Stat-Ease Blog

The Peculiar Math Behind Mixture Experiments: A Sugar-Sweetness Case Study

posted by Mark Anderson on Aug. 25, 2026

Ever run a mixture experiment where every component looks like a win, only to have the trace plot tell a different story? The following FAQ tackles that exact puzzle — why some ingredients can show a “negative” track in a trace plot even when they contribute positively overall. Stat-Ease consultant Mark Anderson breaks down the mixture-model math behind it using a simple sugar-sweetness example.

Original question from a chemist:

“I completed a mixture screening experiment to assess the effects of 3 components. All ingredients produced positive effects. However, the trace plot contradicts this outcome—several of the components (A, B and C) displaying negative tracks. How can this be?”

Answer from Stat-Ease:

“This is a peculiarity of the mixture models (also known as Scheffé polynomials). I created a similar example on a hypothetical mixture of 3 types of sugar by setting up an equation-only model: R = 1A + 2B + 3C. Then I generated a trace plot showing how the predicted response changes when you increase one component while keeping the ratios of the other components constant.

Trace plot from mixture screening experiment

The plot shows the downward impact of A (sugar S1) on sweetness due to it having the lowest coefficient of the three ingredients. This is relative to the other ingredients, adding more of that specific component does not lower the response on its own. Component B (sugar S2) generates a flat track—it’s impact on sweetness is ‘middling.’ The most impactful ingredient is C (sugar S3), as evidenced by its upward track.

For another example showing the trace plot being put to good use, see the November 2024 blog Perfecting pound cake via mixture design for optimal formulation.

March Publication Roundup

posted by Stat-Ease Team on April 2, 2026

Here's the latest Publication Roundup! In these monthly posts, we'll feature recent papers that cited Design-Expert® or Stat-Ease® 360 software. Please submit your paper to us if you haven't seen it featured yet!

While none of this month's publications met our standards for a featured article (publicly accessible & correctly applying DOE), they're still all quite interesting! Take a look.

New publications from March

Development of engineered magnetic liposome/exosome hybrid as a novel caffeine nanocarrier for restraining liver fibrosis induced in rats
Scientific Reports volume 16, Article number: 5349 (2026)
Authors: Yara E. Elakkad, Hanan Refai, Hanaa H. Ahmed, Ahmed N. Abdallah, Menna M. Abdellatif, Ola A. M. Mohawed, Rehab S. Abohashem
Correlation between carbon percentage and nanocomposite performance in commodity and engineering thermoplastics (ABS, HIPS, PP, and PC)
Scientific Reports volume 16, Article number: 8492 (2026)
Authors: Mahmoud A. Essam, Amal Nassar, Eman Nassar, Mona Younis
Design expert and python-based optimization of recycled aggregate concrete with a comparative analysis of ANN and M5P-tree models for predicting compressive strength
Journal of Building Engineering, Volume 123, 1 April 2026, 115865
Authors: Yousif J. Bas, Jamal I. Kakrasul, Kamaran S. Ismail, Samir M. Hamad

October Publication Roundup

posted by Rachel Poleke, Mark Anderson on Nov. 3, 2025

Featured Article

Green extraction of poplar type propolis: ultrasonic extraction parameters and optimization via response surface methodology
BMC Chemistry, 19, Article number: 266 (2025)
Authors: Milena Popova, Boryana Trusheva, Ralitsa Chimshirova, Hristo Petkov, Vassya Bankova

Mark's comments: A worthy application of response surface methods for optimizing an environmentally friendly process producing valuable bioactive compounds. I see they used Box-Behnken designs appropriately - good work!

Be sure to check out this important study, and the other research listed below!

