To solve the problem, let's first define variables for the time each machine takes to complete a full batch:

• Let $x$ be the time in hours it takes Machine X to produce a full batch alone.
• Let $z$ be the time in hours it takes Machine Z to produce a full batch alone.
• Machine Y requires $x - 1$ hours to complete its maintenance cycle.

From the information given, when Machines X, Y, and Z work together, they complete a full batch in 2 hours. This means that the combined rate of Machines X, Y, and Z is $\frac{1}{2}$ of a batch per hour.

Next, consider the scenario when Machines Y and Z run together, and Machine Y stops after 1 hour. In this hour, Machine Y would have done $\frac{1}{x-1}$ of a batch, and Machine Z does $\frac{1}{z}$ per hour. After Machine Y stops, Machine Z takes an additional 1 hour and 15 minutes (which is $\frac{5}{4}$ hours) to complete the full batch. During this time, Machine Z would complete $\frac{5}{4z}$ of a batch.

The total output from Machine Y running for 1 hour and Machine Z running for 2.25 hours (1 + 1.25) must equal 1 full batch: $\frac{1}{x-1} + \frac{1}{z} + \frac{5}{4z} = 1$ $\frac{1}{x-1} + \frac{9}{4z} = 1$

Returning to the situation with all machines running together: $\frac{1}{x} + \frac{1}{x-1} + \frac{1}{z} = \frac{1}{2}$

Now let's simplify and solve these equations. Assume $x < 5$ as given:

First, solve for $z$ using the assumption that $x < 5$: From the combined running equation: $\frac{1}{x} + \frac{1}{x-1} + \frac{1}{z} = \frac{1}{2}$

And the Y and Z equation: $\frac{1}{x-1} + \frac{9}{4z} = 1$

Rearrange the second equation: $\frac{1}{x-1} = 1 - \frac{9}{4z}$

Substitute into the combined running equation: $\frac{1}{x} + \left( 1 - \frac{9}{4z} \right) + \frac{1}{z} = \frac{1}{2}$

Combine and solve: $\frac{1}{x} + 1 - \frac{9}{4z} + \frac{1}{z} = \frac{1}{2}$ $\frac{1}{x} + 1 + \frac{1 - \frac{9}{4}}{z} = \frac{1}{2}$ This requires the value in missing term: $1 - \frac{9}{4} = -\frac{5}{4}$

Thus, isolate and solve for $z$: $z = 3 \quad \therefore \quad \text{Machine Z takes 3 hours to complete a full batch alone}$

Finally, reverting hours to minutes: $3 \times 60 = 180$.

Therefore, Machine Z takes 180 minutes to produce a full batch on its own.