Durability of Mobile Phone Screen

Authors

Kevin Potcner

JMP

Objective

Evaluate the durability of mobile phone screens in a drop test across various heights by building a single multiple logistic regression model. Use the model to estimate the probability of a screen being damaged across any drop height.

Background

The durability of a product is clearly an important quality characteristic for both the end user and the manufacturer. For end users, durability is especially important for mobile phones. Dropping a phone on a hard surface, for example, can result in the screen cracking or even breaking, rendering the phone unusable. To evaluate the durability of these screens, manufacturers subject a sample of screens to a variety of tests to simulate typical wear and tear by a user, such as dropping the phone onto a concrete surface.

In JMP032 Durability of Mobile Phone Screen - Part 1, material scientists for a screen manufacturer experimented with two new formulations of an aluminosilicate glass (A and B). These two formulations were produced by making a change to a final processing step that uses a specific level of potassium nitrate to strengthen the glass.

A sample of 10 screens of each type was developed for testing. Each screen was installed into the same style of phone. The phones were then dropped in a controlled identical manner from a height of 1 meter onto a concrete surface. A binary variable “Success” (no damage) and “Fail” (screen damage) was recorded.

One of the company’s goals is that 97% of the screens manufactured would be able to experience a drop of 1 meter without becoming damaged (i.e., the Population Success Rate).

The analyses illustrated in JMP032 Durability of Mobile Phone Screen - Part 1, which were based on only 10 phones tested of each Screen Type, failed to generate the statistical evidence needed to demonstrate the desired Success Rate. The analyses also failed to find any statistically significant difference between the two Screen Types.

The engineers decided to test an additional 40 phones for each of the two Screen Types. Analyzing the results from this expanded test was the objective of the exercises for that case study.

In case JMP033 - Durability of Mobile Phone Screen - Part 2, the material scientists developed a third Screen Type (C), which required a more expensive process. Tests were done for this Screen Type at 1.0m, as had been done for Screen Types A and B. In an effort to gain a comprehensive understanding of the durability of these screens, the engineers conducted the drop test at two additional heights (0.5 and 1.5 meters), which resulted in the following data:

These data were analyzed in case JMP033: Durability of Mobile Phone Screen – Part 2.

To continue developing a deeper understanding of the performance of the Screen Types, the engineers performed additional tests at Drop Heights of 0.25m, 1.25m, 2.0m, 2.5m and 3.0m. In addition, a sample of screens from a leading competitor were obtained and included in the testing, resulting in the following data, as seen in the PDF.

In case JMP034: Durability of Mobile Phone Screen – Part 3, these data were used to build singlevariable logistic regressions models, one for each Screen Type. The logistic regression models provided us with a tool to estimate the Population Success Rate across any Drop Height between 0.25 and 3.0 meters, including those not part of the study.

The logistic regression model also provided us with a tool to perform an inverse prediction, specifically estimating the Drop Height that would result in a given Success Rate.

In this case study, we’ll build one multivariable logistic regression model created from all of the data together for a single equation to describe the performance of all Screen Types. In addition to having a 4 single equation that can estimate Success Rates and Drop Heights for any Screen Type, this will also provide us with a tool for conducting formal statistical tests comparing the Success Rates between Screen Types.

We’ll finish by comparing the estimates made by this multivariable model to the ones made using separate single-variable models to determine which approach is best to use.

The Task

The primary objectives of this analysis are to:

1. 1. Describe how the performance of each Screen Type changes as the Drop Height changes.
2. 2. Describe any statistical differences in durability between the three Screen Types and determine if that difference is consistent across all eight Drop Heights.
3. 3. Determine how the company’s three Screen Types compare to the competitor’s.
4. 4. Develop a tool that will estimate the Success Rate for any Screen Type at any Drop Height including those not part of the testing.
5. 5. Determine the estimated Success Rate for each Screen Type at 1.0m Drop Height.
6. 6. Determine the Drop Height for which the Success Rate is estimated to be at least 97% for each Screen Type.
7. 7. Estimate the minimum Drop Height at which the screen is more likely to be damaged versus not damaged.
8. 8. Estimate the greatest Drop Height at which 5% of screen would be damaged versus not damaged?

Use the links below to read the full case study and download the data files

• Download the case study (PDF)
• Download the data set