You’ve been hired as a Quality Improvement Specialist at a local hotel and your first assignment is to analyze customer satisfaction (with hotel housekeeping services) data over the past two years. With the following data, create a p chart and determine the UCL, LCL and if, based on this history, your housekeeping process is in control Month Number of Guests Number Unsatisfied 1 549 10 2 402 15 3 334 12 4 507 10 5 380 7 6 498 15 7 531 22 8 361 9 9 514 12 10 423 6 11 500 13 12 345 22 13 424 9 14 378 16 15 515 10 16 487 16 17 334 9 18 410 17 19 485 27 20 451 8 21 390 9 22 420 11 23 450 8 24 437 12

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

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