Quality is the degree to which products or services meet the needs of customers. Common goals for quality professionals include reducing defect rates, manufacturing products within specifications, and standardizing delivery time.

Minitab offers many methods to help you assess quality in an objective, quantitative way. These methods include control charts, quality planning tools, measurement systems analysis (gage R&R studies), process capability, and reliability/survival analysis. This chapter focuses on control charts and process capability.

You can customize Minitab's control charts in the following ways:

- Automatically update the chart after you add or change data.
- Choose how to estimate parameters and control limits.
- Display tests for special causes and historical stages.
- Customize the chart, such as adding a reference line, changing the scale, and modifying titles.

You can customize control charts when you create them or later.

With Minitab's capability analysis, you can do the following:

- Analyze process data from many different distributions, including normal, exponential, Weibull, gamma, Poisson, and binomial.
- Display charts to verify that the process is in control and that the data follow the chosen distribution.

The graphical and statistical analyses that you performed in the previous chapter show that the Western shipping center has the fastest delivery time. In this chapter, you determine whether the Western shipping center’s process is in control and is capable of operating within specifications.

Unusual patterns in your data indicate the presence of special-cause variation, that is, variation that is not a normal part of the process. Use control charts to detect special-cause variation and to assess process stability over time.

Minitab control charts display process statistics. Process statistics include subgroup means, individual observations, weighted statistics, and numbers of defects. Minitab control charts also display a center line and control limits. The center line is the average value of the quality statistic that you choose to assess. If a process is in control, the points will vary randomly around the center line. The control limits are calculated based on the expected random variation in the process. The upper control limit (UCL) is 3 standard deviations above the center line. The lower control limit (LCL) is 3 standard deviations below the center line. If a process is in control, all points on the control chart are between the upper and lower control limits.

For all control charts, you can modify Minitab’s default chart specifications. For example, you can define the estimation method for the process standard deviation, specify the tests for special causes, and display historical stages.

Create an Xbar-S chart to assess both the mean and variability of the process. This control chart displays an Xbar chart and an S chart on the same graph. Use an Xbar-S chart when your subgroups contain 9 or more observations.

To determine whether the delivery process is stable over time, the manager of the Western shipping center randomly selected 10 samples for 20 days.

- If you are continuing from the previous chapter, choose . If not, start Minitab.
- Choose .
- Double-click the Getting Started folder, then double-click Quality.MTW.
- Choose .
- From the drop-down list, select All observations for a chart are in one column, then enter
`Days`. - In Subgroup sizes, enter
`Date`. To create a control chart, you only need to complete the main dialog box. However, you can click any button to select options to customize your chart. - Click OK.

Hold the pointer over points on a control chart or graph to view information about the data.

All of the points on the control chart are within the control limits. Thus, the process mean and process standard deviation appear to be stable or in control. The process mean () is 2.985. The average standard deviation () is 0.631.

You can use stages on a control chart to show how a process changes over specific periods of time. At each stage, Minitab recalculates the center line and control limits.

The manager of the Western shipping center made a process change on March 15. You want to determine whether the process was stable before and after this process change.

- Press Ctrl+E to open the last dialog box, or choose .
###### Tip

Minitab saves your dialog box settings with your project. To reset a dialog box, press F3.

- Click Xbar-S Options.
- On the Stages tab, in Define stages (historical groups) with this variable, enter
`Date`. - Under When to start a new stage, select With the first occurrence of these values, and enter
`3/15/2013`. - Click OK in each dialog box.

All the points on the control chart are within the control limits before and after the process change. For the second stage, the process mean () is 2.935 and the average standard deviation () is 0.627.

By default, Minitab displays the control limits and center line labels for the most recent stage. To display labels for all stages, click Xbar-S Options. On the Display tab, under Other, select Display control limit / center line labels for all stages.

When your data change, you can update any control chart or graph (except stem-and-leaf plot) without re-creating the graph.

After you create the Xbar-S chart, the manager of the Western shipping center gives you more data, which was collected on 3/24/2013. Add the data to the worksheet and update the control chart.

You need to add date/time data to C1 and numeric data to C2.

- Click the worksheet to make it active.
- Click any cell in C1, and then press End to go to the bottom of the worksheet.
- To add the date, 3/24/2013, to rows 201–210:
- Enter
`3/24/2013`in row 201 in C1. - Select the cell that contains 3/24/2013, and point to the Autofill handle in the lower-right corner of the cell. When the pointer becomes a cross symbol ( + ), press Ctrl and drag the pointer to row 210 to fill the cells with the repeated date value. When you press and hold Ctrl, a superscript cross appears above the Autofill cross symbol ( +
^{+}). The superscript cross indicates that repeated values, instead of sequential values, will be added to the cells.

- Enter
- Add the following data to C2, starting in row 201:
`3.60 2.40 2.80 3.21 2.40 2.75 2.79 3.40 2.58 2.50`As you enter data, press Enter to move to the next cell down. If the data-entry direction arrow points to the right, click the arrow so that it points down. - Verify that you entered the data correctly.

- Right-click the Xbar-S chart, then choose Update Graph Now.

The Xbar-S chart now includes the new subgroup. The mean ( = 2.926) and standard deviation ( = 0.607) changed slightly, but the process still appears to be in control.

To update all graphs and control charts automatically, choose Graphics, then select Other Graphics Options. Select On creation, set graph to update automatically when data change.

. ExpandBy default, the subgroups on Xbar-S charts are labeled in consecutive numeric order. You can edit the x-axis to display dates instead.

- Double-click the x-axis on the Xbar chart (the top chart).
- On the Time tab, under Time Scale, select Stamp. In Stamp columns (1-3, innermost first), enter
`Date`. - Click OK.
- Repeat for the x-axis on the S chart.

The x-axis for each chart now shows the dates instead of the subgroup numbers.

After you determine that a process is in statistical control, you want to know whether that process is capable. A process is capable if it meets specifications and produces good parts or results. You assess process capability by comparing the spread of the process variation to the width of the specification limits.

Do not assess the capability of a process that is not in control because the estimates of process capability might be incorrect.

Capability indices, or statistics, are a simple way of assessing process capability. Because capability indices reduce process information to single numbers, comparing one process to another is easy.

Now that you know that the delivery process is in control, perform a capability analysis to determine whether the delivery process is within specification limits and produces acceptable delivery times. The upper specification limit (USL) is 6 because the manager of the Western shipping center considers an order to be late if it is delivered after 6 days. The manager does not specify a lower specification limit (LSL). The distribution is approximately normal, so you can use a normal capability analysis.

- Choose .
- Under Data are arranged as, select Single column. Enter
`Days`. - In Subgroup size, enter
`Date`. - In Upper spec, enter
`6`. - Click OK.

Cpk is a measure of potential process capability. Ppk is a measure of overall process capability. Both Cpk and Ppk are greater than 1.33, which is a generally accepted minimum value. These statistics indicate that the Western shipping center’s process is capable and that the shipping center delivers orders in an acceptable amount of time.

Save all your work in a Minitab project.

- Choose .
- Browse to the folder that you want to save your files in.
- In File name, enter
`MyQuality`. - Click Save.

The quality analysis indicates that the Western shipping center’s process is in control and is capable of meeting specification limits. In the next chapter, you design an experiment and analyze the results to investigate ways to further improve the delivery process at the Western shipping center.

Go to Designing an Experiment.