Lusser's Law and Applicability
April 07, 2021

Terry Critchley
Author of "Making It in IT"

Share this

Availability Probabilities

Application availability depends on the availability of other elements in a system, for example, network, server, operating system and so on, which support the application. Concentrating solely on the availability of any one block will not produce optimum availability of the application for the end user.

In the following diagram, a "linear" or "non-redundant" configuration of elements supporting the user application is shown. In vendor engineering publications, these elements are referred to as "blocks," although other publications may refer to them as "components."

It is evident that if any block in the series configuration fails, the user loses the use of the application. The application is as available as the weakest link in the chain, or so it would appear.

The following figure is a schematic showing a linear chain of blocks, henceforth known as non-redundant blocks or blocks in series. It is easy to see that the failure of any block in the chain will cause a failure of the service to the end user.

There are, of course, other blocks in the chain, such as operating system, middleware and so on (not shown here) but the principle is the same. A single component whose failure causes overall failure is called a single point of failure or SpoF.


The equations above demonstrate that a series of blocks is weaker than its weakest component simply because of the multiplication of several factors, all of which are less than or equal to 1.

Lusser's Law

Lusser's Law is a prediction of reliability named after Robert Lusser (He worked on Wernher von Braun's US rocketry program post-WW2) . It states that the reliability of a series system (of our "blocks") is equal to the product of the reliability of its component subsystems, if their failure modes are known to be statistically independent. This is what we see in the above diagram. The law can be stated as follows:


This lays to rest the theory that a chain is as strong as its weakest link, the thinking at the time. Lusser's Law deals with the reality of this situation.

Next in this document we will discuss using components in parallel and how to make the assessment of availability more IT-specific and not just deal with anonymous blocks or components which might represent anything in a reliability context - valves, pipes etc.

Part of availability management is the examination of the service failure points in the configuration between application and user, assess their impact on service availability and design round them. Obviously there are cost implications to going over the top in design, especially in the cases below.

Effect of Redundant Blocks on Availability

The discussion so far has dealt with linear chains of blocks (blocks in series, to use an electrical analogy), where the whole chain is weaker than its weakest link – Lusser's Law.
To carry this analogy further, it is possible to use blocks in parallel to increase the availability of the chain, assuming that one block can take over from a failed block, assuming that the blocks fail independently. The following diagram illustrates this for two blocks:


These blocks might be NICs, disks, server or other parts of a working system. The general case for 'n' parallel blocks is shown below, together with the equations for availability and non-availability probabilities.

Parallel (Redundant) Components

The next figure illustrates components configured in parallel as opposed to in series as we have seen already. The mathematics of these configurations is similar to Lusser's mathematics except we deal with 'unreliability' instead of 'reliability' entities in the math.

The basic premise in these calculations is that if the probability of being available is P, then the probability of not being available is N where;

N = (1-P) and P = (1-N)

since the total availability of being available or not available is 1. In reality, a system will consist of several sets of redundant components, for example disks, servers, network card, lines and so on. These will feed into each other, possibly mixed with single components.

The figure below shows the general case of "n" blocks in a parallel configuration. This might represent one set of components for a subsystem such as a RAID configuration or set of network interface cards (NICs). Such a configuration can be difficult to handle mathematically so a 'reduction' technique is usually employed.


Two Parallel Blocks: Example

Picture two components in parallel, one with availability probability Pa and the other Pb. The probability of both blocks being unavailable, that is, the chain is broken, is:


This assumes the blocks have different availability characteristics, Pa and Pb..If they were the same, say Pa = Pb = P, then the probability that both are not available is given by the relationship:


which is essentially a variation of Lusser's Law using the non-availability probabilities as multipliers instead of availability probabilities. The probability that 'n' redundant blocks are unavailable is (1 - P)n and the probability that they are all available is given by the relationship [1- (1 - P)n ]

As an example, consider two parallel blocks, each with an availability of 99.5 %. The probability that both are unavailable is:

N = (1 - 0.995) x (1 - 0.9995) = 0.000025

Hence its availability (compared with the availability of a single non-redundant case of 99.5%) is:

A(%)=(1-N) x 100=(1-0.000025) x 100%=99.999975%

The knowledge of each value of "P" and some mathematical skills would be needed to solve the problem of service availability for a combination of serial and parallel service blocks, which is often the case in real life. The book High Availability IT Services covers this latter case.

Dr. Terry Critchley is an IT consultant and author who previously worked for IBM, Oracle and Sun Microsystems
Share this

The Latest

April 21, 2021

Few tools provide early detection of mission-critical mail outages. On March 15, Microsoft had a service outage worldwide that impacted its services such as Teams AV, Yammer, OneDrive, and Azure Active Directory. Users reported not being able to login into either of these services and were getting timeout messages ...

April 20, 2021

More than half (60%) of IT organizations are investing in improving employee experience to support remote workforce productivity and performance according to The Changing Role of the IT Leader study by Elastic ...

April 19, 2021

Why are CDNs becoming more important to so many businesses? And how will they handle the new applications coming out over the next few years? APMdigest sat down with Mehdi Daoudi, CEO and co-founder of Catchpoint Systems, to find out ...

April 15, 2021

A growing need for process automation as a result of the confluence of digital transformation initiatives with the remote/hybrid work policies brought on by the pandemic was uncovered by an independent survey of over 500 IT Operations, DevOps, and Site Reliability Engineering (SRE) professionals commissioned by Transposit for its inaugural State of DevOps Automation Report ...

April 14, 2021

As the Covid-19 pandemic forces a global reset of how we gather and work, 60% of organizations are looking forward to increased spending in 2021 to deploy new technologies, according to the 14th annual State of the Network global study of enterprise networking and security challenges released by VIAVI Solutions ...

April 13, 2021

Complexity breaks correlation. Intelligence brings cohesion. This simple principle is what makes real-time asset intelligence a must-have for AIOps that is meant to diffuse complexity. To further create a context for the user, it is critical to understand service dependencies and correlate alerts across the stack to resolve incidents ...

April 12, 2021

We're all familiar with the process of QA within the software development cycle. Developers build a product and send it to QA engineers, who test and bless it before pushing it into the world. After release, a different team of SREs with their own toolset then monitor for issues and bugs. Now, a new level of customer expectations for speed and reliability have pushed businesses further toward delivering rapid product iterations and innovations to keep up with customer demands. This leaves little time to run the traditional development process ...

April 08, 2021

On Wednesday January 27, 2021, Microsoft Office 365 experienced an outage affected a number of its services with a prolonged outage affecting Exchange Online. Despite Microsoft indicating that it was just Exchange Online affected during this outage, some monitoring tools detected that Azure Active Directory and dependent services like SharePoint and OneDrive were also affected at the time. The outage information indicated a rollout and rollback but we wouldn't expect to see such a widescale outage and slowdown just affecting some of the schema unless everything had to be taken offline ...

April 07, 2021

Application availability depends on the availability of other elements in a system, for example, network, server, operating system and so on, which support the application. Concentrating solely on the availability of any one block will not produce optimum availability of the application for the end user ...

April 06, 2021

A hybrid work environment will persist after the pandemic recedes, with over 80% stating that they expect over a quarter of workers to remain remote, and over two-thirds desiring flexibility between on-premises and remote deployments according to the 2021 State of the WAN report released by Aryaka ...