Constructing and Interpreting a Control Chart As indicated in the text, various tools from operations management and statistics are used to help support Six Sigma goals and process improvements in a lean environment. One such tool is a control chart-a key element used to assess statistical process control (SPC). You are given the following error rates for a loan-processing activity at a bank: 2.8, 2.4, 2.4, 4.2, 1.8, 2.8, 3.8, 3.4, 3.2, 3.2, 2.2, 1.6, 1.4, 1.4, 2.4, 1.8, 2.6, 2.0, 2.4, 2.4, 2.2, 2.8, and 2.4.

Required

1. Define the term control chart. What is the difference between a control chart and a run chart? What do these charts have in common?

2. Use the data on error rates to construct a control chart for the loan-processing operation. Although there are various ways to construct the chart (see any text on Operations Management or Quality Control for details), define the upper-control limit (UCL) of your chart as the mean plus 2 standard deviations; define the lower-control limit (LCL) of your chart as the mean less 2 standard deviations. (In each case, use the sample standard deviation for the data set at hand.)

3. Supply an interpretation of the control limits you established above in (2).

4. What techniques can be used to judge, using a control chart, whether a process is in statistical control?

5. Control charts were developed many years ago for application in the manufacturing sector. However, these charts can be used in other contexts as well. What quality measure might you collect, for use in a control chart, for each of the following nonmanufacturing settings: hospital, insurance company, hotel, and local police department?