Page 256 - Six Sigma Demystified

236 Six SigMa DemystifieD

Poisson Distributions

Example
Estimate the probability of finding exactly 300 typographic errors in a sample
of 150 orders (i.e., 2 errors per order) when the process is known to average
4 typographic errors per order.

Minitab

Use Calc\Probability Distributions\Poisson|Probability. Set Mean = 4; Input Con-
stant = 2.

Result (From Session Window)
Probability Density Function
Poisson with mean = 4.
x P(X = x)
2 0.146525
Note: To find the probability of 3 or fewer orders, use the Cumulative Prob-
ability option. Result = 0.24 (or 24 percent).

Excel

Enter =POISSON(2, 4, 0) into an Excel cell. The solution provided is 14.65

percent. The last parameter in the Excel formula (zero in this case) indicates
whether the solution provides the cumulative result or the finite result. Use
POISSON(2, 4, 1) to calculate the cumulative probability. Note that the cu-
mulative probability also may be calculated as the sum of POISSON(0, 4, 0),
POISSON(1, 4, 0), and POISSON(2, 4, 0).

Exponential Distribution
The distributional parameter λ (lambda) is calculated as 1/µ, where µ is the
average time between occurrences.