Question

A control chart is used for a painting process to monitor the surface imperfections of a metal toaster oven cover. The inspection is on a random sampling basis with 10 covers forming a subgroup. The most recent 20 subgroups contained 180 imperfections. Please determine the control limits for the appropriate chart.

Answer 1

Given ,

There are 20 sub-groups , each sub-group containing 10 covers .

In all total , the 20 sub-groups contained 180 imperfections.

Let c be the number of imperfections.

In most cases , c follows Poisson Distribution with parameter .

If the Standards were mentioned , then E(c) = and Standard Deviation (c) = 1/2

Since , Standards are not mentioned ,

An Estimate of would be =  ci / m (where - m is the number of Sub-groups , ci is number of imperfections from the ith sample)

Already given , m = 20 and ci = 180

Therefore , = 180/20 = 9

Now, the control limts are -

Lower Control Limit (L.C.L.) = - 31/2 = 9 - (3 x 3) = 0

Central Line = = 9

Upper Control Limit (U.C.L.) = + 31/2 = 9 + (3 x 3) = 18

(NOTE THAT : Here we are taking the 3 - Sigma limits)

The above chart is knpwn as the c - chart (where c is the number of defects / imperfections in the sample)