Question

Calculate p-chart three-sigma control limits to asses whether the capping process is in statistical control. SHOW ALL WORK

17. Management at Webster, in Problem 16, is now 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 144. Several boxes are inspected, and the following numbers of leaking tubes are found: Sample Tubes Sample Tubes Tubes Sample 38 15 5 16 0 17 2 11 2 18 12 6 / 191 Ivo 4 13 5 20 14 Totai Calculate p-chart three-sigma control limits to assess whether the capping process is in statistical control.

Answer 1

we first calculate p-bar i.e the center line

p-bar =Average of the fraction defective values=AVERAGE(E3:E22)=0.025

Next, we calculate Sp =sqrt(p-bar(1-p-bar)/n))

=sqrt(0.025*(1-0.025)/144))

=0.013

UCLp =p-bar+z *Sp=0.025+3*0.013=0.064

LCLp=p-bar-z*Sp=0.025-3*0.013=-0.014

From the p-chart,it is evident that all the fraction defective values lie within the control limits and hence the process is in statistical control.

Calculations are as shown below:

C28 fc =C26+(3*C27) BC DE G H I J K L M N O P Q R S T 0.070 2 Sample n * 0.060+ * * * * * * * * * * * * * * * * * * 0.050 SMANE 0.040 10 11 Number of leaking Fraction tubes defective(p) 144 0.021 144 0.035 144 0.021 144 0.028 144 0.014 144 0.028 144 0.014 144 0.042 144 0.028 144 0.063 144 0.014 144 0.042 144 0.035 144 0.007 144 0.035 144 0.000 144 0.014 144 0.042 144 0.014 144 0.007 12 10 0.030 13 14 15 16 + Fraction defective(p) *UCL *LCL -p-bar Mula 0.020 23/ 17 0.010 18 19 20 17 18 19 21 0.000+TTTTTTT 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 22 - 20 23 -0.0104 24 Total 1440 25 -0.020 26 p-bar 27 Sp 28 UCL | 29 LCL 0.025 0.013 0.064 -0.014