5. Home Federal Savings has found that customer perceptions of accuracy, timeliness, and responsiveness have a very large influence on their overall perceptions of the quality of service provided. Accordingly, HomeFed constantly monitors and charts almost 500 different indicators of these characteristics. For example, accuracy is measured by the error/reject rate in processing transactions, timeliness is measured by the delays in collecting funds, and responsiveness by the speed in resolving customer inquiries or complaints. For each measure, HomeFed has established minimal acceptable performance (MAP) level; initially set at a level comparable to the industry-wide mean performance, but periodically ratcheted upward to spur continuous improvements in service quality.
Over a six month period, HomeFed recorded the following weekly errors for all types of collection activities. HomeFed’s statistical specialists have found that these errors follow a Poisson distribution (see p. 226 of your text for a mathematical description of this distribution, including its mean (lamda) and variance (sigma^2)).
Week Errors Week Errors Week Errors Week Errors
1 0 8 2 14 5 21 0
2 2 9 1 15 15 22 2
3 0 10 0 16 5 23 0
4 17 11 0 17 10 24 0
5 2 12 5 18 5 25 0
6 4 13 6 19 2 26 1
7 0 20 2
The Bank Administration Institute reports that the average error rate for such transactions is 1.5%.
a. What kind of a control chart should HomeFed use to help control this process? (1/2 pt)
b. Determine the 3-sigma process control limits errors/1K transactions that HomeFed should use for its collection activities. Plot the observations, the process mean, the upper and lower control limits, and the industry average. (1/2 pt)
c. Analyze the resulting chart and address the following: (1/2 pt)
i. How does HomeFed’s performance compare with the industry?
ii. Is HomeFed’s collection process in control with respect to this attribute? Why or why not?
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