The manager of the customer service department of Data Tech Credit Card Service
ID: 425347 • Letter: T
Question
The manager of the customer service department of Data Tech Credit Card Service Company is concerned about the number of defects produced by the billing process. Every day a random sample of 250 statements was inspected for errors regarding incorrect entries involving account numbers, transactions on the customer's account, interest charges, and penalty charges. Any statement with one or more of these errors was considered a defect. The study lasted 30 days and yielded the data in the table below: Number of Errors in Sample of 250 12 Samples 1-10 11-20 21-30 3 4 13 2 5 12 7 10 5 2 a. Construct a p-chart for the billing process Set up the p-chart by specifying its control limits and center line. (Enter your responses rounded to four decimal places. If your answer for LCLp is negative enter this value as 0,) UCLp = LCLp?Explanation / Answer
Total number of errors in 30 samples
= Sum of all errors as provided in the problem
= 191
Total number of observations = 250 / sample x 30 ( number of samples ) = 7500
Therefore , proportion of errors, pbar
= Total number of errors/ Total number of observations
= 191 / 7500
= 0.0255 ( rounded to 4 decimal places )
Control limits for p chart :
Sample size = n = 250 statements
Centerline, pbar = 0.0255
Upper control Limit , UCLp
= pbar + 3 x Square root ( pbar x ( 1 – pbar)/n)
= 0.0255 + 3 x Square root ( 0.0255 x 0.9745/250)
= 0.0255 + 3 x 0.00997
= 0.0255 + 0.0299
= 0.0554
Lower Control Limit , LCLp
= Maximum ( 0, pbar – 3 x square root ( pbar x ( 1 – pbar)/n) )
= Maximum ( 0 , 0.0255 – 0.0299 )
= Maximum ( 0, - 0.0044)
= 0
UCLp = 0.0554
Pbar = 0.0255
LCLp = 0
UCLp = 0.0554
Pbar = 0.0255
LCLp = 0
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