Example of a Covering Array with Factor Level Restrictions

The following example is patterned after an example described in Dalal and Mallows (1998). An originating phone (Near Phone) calls a receiving phone (Far Phone). Each phone call goes through an interface of type A or B. Five factors are of interest:

•	Market: USA, UK, Canada, France, Mexico

•	Near Phone: ISDN, Bus (Business), Coin, Res (Residential)

•	Near Interface: A or B

•	Far Phone: ISDN, Bus (Business), Coin, Res (Residential)

•	Far Interface: A or B

You are interested in which combinations of pairs of these factors are likely to cause failures. However, certain combinations are not possible:

•	An ISDN line on either phone (Near or Far) cannot use interface A.

•	Business and Residential lines on the originating phone (Near) cannot use interface B.

Create the Design

The factors and their settings are given in the data table Phone Factors.jmp. Create a Strength 2 covering array by following these steps.

Load Factors

1.	Select Help > Sample Data Library and open Design Experiment/Phone Factors.jmp.

The Phone Factors.jmp data table contains the factors and their settings.

2.	Select DOE > Covering Array.

Notice that the menu next to Strength: t = , is set to 2 by default.

3.	From the Covering Array red triangle menu, select Load Factors.

The Factors outline is populated with the five factors and their levels.

Factors Outline for Phone Factors

4.	Click Continue.

The Restrict Factor Level Combinations outline opens.

Restrict Factor Level Combinations

You can specify disallowed combinations in two ways:

•	Use Disallowed Combinations Filter

•	Use Disallowed Combinations Script

The filter gives an intuitive way to specify disallowed combinations. The script provides a quick and easy way to specify disallowed combinations, but requires that you have written or saved a script. In this example, if you do not want to specify combinations using the filter, skip to Specify Disallowed Combinations Using a Script.

Recall that the restrictions are the following:

•	An ISDN line on either phone (Near or Far) cannot use interface A.

•	Business and Residential phones on the originating phone (Near) cannot use interface B.

Specify Disallowed Combinations Using the Filter

Use this approach to enter disallowed combinations using the filter interface. Alternatively, you can paste a script as shown in Specify Disallowed Combinations Using a Script.

1.	Select Use Disallowed Combinations Filter.

2.	From the Add Filter Factors list, select Near Phone and Near Interface and click Add.

3.	Hold down the Ctrl key and click ISDN under Near Phone and A under Near Interface.

Disallowed Combinations Panel Showing First Constraints

Both blocks should turn dark. You have added the constraint that an ISDN line on the originating phone (Near) cannot use interface A.

Click OR.

5.	From the Add Filter Factors list, select Far Phone and Far Interface and click Add.

6.	Hold down the Ctrl key and click ISDN under Far Phone and A under Far Interface.

You have added the constraint that an ISDN line on the receiving phone (Far) cannot use interface A.

Click OR.

8.	From the Add Filter Factors list, select Near Phone and Near Interface and click Add.

9.	Hold down the Ctrl key and click Bus and Res under Near Phone and B under Near Interface.

You have added the restriction that Business and Residential lines on the originating phone (Near) cannot use interface B.

Completed Disallowed Combinations Filter

Specify Disallowed Combinations Using a Script

Alternatively, you can specify disallowed combinations by constructing a script. After loading your factors (Load Factors), do the following:

1.	Click Continue.

2.	Select Use Disallowed Combinations Script.

3.	Copy the following script and paste it in the Disallowed Combinations Expression script box:

(Near Phone == "ISDN" & Near Interface == "A") |

(Far Phone == "ISDN" & Far Interface == "A") |

(Near Phone == "Bus" & Near Interface == "B") |

(Near Phone == "Res" & Near Interface == "B")

Completed Disallowed Combinations Script Window

Note: In DOE platforms other than Covering Arrays, a script for disallowed combinations must specify the level number rather than the level name.

Construct the Design Table

Note: Setting the Random Seed in the next two steps reproduces the exact results shown in this example. When constructing a design on your own, these steps are not necessary.

1.	From the red triangle menu, select Set Random Seed.

2.	Enter 632 and click OK.

3.	Click Make Design.

The Design outline opens to show a 20-run design. A Metrics outline is added to the window.

Metrics Outline for Phone Design

The Metrics outline indicates that Strength 2 coverage is 100%. This means that all permissible two-factor combinations are represented in the design. The design also covers 65% of all three-factor combinations.

4.	Click Make Table.

The design is placed in a design table. A column for the response is provided, as well as various scripts.

Covering Array Design Table

Analyze the Experimental Data

Now that you have your design table, you can conduct your experiment and record your data in the Response column of the design table. Your experimental results are in the Phone Data.jmp sample data table.

1.	Select Help > Sample Data Library and open Design Experiment/Phone Data.jmp.

2.	In the Table panel, click the red triangle next to Analysis and select Run Script.

Analysis of Phone Experimental Data

The Summary outline indicates that three tests failed.

The Failure Analysis Details outline contains a 2 Factor Interactions report, because a two-way interaction is the lowest level interaction that detects a failure.

The 2 Factor Interactions report shows the combinations that might have caused the three failures. It is possible that one combination, Near Interface set to A and Far Phone set to Coin, is responsible for all three failures. Or it is possible that two or three other combinations caused the three failures.

3.	Select the first line in the 2 Factor Interactions report.

In the data table, rows 1, 3, and 15 are selected. Failures occur for these combinations, regardless of the settings for Market, Near Phone, and Far Interface. But note that other combinations of factor settings could account for these failures as well.