More new publications from October

Development and evaluation of a battery powered harvester for sustainable leafy vegetable cultivation
Scientific Reports, volume 15, Article number: 33812 (2025)
Authors: Kalluri Praveen, Yenikapalli Anil Kumar, Atul Kumar Shrivastava
Rutin/ZnO/mesoporous Silica-based Nano-hydrogel accelerated topical wound healing in albino mice via potential synergistic bioactive response
European Journal of Pharmaceutics and Biopharmaceutics, Volume 216, November 2025, 114875
Authors: Huma Butt, Haji Muhammad Shoaib Khan, Muhammad Sohail, Amina Izhar, Farhan Siddique, Maryam Bashir, Usman Aftab, Hasnain Shaukat
Production of improved Ethiopian Tej using mixed lactic acid bacteria and yeast starter cultures
Scientific Reports, volume 15, Article number: 33460 (2025)
Authors: Ketemaw Denekew, Fitsum Tigu, Dagim Jirata Birri, Mogessie Ashenafi, Feng-Yan Bai, Asnake Desalegn
Design and Optimization of Trastuzumab-Functionalized Nanolipid Carriers for Targeted Capecitabine Delivery: Anti-Cancer Effectiveness Evaluation in MCF-7 and SKBR3 Cells
International Journal of Nanomedicine, Volume 2025:20 Pages 12075—12102, 3 October 2025
Authors: Shubhashree Das, Bhabani Sankar Satapathy, Gurudutta Pattnaik, Sovan Pattanaik, Yahya Alhamhoom, Mohamed Rahamathulla, Mohammed Muqtader Ahmed, Ismail Pasha
**Design and test analysis of a rotary cutter device for root cutting of golden needle mushroom
Scientific Reports, volume 15, Article number: 37219 (2025)
Authors: Limin Xie, Yuxuan Gao, Zhiqiang Lin, Feifan He, Wenxin Duan, Dapeng Ye
Central composite design optimized fluorescent method using dual doped graphene quantum dots for lacosamide determination in biological samples
Scientific Reports, volume 15, Article number: 36507 (2025)
Authors: Ahmed Serag, Rami M. Alzhrani, Reem M. Alnemari, Maram H. Abduljabbar, Atiah H. Almalki
Innovation in functional bakery products: formulation and analysis of moringa-fortified millet cookies
Journal of Food Measurement and Characterization, Published: 17 October 2025
Authors: Anshu, Neeru & Ashwani Kumar
Improving the efficacy and targeting of letrozole for the control of breast cancer: in vitro and in vivo studies
Naunyn-Schmiedeberg's Archives of Pharmacology, Published: 13 October 2025
Authors: Shahira F. El Menshawe, Seif E. Ahmed, Amr Gamal Fouad, Amira H. Hassan
Optimization and Evaluation of Functionally Engineered Paliperidone Nanoemulsions for Improved Brain Delivery via Nasal Route
Molecular Pharmaceutics, Published October 7, 2025
Authors: Niserga D. Sawant, Pratima A. Tatke, Namita D. Desai
Innovative inhalable dry powder: nanoparticles loaded with Crizotinib for targeted lung cancer therapy
BMC Cancer, volume 25, Article number: 1526 (2025)
Authors: Faiza Naureen, Yasar Shah, Maqsood Ur Rehman, Fazli Nasir Fazli Nasir, Abdul Saboor Pirzada, Jamelah Saleh Al-Otaibi, Maria Daglia, Haroon Khan

September Publication Roundup

posted by Rachel Poleke, Mark Anderson on Oct. 1, 2025

When choosing a featured article for each month, we try to make sure it's available for everyone to read. Unfortunately, none of this month's publications that met our standards are available to the public, so there's no featured article this month. We still recommend checking out the incredible research done by these teams, and congratulations to everyone for publishing!

