Question

1. In a manufacturing operation, the percentage defective averages 2.5 percent and sample size in 200.

1. Compute the center line for the p chart.
2. Compute the 3 control limits for the chart (i.e., z-value = 3.0).
3. Plot these recent data collected from daily samples and decide if the operation is in control: Number of defectives per sample = 2,9,7,5,0,3,8,7,2,5,3,2

Answer 1

p_bar = 0.025
Sample size, N = 200

Standard error, Sp = √[(p_bar*(1 - p_bar) / N] = √(0.025*(1 - 0.025) / 200) = 0.011

So,

Central line, CL = p_bar = 0.025

UCLp = p_bar + 3 * Sp = 0.025 + 3*0.011 = 0.058
LCLp = Max(0, p_bar - 3 * Sp) = Max(0, 0.025 - 3*0.011) = 0

The process is out of statistical control as sample 2, 3, 7, and 8 are out of UCL.