Graphical Analysis and Before/After Control ChartsCan You Bike to Work on Time?

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    Can You Bike to Work on Time?

    Riding his bike to work instead of driving seemed like a no-brainer—Joel got more exercise, saved money on gas, and usually even made it to the office a few minutes early. But after six months, his boss called him in. Over the past few weeks, the boss warned, Joel had not only failed to arrive early, but frequently arrived late.

    Joel believed the boss’s impression had to be incorrect. Joel was a methodical person. He left his apartment every day at 7:30 a.m., and he kept a log of how long his daily commute took. He knew it took about 25 minutes to bike to work, which allowed time to spare.

    He decided to prove it with the Assistant in Minitab Statistical Software.

    This data set contains Joel’s commuting times since he began biking to work about six months ago. Does the evidence confirm or refute Joel’s punctuality?

    Let’s find out with the Assistant in Minitab Statistical Software.

    Step 1: Graph the Data

    Seeing your data in graphical form is always a good place to start, so select Assistant > Graphical Analysis.

    The Assistant presents different graph options for each of three possible objectives.

    To look at the distribution of how long it takes Joel to bike to the office, click the Graphical Summary button and complete the dialog box as shown.

    The Assistant outputs a Diagnostic Report, a Report Card, and the Summary Report shown below.

    The Summary Report looks like good news—at first. It reveals that Joel’s mean commute time is a bit over 26 minutes; a little longer than he thought, but still good enough to reach the office before 8:00 a.m.

    But the list of Descriptive Statistics reveals that the standard deviation is greater than 4 minutes. That means there’s a lot of variation in how long it takes to reach the office from day to day. The graph of the Distribution of Data bears this out, showing that his commuting times have ranged from under 18 minutes to about 36 minutes.

    Then there’s the graph of the Data in Time Order: a quick look suggests that while on average Joel’s commute got him to work within 25 minutes when he started biking, the length has increased over the past several weeks. His boss may be right.

    2. Create a Control Chart

    This initial look at the data has convinced Joel that his boss is right about arriving late. But is the process truly drifting, or is the variation we’re seeing just common-cause variation that is naturally inherent in the process?

    The Assistant can create control charts to assess the stability of a process. Select Assistant > Control Charts…

    The Assistant presents a decision tree to guide you to the appropriate control chart for your situation. Since this is continuous data that has not been collected in subgroups, press the I-MR Chart button.

    In the dialog box, select the appropriate data column. If you already know the upper and lower control limits and center line for your process—for instance, if you’re monitoring a manufacturing process with established control limits—you can enter them. In this case, since Joel doesn’t have predetermined control limits, let the Assistant estimate them from the data.

    When you select this option, the Assistant automatically reviews your data and notifies you if it finds any out-of-control points. If an out-of-control point has a special cause—such as an equipment failure—you can tell the Assistant not to use it when calculating the control limits.

    The Assistant has flagged several points in this data set, but Joel can’t identify any special causes that would justify removing them, so they should remain in the calculations.

    When you press OK, the Assistant produces a Report Card, Diagnostic Report, and the Summary Report shown below.

    The Summary Report confirms that with the process Joel is using now, the process mean is not stable and he cannot accurately predict whether he’s going to make it to work on time or not.

    As Joel thinks about his situation, he identifies factors that might be influencing the time it takes him to get to work. Since he shares the road with drivers, fluctuations in traffic affect his daily journey. Sometimes accidents or maintenance crews force him to take detours. Even when his route is clear, he still must contend with ill-timed traffic signals and other realities of sharing the road.

    But instead of using the road bike, which keeps him strictly tethered to the pavement, Joel could ride his mountain bike. The ride might not be as smooth, but it would let him take a much more linear—and less crowded—route to the office. For the next six weeks, he tries it.

    3. Create a Before/After Control Chart

    Since he switched to the mountain bike, the boss hasn’t said anything further about Joel’s arrival time. Changing his route seemed to solve the punctuality problem. But Joel’s still bothered by the amount of variation he saw in his road bike data. He wants to be sure he can count on getting to work on time, unless some unusual situation occurs.

    Has switching to the mountain bike made his commute time more consistent?

    Choose Assistant > Before/After Control Charts… to create a chart that makes it easy to compare the mean and variation for his old route to the new one.

    With continuous data that was not collected in subgroups, the Assistant’s decision tree directs you to the Before/After I-MR Chart.

    The data Joel has collected since switching to the mountain bike appears in a second column of the worksheet, so complete the Before/After I-MR Chart dialog box as shown:

    The Assistant produces all the output you need in a clear, easy-to-follow format. The Diagnostic Report offers detailed information about the analysis, while the Report Card flags potential problems. In this case, there are no concerns with the process mean and variation.

    The Summary Report gives you the bottom-line results of the analysis.

    Both the process mean and the standard deviation have been significantly reduced. Joel’s mean commute time has dropped to less than 15 minutes, and the standard deviation was reduced by 55.9%.

    The Assistant has made it easy to see that Joel’s commute process now fits within much tighter control limits, and has far less variation than it did when he traveled on his road bike. So with a right-click on the graph, he exports the Assistant’s Summary Report to Word for his weekly status update, and sends it to his boss. Mission accomplished!

    You’ve Arrived!

    Whether you bike, drive, or walk to work, you’ve completed this analysis in a timely manner! You have seen how the Assistant can help you view the distribution of your data and create before-and-after control charts for assessing the stability of your process.

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