New publications from September

Evaluating the efficacy of nintedanib-invasomes as a therapy for non-small cell lung cancer
European Journal of Pharmaceutics and Biopharmaceutics, Volume 214, September 2025, 114810
Authors: Tamer Mohamed Mahmoud, Mohamed AbdElrahman, Mary Eskander Attia, Marwa M. Nagib, Amr Gamal Fouad, Amany Belal, Mohamed A.M. Ali, Nisreen Khalid Aref Albezrah, Shatha Hallal Al-Ziyadi, Sherif Faysal Abdelfattah Khalil, Mary Girgis Shahataa, Dina M. Mahmoud
Optimization of fermentation conditions for bioethanol production from oil palm trunk sap
Journal of the Indian Chemical Society, Volume 102, Issue 9, September 2025, 101943
Authors: Abdul Halim Norhazimah, Teh Ubaidah Noh, Siti Fatimah Mohd Noor
Microwave-assisted modification of a solid epoxy resin with a Peruvian oil
Progress in Organic Coatings, Volume 206, September 2025, 109333
Authors: Daniel Obregón, Antonella Hadzich, Lunjakorn Amornkitbamrung, G. Alexander Groß, Santiago Flores
Authors: Hüsniye Hande Aydın, Esra Karataş, Zeynep Şenyiğit, Hatice Yeşim Karasulu
Development of an innovative method of Salmonella Typhi biofilm quantification using tetrahydrofuran and response surface methodology
Microbial Pathogenesis, Volume 208, November 2025, 107992
Authors: Aditya Upadhyay, Dharm Pal, Awanish Kumar
Bauhinia monandra derived mesoporous activated carbon for the efficient adsorptive removal of phenol from wastewater
Scientific Reports volume 15, Article number: 31790 (2025)
Authors: Bhojaraja Mohan, Chikmagalur Raju Girish, Gautham Jeppu, Praveengouda Patil
Quality by Design-Driven Development, Greenness, and Whiteness Assessment of a Robust RP-HPLC Method for Simultaneous Quantification of Ellagic, Sinapic, and Syringic Acids
Separation Science Plus, Volume 8, Issue 9, September 2025, e70126
Authors: V. S. Mannur, Rahul Koli, Atith Muppayyanamath
Dissolution and separation of carbon dioxide in biohydrogen by monoethanolamine-based deep eutectic solvents
Journal of Chemical Technology and Biotechnology, Early View, 12 September 2025
Authors: Xiaokai Zhou, Yanyan Jing, Cunjie Li, Quanguo Zhang, Yameng Li, Tian Zhang, Kai Zhang
Strategic Implementation of Analytical Quality by Design in RP-HPLC Method Development for Andrographis paniculata and Chrysopogon zizanioides Extract-Loaded Phytosomes
Separation Science Plus, Volume 8, Issue 9, September 2025, e70125
Authors: Abisesh Muthusamy, Vinayak Mastiholimath, Darasaguppe R. Harish, Atith Muppayyanamath, Rahul Koli
Improving the bioavailability and therapeutic efficacy of valsartan for the control of cardiotoxicity-associated breast cancer
Journal of Drug Targeting, Published online: 29 Sep 2025
Authors: Mary Eskander Attia, Fatma I. Abo El-Ela, Saad M. Wali, Amr Gamal Fouad, Amany Belal, Fahad H. Baali, Nisreen Khalid Aref Albezrah, Mohammed S. Alharthi, Marwa M. Nagib

July Publication Roundup

posted by Rachel Poleke, Mark Anderson on Aug. 4, 2025

Featured Articles

Microwave-assisted extraction of bioactive compounds from Urtica dioica using solvent-based process optimization and characterization
Scientific Reports volume 15, Article number: 25375 (2025)
Authors: Anjali Sahal, Afzal Hussain, Ritesh Mishra, Sakshi Pandey, Ankita Dobhal, Waseem Ahmad, Vinod Kumar, Umesh Chandra Lohani, Sanjay Kumar

Mark's comments: Kudos to this team for deploying a Box-Behnken response-surface-method design--convenient by only requiring 3 levels of each of their 3 factors (power, time and sample-to-solvent ratio)--to optimize their process. Given all the raw data I was able to easily copy it out and import it into my Stat-Ease software and check into the modeling--no major issues uncovered. The authors did well by diagnosing residuals and making use of our numerical optimization tools to find the most desirable factor combination for their multiple-response goals.