Let's break down the step-by-step solution for the integration sequence for the given module hierarchy (usually a question about **top-down integration testing**): ### Step-by-Step Solution: #### 1. **Start with the root module (M1):** - Begin by implementing and testing `M1`. - Since `M1` calls `M2`, `M3`, and `M13`, but these are not ready yet, **use stubs** for `M2`, `M3`, and `M13`. #### 2. **Integrate M2:** - Integrated System (IS) = `M1` and `M2` (stub for `M3`, `M13`) - `M2` calls `M4` and `M5` (use stubs for these). #### 3. **Integrate M3:** - IS = (`M1`, `M2`) and `M3` (stub for `M13`) - `M3` calls `M6` and `M7` (use stubs for these). #### 4. **Integrate M13:** - IS = (`M1`, `M2`, `M3`) and `M13` - `M13` calls `M14` (use stub for `M14`). #### 5. **Integrate M4:** - IS = (`M1`, `M2`, `M3`, `M13`) and `M4` - `M4` calls `M8` (use stub for `M8`). #### 6. **Integrate M5:** - IS = (`M1`, `M2`, `M3`, `M13`, `M4`) and `M5` - `M5` calls `M9` (use stub for `M9`). #### 7. **Integrate M6:** - IS = (`M1`, `M2`, `M3`, `M13`, `M4`, `M5`) and `M6` - `M6` calls `M10` (use stub for `M10`). #### 8. **Integrate M7:** - IS = (`M1`, `M2`, `M3`, `M13`, `M4`, `M5`, `M6`) and `M7` - `M7` calls `M11` and `M12` (use stubs for these). #### 9. **Integrate M14:** - IS = (`M1`, `M2`, `M3`, `M13`, `M4`, `M5`, `M6`, `M7`) and `M14` #### 10. **Integrate M8:** - IS = (`M1`, `M2`, `M3`, `M13`, `M4`, `M5`, `M6`, `M7`, `M13`, `M14`) and `M8` #### 11. **Integrate M9:** - IS = (all above) and `M9` #### 12. **Integrate M10:** - IS = (all above) and `M10` #### 13. **Integrate M11:** - IS = (all above) and `M11` #### 14. **Integrate M12:** - IS = (all above) and `M12` --- ## **Final Integration Sequence (with stubs):** 1. IS = `M1` (stubs for `M2`, `M3`, `M13`) 2. IS = IS + `M2` (stubs for `M3`, `M13`, `M4`, `M5`) 3. IS = IS + `M3` (stubs for `M13`, `M4`, `M5`, `M6`, `M7`) 4. IS = IS + `M13` (stubs for `M4`, `M5`, `M6`, `M7`, `M14`) 5. IS = IS + `M4` (stubs for `M5`, `M6`, `M7`, `M14`, `M8`) 6. IS = IS + `M5` (stubs for `M6`, `M7`, `M14`, `M8`, `M9`) 7. IS = IS + `M6` (stubs for `M7`, `M14`, `M8`, `M9`, `M10`) 8. IS = IS + `M7` (stubs for `M14`, `M8`, `M9`, `M10`, `M11`, `M12`) 9. IS = IS + `M14` (stubs for `M8`, `M9`, `M10`, `M11`, `M12`) 10. IS = IS + `M8` (stubs for `M9`, `M10`, `M11`, `M12`) 11. IS = IS + `M9` (stubs for `M10`, `M11`, `M12`) 12. IS = IS + `M10` (stubs for `M11`, `M12`) 13. IS = IS + `M11` (stub for `M12`) 14. IS = IS + `M12` --- ## **Summary Table** | Step | Integrated System (IS) | Required Stubs | |------|----------------------------------------|-------------------------| | 1 | M1 | M2, M3, M13 | | 2 | M1, M2 | M3, M13, M4, M5 | | 3 | M1, M2, M3 | M13, M4, M5, M6, M7 | | 4 | M1, M2, M3, M13 | M4, M5, M6, M7, M14 | | 5 | ... | ... | | ... | ... | ... | | 14 | All modules integrated | None | --- ## **Final Answer** **The integration testing sequence is:** M1 → M2 → M3 → M13 → M4 → M5 → M6 → M7 → M14 → M8 → M9 → M10 → M11 → M12 At each step, you replace a stub with the actual module, starting from the top and moving down, until all modules are integrated. --- **Please let me know if you want the sequence in a different format or as a diagram!**

Certainly! Based on the provided diagram and the hints, it appears you are dealing with a **top-down integration testing** approach for a system composed of multiple modules. The goal is to determine the **integration sequence** of modules, replacing test stubs with real modules step-by-step. Since the question refers to **detailed calculations and explanations**, I will interpret each step carefully, explaining **why** each module is integrated at that point, and how the stubs are replaced in sequence. --- ### Understanding the Module Hierarchy From the diagram, the modules are organized as follows: - **M1** is the topmost module. - **M1** calls modules **M2**, **M3**, and **M13**. - **M2** calls **M4** and **M5**. - **M3** calls **M6** and **M7**. - **M13** calls **M14**. - **M4** calls **M8**. - **M5** calls **M9**. - **M6** calls **M10**. - **M7** calls **M11** and **M12**. The goal is to perform integration testing starting from the top, gradually replacing stubs with actual modules as they become ready. --- ### Step-by-step Integration Sequence with Explanations **Key Concept**: - *Stubs* are dummy modules used during early testing. - As modules are integrated, their respective stubs are replaced with actual modules. --- ### Step 1: **Integrate M1 (with stubs for M2, M3, M13)** - **Why?