Question

Management at Webster Chemical Company is concerned as to whether caulking tubes are being properly capped. If a significant proportion of the tubes are not being sealed, Webster is placing its customers in a messy situation. Tubes are packaged in large boxes of 135. Several boxes are inspected, and the following numbers of leaking tubes are found Tubes Sample 15 16 17 18 Tubes Sample Tubes Sample 4 10 4 4 12 13 20 Total 87 Calculate p-chart three-sigma control limits to assess whether the capping process is in statistical control The UCLp eqalsand the LCp equals(Enter your responses rounded to three decimal places. If your answer for LCLp is negative, enter this value as 0.)

Answer 1

Sample size = n= 135

Number of samples = 20

Total number of observations ($\dpi{80} \sum$n) = sample size x number of samples = 135 x 20 = 2700

At 3 sigma control limit the value of Z = 3

Total of number of leaking tubes ($\dpi{80} \sum$np) = 87

P-bar = np/ n = 87/2700 = 0.032

Sp = Sqrt of {[P-bar(1-P-bar)] / n}

= Sqrt of {[0.032(1-0.032)] / 135}

= Sqrt of [(0.032 x 0.968)/135]

= 0.015

UCL = P-bar + Z(Sp) = 0.032 + (3x0.015) = 0.032 + 0.045 = 0.007

LCL = P-bar - Z(Sp) = 0.032 - (3x0.015) = 0.032 - 0.045 = -0. 013 = 0 (when the value is negative it is taken as 0)