Question

In each of several consecutive days of production of certain AAA batteries, 150 batteries are tested and the number of defects each day are listed below:

4, 4, 14, 6, 6, 8, 8, 6.

For the control chart for the proportion of deficient batteries produced during the 8 days, find the following:

(a) The center line: p¯=p¯=

(b) The proportion: q¯=q¯=

(c) The upper control limit: UCL =

(d) The lower control limit: LCL=

Answer 1

(a) The center line: p¯= Total number of defectives / (n * number of samples)

= (4 + 4 + 14 + 6 + 6 + 8 + 8 + 6) / ( 8 * 150)

= 0.0467

(b) The proportion: q¯= 1- p¯ = 1 - 0.0467 = 0.9533

(c)

Standard error, SE = = 0.0172

The upper control limit: UCL = p¯ + 3 * SE = 0.0467 + 3 * 0.0172 = 0.0983

(d)

The lower control limit: LCL= p¯ - 3 * SE = 0.0467 - 3 * 0.0172 = -0.0049 0 (proportion cannot be negative)