Lusser's law

Key takeaways

Lusser's law belongs to engineering; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Lusser's law to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Lusser's law from memory before moving on to harder problems.

Reference excerpt

Lusser's law in systems engineering is a prediction of reliability. Named after engineer Robert Lusser, and also known as Lusser's product law or the probability product law of series components, it states that the reliability of a series of components is equal to the product of the individual reliabilities of the components, if their failure modes are known to be statistically independent. For a series of N components, this is expressed as:

R s = ∏ i = 1 N r i = r 1 × r 2 × r 3 × . . . × r n {\displaystyle R_{s}=\prod _{i=1}^{N}r_{i}=r_{1}\times r_{2}\times r_{3}\times ...\times r_{n}}

where Rs is the overall reliability of the system, and rn is the reliability of the nth component. If the failure probabilities of all components are equal, then as Lusser's colleague Erich Pieruschka observed, this can be expressed simply as:

R s = r N {\displaystyle R_{s}=r^{N}}

Lusser's law has been described as the idea that a series system is "weaker than its weakest link", as the product reliability of a series of components can be less than the lowest-value component. For example, given a series system of two components with different reliabilities — one of 0.95 and the other of 0.8 — Lusser's law will predict a reliability of

R s = 0.95 × 0.8 = 0.76 {\displaystyle R_{s}=0.95\times 0.8=0.76}

which is lower than either of the individual components.

References

Worked examples

Example 1 — a first encounter with Lusser's law

Start with the simplest possible case. Write down what Lusser's law claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In engineering, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Lusser's law before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Lusser's law ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Lusser's law

In research: Lusser's law appears in engineering research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Lusser's law in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Lusser's law is common in secondary-school and first-year university syllabi. It links to neighbouring topics Engineering failures, Reliability analysis, Reliability engineering, so understanding it makes those chapters shorter.
In everyday life: Look for Lusser's law outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Lusser's law in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Lusser's law means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Lusser's law out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Lusser's law in simple terms?

Lusser's law in systems engineering is a prediction of reliability. Named after engineer Robert Lusser, and also known as Lusser's product law or the probability product law of series components, it states that the reliability of a series of components is equal to the product of the individual reli…

Why does Lusser's law matter?

Because it connects several engineering ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Lusser's law?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Lusser's law.