Question

If the average number of imperfections in a painted surface is 6 and if you want alpha to be 0.10, what should be the "best" UCL and LCL? (assume Poisson distribution for the number of defects on the surface).

Answer 1

Average number of imperfections, λ = 6

For alpha to be 0.10, lower limit of Cumulative probability distribution function is 0.1/2 = 0.05 and and the upper limit is 1-0.05 = 0.95

Cumulative poisson function

$\sum_{k=0}^{2} \frac{e^{\lambda}\lambda^{k}}{k!}$ = 0.062

and,

$\sum_{k=0}^{10} \frac{e^{\lambda}\lambda^{k}}{k!}$ = 0.9574

Therefore, the best estimate of LCL and UCL are 2 and 10 respectively

LCL = 2

UCL = 10