Authors
Kevin Potcner
JMP
Objective
Analyze the results of an experiment to determine if there is statistical evidence demonstrating an improvement in a new laundry detergent formulation. Explore and describe the affect that multiple factors have on a response, as well as identify conditions with the most and least impact.
Background
The effectiveness of a consumer product is of paramount importance, both to the company that manufacturers it and the consumer who uses it. This effectiveness determines the product’s price point, customer satisfaction, and ultimately profitability for the company. One such consumer product used in almost every household is laundry detergent.
Detergent manufacturers are constantly working on developing new formulations that can perform better than the current one and be manufactured at a lower cost. The R&D team for one such manufacturer has developed a promising new laundry detergent formulation that can be produced with a 10% cost reduction.
To study the effectiveness of this new detergent formulation and to compare its performance to the current formulation, the following experiment was performed and the results stored in a JMP data table.
A set of cotton fabric specimens were prepared by being soiled with a dirt-based substance uniformly across the fabric. The test specimens were cut into two sub-specimens. One of them was washed using the current formulation of detergent and the other with the new formulation. After washing, each subspecimen was measured using a reflective densitometer to obtain a brightness measure. The difference between the two brightness readings was used to create a metric that is a measure of the percent increase in brightness of the new formulation versus the current one. Specifically, the value 0 represents no difference in the brightness readings of the two sub-specimens, a value of 10.0 represents 10% more brightness in the sub-specimen washed with the new formulation compared to the current formulation, and a value of -10.0 represents the sub-specimen washed with the new detergent having a brightness reading 10% less than the one washed with the current formulation.
In order to study the effectiveness of the new formulation across a range of washing conditions, all combinations of three water temperatures (Cold, Warm, Hot), two washing times (20 minutes, 40 minutes), and three agitation levels (Low, Med, High) was used. This resulted in 3x2x3=18 experimental treatment combinations.
An important principle in designing experiments is to obtain an estimate of experiment error, which is an estimate of the variation that occurs between experimental units receiving the same treatment. The experimenters decided to replicate the experiment so that each treatment combination of Temp, Time, and Agitation was performed twice, resulting in 36 experimental runs, since (3x2x3)x2=36.
A diagram of the experiment is shown in Exhibit 1 (see PDF).
The Task
The primary objectives of this experiment are to:
- 1. Compare the performance between the two formulations quantifying the cleaning effectiveness of the new formulation compared to the current.
- 2. Determine if the difference in cleaning effectiveness between the two formulations is consistent across all Temperatures, Agitation Levels, and Washing Times or if the difference is dependent upon the specific washing conditions.
- 3. Determine the specific temperatures, agitation levels, and washing times that result in the greatest difference in cleaning effectiveness between the two formulations. Determine the conditions that result in the least difference. Determine if there any conditions where there is either no difference or the new formulation performs worse.