In Developer Mode, find the Production Order Report from Settings --> Technical --> Actions --> Reports and open it.

Click the Qweb Views button at the top and open the XML record that defines the report.

Although this is technical what you see defines what is shown in the report, and taking inspiration from the way the Work Orders are shown (if they exist), we can generate our own Inherited View that extends the base report:

<div t-if="o.move_raw_ids" position="after">
    <div t-if="o.check_ids">
        <h3>Quality Checks</h3>
        <table class="table table-sm">
            <tr>
                <th>Reference</th>
                <th>Type</th>
                <th>Title</th>
                <th>Checked</th>
                <th>Employee</th>
                <th>Status</th>
            </tr>
            <tr t-foreach="o.check_ids" t-as="lineq">
                <td><span t-field="lineq.name"/></td>
                <td><span t-field="lineq.test_type_id"/></td>
                <td><span t-field="lineq.title"/></td>
                <td><span t-field="lineq.control_date"/></td>
                <td><span t-field="lineq.user_id.name"/></td>
                <td><span t-field="lineq.quality_state"/></td>
            </tr>
        </table>
    </div>
</div>

The result: