Home > 6 Sigma, Industrial Dynamics > Boston Bombing, Earthquake in China and Cost of Quality (COQ)

Boston Bombing, Earthquake in China and Cost of Quality (COQ)

The Powerful Power Law


What does last week’s devastating events of Boston bombing and earthquake hitting Sichuan of China have in common with the nature of COQ at a manufacturing company? In fact they all are observed to follow a simple statistical rule called the power law. Simply put, plotting the logarithm of the magnitude of the events against the logarithm of the probability of occurrence will result in a straight line with a negative slope relationship. In the case of a terrorist event, the magnitude can be measured by the number of casualty. A number of research has shown that this obeys the power law. In case of an earthquake, the relationship between magnitude and the probability of occurrence at a given time and region is described by the Gutenberg-Richter law as a type of power law distribution.

How are these related to COQ? This figure is an analysis of the warranty claim data of an automotive tier 1 supplier within a period of 1 year.

This data set indicates that the larger claims (above $10,000) follow the power law very well. The circled area are smaller claims that most likely indicates many smaller size defects have skipped the system and hence have lower occurrence than predicted by the power law. Typically, empirical earthquake data also demonstrates similar behavior known as “roll-off”. Assuming these data are representative patterns, they are showing that the power constant is approximately equal to -1. This means that the occurrence of above $100K claim is about 100 cases in a year, that of above $1M claim is about 10 cases/year and that of above $10M claim is about once every year.

Studies on terror events all over the world have found that very similar relationship exists between casualty and the probability of occurrence. In fact the power constant for terrorism is found to be about -2.5. In other words, the occurrence of a 200 casualty event such as the Boston bombing is approximately 10^2.5= 316 times more likely than a casualty 2000 and above event such as Sept 11.

Why do important quality events exhibit Power Law behavior?


There are 2 main reasons, both are results of the network nature of the manufacturing supply chain.

  1. Interdependency – Supply chain elements are highly interdependent. An example is that during my early career as a storage media quality engineer, there was an incidence that one day a small crack was discovered at the glass furnace at a remote factory in Japan. This turned out to be a devastating event because this glass furnace was the only one that made glass substrate for storage media in multiple brands of magnetic disk drives. These drives were supplied to make servers and PCs. That small crack hence stalled the entire server and PC supply chain for days costing millions of dollars.
  2. Positive feedback – An example of how positive feedback works is Toyota ‘s “unintended acceleration” case that ended up costing Toyota over billion dollars. At first those were considered isolated cases but as more cases were suspected to be connected, Toyota identified potential root cause as the floor mats from certain suppliers. Number of reports increased as the publicity of the case increased which in turn lead to the suspicion of Toyota hiding something increased. Toyota was drawn by Congress for hearing and later being fined for about $1.1B even there had been no proof that could relate the unintended acceleration cases to any electronic or software defects. Each cycle of litigation and probes reinforced the public’s suspicion of something was wrong with Toyota till the point of avalanche even when no major defects were identified by those investigations.

Six Sigma and the Power law


This power law behavior of COQ offers important insights on how quality executives should deal with important quality events. This is particular counter-intuitive to many quality professionals who have gone through six sigma training or are themselves six sigma professionals. The foundation of six-sigma builds on the normal distribution or the Bell curve. COQ, however, observes the power distribution, not the normal distribution. Here are some major differences.

  • There is no average – In other words, it is meaningless to talk about the average size of a warranty claim. The Power distribution has no average value like the Normal distribution.
  • The most important data points are the outliners – In our data set, the top 10 claims among the total of 412 claims contributed to more than 50% of the total warranty cost. These large claims are the outliners that are typically ignored by six-sigma methodology.
  • Black swan events occur – The theory was developed by Nassim Nicholas Taleb to describe highly unlikely events that determines the course of human history. According to the above data set and the underlying power law, a warranty claim that costs over billion dollars occurs in about every century. Such event though rare can easily lead to termination of responsible executives or even bankruptcy of the business.

The Power law Strategy


Just like security gates alone cannot eliminate terrorist events, government bodies run drills and set early warning systems to reduce the risk of terrorist events. Similar method can be applied to catch quality defects.

In order to tackle the Power Law phenomenon, a strategy is needed to tackle its fundamental elements. This involves 3 major steps. The first step is to enable track and trace of the interdependency of the supply chain. Once interdependency tracking is established, the second step is to conduct further analysis that enables early warning (such as using Big data technology) based on the interdependency. Warning signals detected need to tie to a series of actions that involves PDCA cycles. The third step is a containment strategy to quickly respond to quality events before their effects were amplified by positive feedback. These measures will significantly lower the probability of isolated events escalating into catastrophic events through self-reinforcing cycles of positive feedback. It is worth noting that traditional ROI analysis based on average annual return rarely can be used to justify investment on implementing such strategies and solutions. When dealing with the potential catastrophic effect of the Power law, executive decision is required to set organizational direction. Seeking average annual return of such investment just does not make sense in the world of Black Swan events.



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