How to Determine the Worst Case for a Process

Have confidence in the confidence interval

How do you determine the “worst case” scenario for a process? Is it by assuming the worst case for each process task or step? No. The reason is that the probability of every step having its worst case at the same time is practically zero. What we’re looking for is a value that will occur a very small percentage of the time, but still be a possibility.

In statistics, we do this with a confidence interval, typically plus or minus three standard deviations from the mean to achieve 99.7-percent confidence.

For example, let’s say that we have a three-step process, with means and standard deviations of x₁ = 20, s₁= 3; x₂ = 30, s₂ = 5; and x₃ = 60, s₃= 9, respectively. Since variation (variance) is additive, the variance of the entire process is therefore:
S²_Process = 3² + 5² + 9² = 9 +25 + 81 = 115, and the process standard deviation is:
S_Process = SQRT(115) = 10.7.

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Worst Case

There's lies, damn lies and statistics. As a junior engineer, I worked in a factory that started making reject. I was told to keep away while "experts" were brought in to fix it. They made reject for a month and filled a warehouse with product with "hold" tags. Suddenly the factory started making good product again. No one knew why. The experts were sent home.

Where's the probability figures for that?

Several months later, exactly the same problem occurred during the middle of the night when I was on as shift foreman, in control of the whole factory and two others. First step was to find the cause, which I did. The "experts" had forgotten this key action. My next step was to design a solution. By morning I'd made major changes to the process and was making good product again. When management arrived and saw the changes I'd made to the process, I was crucified.