How to Calculate and Solve for Probability of Glass Fracturing | Weibull Statistics | Glass Making Technology

Last Updated on March 8, 2021

The image above represents probability of glass fracturing.

To compute for probability of glass fracturing, three essential parameters are needed and these parameters are Scaling Factor (σ_o), Fracture Strength of Glass (σ) and Weibull Distribution Modulus (m).

The formula for calculating probability of glass fracturing:

P = 1 – exp[-(^σ / _σo)^m]

Where:

P = Probability of Glass Fracturing
σ_o = Scaling Factor
σ = Fracture Strength of Glass
m = Weibull Distribution Modulus

Let’s solve an example;
Find the probability of glass fracturing when the scaling factor is 24, the fracture strength of glass is 10 and the weibull distribution modulus is 8.

This implies that;

σ_o = Scaling Factor = 24
σ = Fracture Strength of Glass = 10
m = Weibull Distribution Modulus = 8

P = 1 – exp[-(^σ / _σo)^m]
P = 1 – exp [-(¹⁰ / ₂₄)⁸]
P = 1 – exp [-(0.416)⁸]
P = 1 – exp [-0.0009]
P = 1 – 0.999
P = 0.0009

Therefore, the probability of glass fracturing is 0.0009.

Nickzom Calculator – The Calculator Encyclopedia is capable of calculating the probability of glass fracturing.

To get the answer and workings of the probability of glass fracturing using the Nickzom Calculator – The Calculator Encyclopedia. First, you need to obtain the app.

You can get this app via any of these means:

Web – https://www.nickzom.org/calculator-plus

To get access to the professional version via web, you need to register and subscribe for NGN 2,000 per annum to have utter access to all functionalities.
You can also try the demo version via https://www.nickzom.org/calculator

Android (Paid) – https://play.google.com/store/apps/details?id=org.nickzom.nickzomcalculator
Android (Free) – https://play.google.com/store/apps/details?id=com.nickzom.nickzomcalculator
Apple (Paid) – https://itunes.apple.com/us/app/nickzom-calculator/id1331162702?mt=8
Once, you have obtained the calculator encyclopedia app, proceed to the Calculator Map, then click on Materials and Metallurgical under Engineering.

Now, Click on Glass Making Technology under Materials and Metallurgical

Now, Click on Probability of Glass Fracturing under Glass Making Technology

The screenshot below displays the page or activity to enter your values, to get the answer for the probability of glass fracturing according to the respective parameters which is the Scaling Factor (σ_o), Fracture Strength of Glass (σ) and Weibull Distribution Modulus (m).

Now, enter the value appropriately and accordingly for the parameter as required by the Scaling Factor (σ_o) is 24, Fracture Strength of Glass (σ) is 10 and Weibull Distribution Modulus (m) is 8.

Finally, Click on Calculate

As you can see from the screenshot above, Nickzom Calculator– The Calculator Encyclopedia solves for the probability of glass fracturing and presents the formula, workings and steps too.