** - M1 is the root module. - Initially, we test the top-level module with dummy stubs for all modules it depends on. - **Result:** - System: M1 + stubs for M2, M3, M13. --- ### Step 2: **Integrate M2 (with stubs for M3, M13, M4, M5)** - **Why?** - Now, replace the stub for M2 with the actual module. - M2 calls M4 and M5, so we create stubs for M4 and M5. - **System now:** - M1 + M2 + stubs for M3, M4, M5, M13. --- ### Step 3: **Integrate M3 (with stubs for M6, M7, M13)** - **Why?** - Replace stub for M3 with real M3. - M3 calls M6 and M7, so create stubs for these. - **System now:** - M1 + M2 + M3 + stubs for M6, M7, M13, M4, M5. --- ### Step 4: **Integrate M13 (with stub for M14)** - **Why?** - Replace stub for M13 with real M13. - M13 calls M14, so create a stub for M14. - **System now:** - M1 + M2 + M3 + M13 + stubs for M14, M6, M7, M4, M5. --- ### Step 5: **Integrate M4 (with stub for M8)** - **Why?** - Replace stub for M4 with real M4. - M4 calls M8, so create a stub for M8. - **System now:** - M1 + M2 + M3 + M13 + M4 + stubs for M8, M14, M6, M7, M5. --- ### Step 6: **Integrate M5 (with stub for M9)** - **Why?** - Replace stub for M5 with real M5. - M5 calls M9; create stub for M9. - **System now:** - M1 + M2 + M3 + M13 + M4 + M5 + stubs for M9, M8, M14, M6, M7. --- ### Step 7: **Integrate M6 (with stub for M10)** - **Why?** - Replace stub for M6 with real M6. - M6 calls M10; create stub for M10. - **System now:** - M1 + M2 + M3 + M13 + M4 + M5 + M6 + stubs for M10, M9, M8, M14, M7. --- ### Step 8: **Integrate M7 (with stubs for M11, M12)** - **Why?** - Replace stub for M7 with real M7. - M7 calls M11 and M12; create stubs for these. - **System now:** - All above modules + M7 + stubs for M11, M12. --- ### Step 9: **Integrate M14 (no further modules)** - **Why?** - Replace stub for M14 with real M14. - **System now:** - M1, M2, M3, M13, M4, M5, M6, M7, M14 + stubs for M8, M9, M10, M11, M12. --- ### Step 10: **Integrate M8 (no further modules)** - **Why?** - Replace stub with real M8. - **System now:** - All modules except M9, M10, M11, M12 are real. --- ### Step 11: **Integrate M9** - **Why?** - Replace stub with real M9. --- ### Step 12: **Integrate M10** - **Why?** - Replace stub with real M10. --- ### Step 13: **Integrate M11** - **Why?** - Replace stub with real M11. --- ### Step 14: **Integrate M12** - **Why?** - Replace stub with real M12. --- ### **Final Integration Sequence Summary** | Step | Modules Integrated | Notes | |---|---|---| | 1 | M1 | Start with top module, stubs for M2, M3, M13 | | 2 | M2 | Replace stub for M2, stubs for M4, M5 | | 3 | M3 | Replace stub for M3, stubs for M6, M7 | | 4 | M13 | Replace stub for M13, stub for M14 | | 5 | M4 | Replace stub for M4, stub for M8 | | 6 | M5 | Replace stub for M5, stub for M9 | | 7 | M6 | Replace stub for M6, stub for M10 | | 8 | M7 | Replace stub for M7, stubs for M11, M12 | | 9 | M14 | Replace stub for M14 | | 10 | M8 | Replace stub for M8 | | 11 | M9 | Replace stub for M9 | | 12 | M10 | Replace stub for M10 | | 13 | M11 | Replace stub for M11 | | 14 | M12 | Replace stub for M12 | --- ## **Final Answer:** The **integration testing sequence** starting from the top (using bottom-up approach with stubs replaced step-by-step) is: **M1 → M2 → M3 → M13 → M4 → M5 → M6 → M7 → M14 → M8 → M9 → M10 → M11 → M12** At each step, the relevant stub is replaced with the actual module, ensuring systematic top-down integration. --- **Would you like this sequence in a specific diagrammatic format or further detailed explanations of each step?**