Gladys Schwartz is the manager of a large loan brokerage firm. She strives for high quality output and is concerned with reducing errors in loan documents. Gladys took 20 samples of 80 loan documents each over a time period that she considered normal and found a total of 40 loan documents containing errors. a. Given the above information, set up a control chart (assuming three standard deviations). b. After developing the control chart in part a, three additional samples were collected. What observations can you make about each of these three samples

Solution and Explanation:

P-chart to be used

Center line = total number of errors/(no of samples*sample size) = 40/(20*80) = 0.025 = p-bar

standard deviation = sqrt((p-bar*(1-p-bar))/sample size) =  = sqrt ((0.025*(1-0.025))/80) = 0.017

UCL = p-bar + z*standard deviation = 0.025 plus 3 multiply 0.0174553 = 0.0773659

LCL = p-bar - z*standard deviation = 0.025 minus 3 mulitply 0.0174553 = -0.0273659 = 0 (Adjusted)

Defect proportion of sample 1 = 5/80 = 0.0625

Defect proportion of sample 2 = 8/80 = 0.1

Defect proportion of sample 3 = 6/80 = 0.075

The process is not in control as Defect proportion of sample 2 is not within the control limits