MT System Consulting
Table of Contents
Utilize your big data to improve your performance, and enhance your continuous improvement with Mahalanobis Taguchi System!
MT system utilizes multivariate data to diagnose, monitor, estimate, forecast and classify outputs from wide range of value creating process to keep output safe always. The core technology of MT system is pattern recognition technology that has been applied in very broad industries for decades from medicine, banking, engineering, and others to control output safely and effectively.
MT system can be applied to almost all the context where we are using data for a decision, and MT system detect abnormality precisely with less samples than artificial intelligence
The advantages of MT system are in it’s efficiency, speed, and effectiveness to classify individual object from unknown group
An illustration showing how MT system works to monitor drilling machine
Develop Classification System
Why MT system
Mahalanobis distance was created by an indian statistician Dr. Mahalanobis in the 1930s to classify animal skulls using inverse covariance matrix, however, it had not been used for long time to solve business problems till 1970s because of difficulty of calculating inverse matrix with multivariate data. In the 1970s as computers were widely used in business, Dr. Taguchi improved Dr. Mahalanobis’s idea, and suggested MT system to diagnose and forecast output with multivariate data.
Dr. Taguchi said that Leo Tolstoy’s masterpiece, Anna Karenina, describes well his concept on MT system.
“ Happy families are all alike; every unhappy family is unhappy in its own way”
— the opening sentence of Anna Karenina, Leo Tolstoy—
If we arrange this text to describe business problems we may rewrite it as follow;
– Good finished goods are all alike; every no good finished good is no good in its own way
– Healthy people are all alike; every unhealthy person is unhealthy in his own way
– Good money borrowers are alike; every bad money borrower is bad in his own way
– Highly performed sales persons are all alike; every low performed sales person is low in its own way
– Highly performed machines are alike; every poorly performed machine is poor in its own way.
Dr. Taguchi said that we need to measure good parts first not defectives to manage quality effectively because it is easier for us to investigate simple patterns of good parts than complicated patterns of defectives.
We call a group of good parts as a “normal group” and a group of defectives as a “abnormal group”.
The importance of Mahalanobis Space
The first step of MT system is to define a normal group(good parts)with enough number of samples.
The second step is to define variables to measure the good parts, and then develop a mahalanobis space (unit space) with the measured normal group samples.
A mahalanobis space is a reference group to classify abnormal samples from unknown group, and forecast output.
Developing high quality mahalanobis space is a challenge and critical in MT System. It requires measurement system and statistical data analysis.
StatSolutions help you develop highly reliable and efficient mahalanobis space using big data to utilize for an automated machine control or process control system.
The uniqueness of MT system
MT system has been studied by engineers, researchers and statisticians in various industries for decades, and now more people accept MT system as a part of artificial intelligence, and MT system is now being used globally as a new solution for the industry 4.0 era in both manufacturing and service industry.
Mahalanobis distance is a distance from the center of a reference group(unit space) to an unknown individual sample. It is accepted among statisticians as a better idea for classification than other statistical methods. The larger Mahalanobis distance has more chance of not belonging to a reference group.
Another unique idea of MT system is to evaluate predictive power of predictors with the SN ratio (signal-to-noise ratio). A predictor having larger SN ratio is more important to detect abnormality.
In pattern recognition, output is influenced by many factors, ranging from process conditions to statistical parameters for computing, and it is a challenge to identify good predictors to diagnose effectively. SN ratio makes it easier and simplify the evaluation process of predictors
Advantage of MT system against AI
Machine learning has been widely used in AI, however, machine learning hardly explain how result comes out, and it results in limited information to problem solvers who need to make countermeasures to solve a problem based on root cause.
MT system explains the meaning of the output mathematically. It helps problem solvers get insights on root cause for developing effective countermeasures. Furthermore MT system is much faster, and consumes less computer memory than that of machine learning or artificial intelligence (AI).
Utilize your buried data to build a smarter factory and to maintain breakthrough improvement.
6 Modules of MT system
Because every customer has different issues and requirements, It is a challenge to meet customer requirements.
StatSolutions tackles this challenge with well organized 6 MT System modules.
MS-MT module to calculate Mahalanobis distance with correlation matrix, and evaluate prediction power of variables.
Module 2. MS-VPM
MS-VPM to calculate Mahalanobis distance without correlation matrix, and evaluate prediction power of variables.
Module 3. MS-MTGS
MS-MTGS module to calculate Mahalanobis distance with Gram-Schmidt’s orthogonal process, and evaluate prediction power of variables.
Module 4. MS-MTA
MS-MTA module to calculate Mahalanobis distance with adjoint matrix, and evaluate prediction power of variables.
Module 5. MS-RT
MS-RT module to calculate Mahalanobis distance with small size of samples, for image classification and evaluate prediction power of variables.
Module 6. FT-T1
FT—T1 module to build a mathematical model to estimate output without inverse matrix. The purpose of T1 method is same as multiple regression.
Case of MT system for problem solving
MT system (Mahalanobis Taguchi system)is a powerful tool to identify root causes of problems as well.
StatSolutions improved productivity of thin transparent conducting films of one of our clients.
The client wanted to improve productivity of transparent conducting films that were coated in a vacuum chamber of a sputtering machine to complete 24 thin layers of coat.
One of the challenges was to handle the big data saved on the storage of a machine, and each layer had 30 to 40 variables to record. Another challenge was that operators had no ideas how the coating process was working in the chamber because operators were not able to see inside of the vacuum chamber. The vacuum chamber was a kind of black box to operators.
StatSolutions consultants investigated the whole sputtering process, and arranged multivariate data saved in CSV file, and divided samples into two groups, normal group, and abnormal group, and calculated Mahalanobis distance for each group, and conducted computer experiments with orthogonal array to verify the accuracy of the Mahalanobis space.
StatSolutions consultants created graphs with Mahalanobis distances, and found significant differences in patterns between good films and no good films as below:
1. Pattern of good films:
the pattern of unknown film(red-dots) is overlapped completely to the pattern of blue dots(unit space=good film)
the pattern of blue dots(good films) and the red dots (unknown films) are not matched. No good films have more peaks(fluctuations) in the same range of time.
the pattern of blue dots(good film) and the red dots(no good film) are not ovelapped. No good films has more peaks and the start point is not matched each other.
With these findings, engineers and operators could understand clearly what had been happened in the vacuum chamber. StatSolutions consultants developed countermeasures with engineers and operators to improve productivity with eliminating chronic quality problems.
At the end of the project, StatSolutions consultant conducted a simulation with computer and optimized the MT system for detecting defects. A benchmark test conducted by StatSolutions has shown that the MT system enables the machine operators to save data analysis time by 70% as well.
Optimizing Mahalanobis Space in MTS
Step 1. Initial Mahalanobis Space
Classification with initial Mahalanobis Space (total 19 variables) all the abnormal samples can be classified with 19 variables.
Step 2. Evaluating Prediction Power of Variables
Evaluating prediction power of variables and identifying root causes with SN ratio (removing 11 variables having negative SN gain). There is a chance to reduce variables to save energy for measurement system and to identify root causes.
Step 3. Optimized Mahalanobis Space
Classification with optimized Mahalanobis Space (total 8 variables). The abnormal samples are more clearly classified with reduced measurement variables.
The Power of Quality Solutions