensure meaningful results.

**How does the Penalty Matrix Approach facilitate Knowledge Discovery? OR How can I verify whether findings from the Penalty Matrix Approach reduce variation in process response?**

Penalty matrices help you to discover main effects and interactions.

A confirmation trial plan should be designed by interpreting p-matrix results, trends published in peer reviewed publications and the existing foundry specific process knowledge held within your organization.

New process knowledge is gained after the confirmation trial demonstrates reduction in the variation of response values.

**What is a Confirmation Trial Plan?**

Aim of a penalty matrix study is to analyse in-process data to discover trends in process parameter settings that have a positive or negative influence on process response(s). The matrix categorizes them as optimal, avoid and no effect settings.

The best way to verify results of the penalty matrix analysis is by performing a confirmation trial in your foundry. A Confirmation Trial Plan is a list of optimal factor settings for multiple process parameters that you have chosen to implement on the shop floor.

**What is tolerance limit optimisation?**

The simultaneous adjustment of multiple factor settings during a confirmation trial is called as 'tweaking the process' or 'tolerance optimisation'. Foundry experts do this all the time. 7Epsilon gives a formal evidence based structure to this process so that the entire process improvement team benefits by gaining new knowledge that has potential to save money.

**How do I choose factor settings for a Confirmation Trial Plan?**

It is easy to convert optimal factor settings into a confirmation trial plan.

For example, middle 50% range of Niobium is optimal for Shrinkage. The minimum value is 0.656 and the maximum value is 0.893. The middle 50% recommended range is {>0.77 & <0.827}.

For avoid settings you need to convert the range to its complementary settings for recommending a confirmation trial plan.

For example, bottom 25% range of Aluminum + Titanium is to be avoided to reduce Shrinkage. The minimum value is 6.204 and the maximum value is 6.527.

The bottom 25% range is 6.204 to 6.299. Hence the recommended range or the top 75% range is 6.299 to 6.527.

**How does the Penalty Matrix Approach facilitate Knowledge Retention and Reuse?**

Preserve and continuously develop process knowledge by compiling a library of case studies.

Capture industry specific product, design and in-process data, compare it with the published literature in order to continuously update the proprietary 'actionable information' or 'knowledge'. Keep track of references used and your observations from the confirmation trial. Store it along with the p-matrix Reports.

This is a simple but most effective way of retaining and reusing expertise within the foundry.

Reuse Data by maintaining traceability on product characteristics, design and in-process data across sub-processes, product types and supply chain. Over the period of time, this collective information will become a valuable intellectual property for your foundry and will help you to stimulate a culture of innovation within your foundry setup.

**How to reduce defects in steps as you collect in-process data?**

You can start analysing data for just 20-30 heats.

New heats can be ordered after analyzing penalty matrices and the subsequent confirmation trial result data be recorded and reanalyzed until the problem is resolved.

Design of experiments is not an option for most of foundries.

To use p-matrix is simple. Just collect your in-process data and input information to p-matrix software and let it discover correlations, main effects and interactions.

**What data do we need for a 7Epsilon penalty matrix study?**

You can choose a project with immediate cost saving potential and start analysing your existing data. It does not require any capital investment.

You can start p-matrix analysis with only 30 observations of in-process data on factors and responses. You do not need data for every process parameter and you may choose your factors/process parameters and responses for the study.

Process parameters range from Continuous parameters like pouring temperate, chemical compositions, density of shell slurry, sand parameters etc to discrete parameters like operator names, oven, furnaces, date and time of shift etc. Responses are the output of your process. They can be defects/material properties.

The best way to begin is to start analyzing your existing data to realize immediate cost saving opportunities.

Simple efforts on tracking time and date of data logging can allow personnel to link in-process data with rejection rate and material properties.

Reasonable traceability will ensure meaningful analysis.

The rewards are immediate and measurable.

**What are steps in performing a 7Epsilon penalty matrix study?**

Step 1: Choose a project with immediate cost saving potential for which you have in-process data on process parameters and responses.

Step2: Send us your data for the study. p-matrix Ltd will perform the study and send you your 1st p-matrix report. Domain knowledge will help you interpret the results.

Step3: p-matrix team will invite you for 1-2 one hour online sessions / WebEx meetings to discuss the results of p-matrix report.

Step4: Cross validate p-matrix results with the published literature to gain confidence in the findings.

Step5: Design your 1st 7Epsilon Confirmation trial plan to verify results of the analysis. p-matrix team will help you to develop the CT.

Step6: Conclude your study with results of the CT.

Step7: Complete the feedback sheet to give us your valuable feedback.

**Definitions**

**In-process or historical data**

Most foundries record data on chemical compositions, process parameters, design changes done, operators and machines, ovens or furnaces etc. This data is linked with one or more process responses via date and time of manufacture along with a corresponding batch/heat number or a unique identifier. This is referred to as production or in-process data.

**Factors/Process parameters**

Factors range from discrete parameters such as operators, shift, furnace to continuous factors like Pouring Time, Pouring Temperature, Chemical Compositions, viscosity, pH and density of shell slurry, sand parameters etc. You do not need data for every factor and you may choose your factors for a study.

**Responses:**

Responses measure the outcome of the process. These can be defects like inclusions, shrinkage, cracks etc, or material properties like UTS, YS, TS etc. Some responses are alloy-specific. E.g. for aluminum alloys - a porosity score can developed based on the distribution and strength of the porosity, whereas for steel alloys response could be related to the rework done. You do not need data for every response and you may choose your responses for a study.