The number of guest vary each month hence the n and p will vary each month.
The number of guests each month is the “n” for the respective month
month 1 n = 549, month 2 n = 402 ans so on
month 1 p = unsatisfied/guests = 10/549 = 0.0182 = 1.82%
similalry we can calculate the p for each month.
Month 1 UCL = p + 3*sqrt{(p*(1-p))/n} = 0.0182 + 3*sqrt{0.0182*(1-0.0182)/549} = 0.0353 = 3.53%
Month 1 LCL = p – 3*sqrt{(p*(1-p))/n} = 0.0182 – 3*sqrt{0.0182*(1-0.0182)/549} = 0.0011 = 0.11%
Similarly all the UCL and LCL can be calculated using excel as shown below.
Hence, the p chart can be created using the LCL and UCL as control limits and the fraction defective calculated in the excel below for each month
https://d2vlcm61l7u1fs.cloudfront.net/media%2F2c9%2F2c912bac-f3b5-4eef-bc5e-d82fa039e05c%2FphpSXWzBl.png
fig1
using this data we can plot the fraction defective, UCL and LCL on graph and see whether the process is in control. the plot is shown below. as shown in plot below the process is in control.
https://d2vlcm61l7u1fs.cloudfront.net/media%2Fc16%2Fc16b2dfe-8189-45e4-908b-6d43f110f78e%2FphpCJRaC3.png