Having Non-Numeric values as measures in Fact table
As you noted in the comments for your other question your fact table data seems to be something like this:

+------------+
+ Sick leave +
+            +
+ Comp off   +
+ Sick leave +
+            +
+------------+


This kind of depends on your ETL loading procedures and reporting requirements.

You essentially have 2 options

Create separate measures

To achieve this you need to have to create 4 columns in  your fact table and have the corresponding value set to 1 or 0.

For example

+--------------------------------------------------------+
| Casual Leave | Sick Leave | UnInformed Leave |Comp off |
+--------------------------------------------------------+
| 1            | 0          | 0                |0        |
| 0            | 0          | 0                |0        |
| 0            | 1          | 0                |0        |
| 0            | 0          | 1                |0        |
| 0            | 0          | 0                |0        |
| 0            | 0          | 0                |1        |
+--------------------------------------------------------+


Then you can have a measure simply using a sum on all four columns to end up with 4 measures.

Create an extra dimension

You could create an extra dimension table for LeaveType like this:

+-----------------------------+
| Type_key | Type_Label       |
+-----------------------------+
| 0        | None             |
| 1        | Casual leave     |
| 2        | Sick leave       |
| 3        | Uninformed leave |
| 4        | Comp off         |
+-----------------------------+


And then in your ETL you can determine which type of leave it is.

+---------------------------+
| Leave_Type   | Leave_Days |
+---------------------------+
| 1            | 1          |
| 0            | 0          |
| 2            | 1          |
| 3            | 1          |
| 4            | 1          |
| 0            | 0          |
+---------------------------+


Then you can link that dimension to your fact table.

Decision points

The ease of implementation depends on your ETL process (do you have one?). One can be easier to implement over the other.

The behavior of the result is also a bit different. For example with multiple measures you have to add every measure to your report, with a dimension you have to put the dimension on an axis. 

It also has an impact on possible ways to do MDX calculations, filtering and so on.

I cannot decide in your place what the best option is and would suggest you do a small proof of concept and play around with it to see what suits you best.

For example if you put your dimension on the horizontal axis in excel the leave types with no values will not be shown.
If you have several measures you will have an empty column the length of your report.

Another example is maintainability. Depending on your tooling and possible ETL setup, how much work is it to add a new leave type 'child sick'.