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Blame Random Events and Covariance

Ever wonder why, after picking what you thought was the shortest line, you’re the last to get through? Or, why traffic can come to an absolute stand-still on the freeway with no apparent reason? There are two mathematical principles at work here (and sad to say, influencing your Plant, Shop, Factory, Project Management and Production Scheduling Plans) that are to blame, random events and covariance.

Random Events

Random events aren’t predictable but also occur in clusters. Think about it. By definition, you can’t predict a random event. “They” always say aircraft crashes happen in threes, or bad things happen together, but there is no other way. If we could predict an airplane crash we wouldn’t fly on that day. The more familiar reference to random events is known as ‘Murphys Law’ — anything that can go wrong, will go wrong.

If the event is not deterministic, or predictable, then it will not fall within a known interval of time. Therefore, some intervals between events will be longer, some shorter. The shorter intervals are referred to as ‘clusters’.

Scatter plot with ellipses highlighting data clusters.


The second, less familiar mathematical principal is a phenomenon called covariance. Typically considered a vary sophisticated mathematical concept with corresponding complex solutions, just having an awareness of it is enough to help you manage the impact.

Covariance formula in mathematical notation.
If there is a possible delay, in a series of events, things tend towards the maximum delay. Now you know why your ‘short’ line is the longest. Teller changes, price checks, paper out, customer has no ID for check, ARGGH!
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