### Article 15

Read Time 5 Minutes

### What is a Factor of Safety?

### Safety Factor is really a measure of our ignorance!

Let me explain. I will start with three short paragraphs from Wikipedia that I have edited for clarity and then follow up with my own thoughts.

Essentially, the factor of safety or “safety factor” is how much stronger the system is than it usually needs to be for an intended load.”

*“Appropriate design (or safety) factors are based on several considerations:*

- The accuracy of predictions on the imposed loads, strength, wear estimates, and the environmental effects to which the product will be exposed in service.

- The consequences of engineering failure.

- The cost of over-engineering the component to achieve that factor of safety.”

“For example, components whose failure could result in substantial financial loss, serious injury, or death may use a safety factor of four or higher (often ten). Non-critical components generally might have a design factor of two. Safety factors for specific applications are often mandated by law, policy, or industry standards.”

“Buildings commonly use a factor of safety of 2.0 for each structural member. The value for buildings is relatively low because the loads are well understood and most structures are redundant. Pressure vessels use 3.5 to 4.0, automobiles use 3.0, and aircraft and spacecraft use 1.2 to 3.0 depending on the application and materials. Ductile, metallic materials tend to use the lower value while brittle materials use the higher values.” [ref. 1]

For factor of safety, industry also uses related terms, such as excess capacity, reserve factor and margin of safety.

For example, Warren Buffet, the legendary investor and 3rd richest billionaire with a an estimated fortune of 61 Billion Dollars[ref. 2], uses Margin of Safety[ref. 3] to calculate a safe share buy-price at which he would buy shares and invest in a company!## Margin of Safety: The Three Most Important Words in Investing

“The three most important words in investing are margin of safety.” That means to buy stuff on sale. That means pay less than what it’s worth. That means buy $10 dollar bills for $5 dollars. That’s the whole secret to great investing. – Warren Buffett [ref. 3]

**Quiz Question:**

Here is a quiz question for all of us engaged in R&D and New Product Development.

Suppose we are creating a new product, a nylon rope to be used for mountain climbing. If our nylon rope fails at 1000 psi, how do we calculate a safe rope size – diameter?

What assumptions do we need to make?

Here are a few:

- What is the maximum weight of a mountain climber? Assume 400 pounds.
- What is a
*good*safety factor? Below are several choices. - Which one is a good choice? Why?

### Answer:

We R&D scientists and engineers are conservative. Should we use safety factor of 1 and round up diameter to 0.75 inch, or use safety factor of 2 and use rope diameter of 1-inch? How about 1.5-inch diameter or 2.25-inch diameter? Since the cost of the rope is relatively low, and we do not want a mountain climber to fall because of a broken rope, should we use a thicker 2-inch diameter rope? Well it may be very safe, but a two-inch rope is likely to be uncomfortably thick and hard to grip. So, how do we select a safe rope?

Now you know why I call the safety factor an ignorance factor! The more ignorant we are, the more risk averse we ought to be, be safe and select a larger size.

Safety Factor is really an ignorance factor. Since we don’t know what we need, we use a gut feel factor as a factor of safety, to cover our risk, our risk of ignorance. Over time, these gut feel factors have become accepted industry norms.

Since we cannot develop a meaningful answer to this gut feel Safety Factor problem through traditional thinking, we need a different approach. We need to recall and use Einstein’s dictum.

We cannot solve our problems with the same thinking we used when we created them. We need to think in a higher plane. – Albert Einstein [ref 4]

**Statistical Thinking** provides us with a higher plane of thinking for this problem.

If you read my last article, Developing Meaningful Product Specifications [ref. 5], I posed a few questions:

- How do you develop product specifications?
- How do you know they are meaningful?
- Where does the needed data come from? When?
- What is the underlying science?

The same questions apply for determining a safe rope diameter.

If we do some testing in the lab, we can determine typical failure rates for say 30 or so lots of nylon ropes. For laboratory testing, we load the rope until failure. Some ropes will fail at low loads, some at higher loads, most in between. From these failure data we calculate the Mean and Standard Deviation.

Let us assume we found Mean = 1000 psi and Standard Deviation = 200 psi.

We extend the table of calculated values above, with some statistical calculations on Percent Chance of Failure.

The calculated values show, if we design for 400 pound load, we have a 50% chance of failure. If we use a factor of safety of 2, we reduce the rope failure rate to slightly less than 3%. For a safety factor of 4 or 5, failure rate is at low parts per million level, an acceptable value.

Now, we can compare the increased safety factor, with increased rope size and the cost of the nylon rope with the cost of a human life for the case of a rare occurrence of a rope failure. Now we have a scientific or logical method of relating safe rope size to economics, and develop a more meaningful conclusion.

Just like product specifications, some product attributes, or process parameters may exhibit a distribution different than the normal distribution, for example log normal, Poisson, binomial etc. For these cases computations formulas change somewhat.

### What If …

This approach leads to too-big-a-size that is technically or economically unviable?

“The field of aerospace engineering uses generally lower design factors because the costs associated with structural weight are high (i.e. an aircraft with an overall safety factor of 5 would probably be too heavy to get off the ground). This low design factor is why aerospace parts and materials are subject to very stringent quality control and strict preventative maintenance schedules to help ensure reliability. A usually applied Safety Factor is 1.5, but for pressurized fuselage it is 2.0, and for main landing gear structures it is often 1.25.”[1]

We can use similar methods to guarantee that a pharma drug has minimum purity, adequate shelf life, or was quality tested within an FDA stipulated time frame.

As I said in one of my previous articles, Part 13 [ref. 3] in Quality arena, the coaches, the Six Sigma Black Belts, the Statisticians and the Quality Managers, all, practice the Deming motto.

In God we trust. All others bring data.

- Edward Deming

R&D scientists and engineers should do the same, because they lead with new technology.

So crank up your Product Development engines... Let us speedup new product development and growth rates. And let the fun begin!

**References:**

- https://en.m.wikipedia.org/wiki/Factor_of_safety#Yield_and_ultimate_calculations
http://www.forbes.com/billionaires/list/ 2016 Rankings

Phil Town, Rule #1: The Simple Strategy for Successful Investing in Only 15 Minutes a Week! Crown Business, 2007.

Mukul Mehta, Developing Meaningful Product Specifications, P 18-20, Chemical News, April, 2016