Example Using SCT to Analyze Tire Maintenance

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Consider a car with four regular tires (RF, LF, RR, LR) and a spare tire (SP). Assume that each tire can fail based on two failure modes, wear and puncture, and:

• The wear failure mode follows a Weibull distribution with Beta = 1.5, Eta = 600 hours.
• The puncture failure mode follows an exponential distribution with a mean of 2 months.
• Regardless of the failure mode, the repair duration (of both wear and puncture) follows a Weibull distribution with Beta = 1.5,Eta = 100 hours.
• If the tire fails due to wear, the tire is replaced with a new one (wear is repaired as-good-as-new).
• If the tire fails due to a puncture, it is patched up and placed back into service (repaired as-bad-as-old).
• When a primary tire (RF, LF, RR or LR) fails, it is replaced with the spare (SP) until that tire is restored. Once restored, the tire is put back in its original position and the spare is removed and put back for later use.

The purpose of this example is to illustrate the following options in State Change Triggers (SCT):

1. State Upon Repair: Always ON, Always OFF
2. Activate a block if any item from these associated maintenance group(s) goes down
3. Deactivate a block if any item from these associated maintenance group(s) is restored
4. Deactivate a block if any item from these associated maintenance group(s) goes down
5. Activate a block if any item from these associated maintenance group(s) is restored

BlockSim Solution

• To model this system, six diagrams are created: Car, Tire_LF, Tire_LR, Tire_RF, Tire_RR and Tire_SP with Car being the main diagram. Create the diagrams as follows:

1. First create diagram Tire_LF with two blocks in series. Block Wear_LF represents the Wear failure mode and Puncture_LF represents the Puncture failure mode for Tire_LF respectively.
   1. Block Wear_LF belongs to maintenance group "Wear_LF" and Block Puncture_LF belongs to maintenance group "Puncture_LF."
   2. Block Wear_LF has state change triggers; its initial state is ON, and the state upon repair is "Always ON." If any item from maintenance group "Puncture_LF" goes down, deactivate this block and if any item from maintenance group "Puncture_LF" is restored, activate this block.
   3. Block Puncture_LF has state change triggers; its initial state is ON, and the state upon repair is "Always ON." If any item from maintenance group "Wear_LF" goes down, deactivate this block and if any item from maintenance group "Wear_LF" is restored, activate this block.
      
2. Create the other three diagrams (Tire_LR, Tire_RF and Tire_RR) following the same logic.
3. In diagram Tire_SP, there are two blocks in series. Block Wear_SP represents the Wear failure mode and Puncture_SP represents the Puncture failure mode for the spare tire. Block Wear_SP belongs to maintenance group "Wear_SP" and Block Puncture_SP belongs to maintenance group "Puncture_SP."
   1. Block Wear_SP has state change triggers; its initial state is OFF, and the state upon repair is "Always OFF." If any item from maintenance group "Puncture_SP" goes down, deactivate this block and if any item from maintenance group "Puncture_SP" is restored, activate this block. If any item from maintenance group "Main Tires" goes down, activate this block and if any item from the maintenance group "Main Tires" is restored, deactivate this block. 
   2. Block Puncture_SP has state change triggers; its initial state is OFF, and the state upon repair is "Always OFF." If any item from maintenance group "Wear_SP" goes down, deactivate this block and if any item from maintenance group "Wear_SP" is restored, activate this block. If any item from maintenance group "Main Tires" goes down, activate this block and if any item from the maintenance group "Main Tires" is restored, deactivate this block.
      
4. In the diagram Car, there are five subdiagram blocks Tire_LF, Tire_LR, Tire_RF, Tire_RR and Tire_SP (each referencing/pointing to the diagram with the same names).
   1. In diagram Car, subdiagram blocks Tire_LF, Tire_LR, Tire_RF and Tire_RR belong to maintenance group "Main Tires."

Blocks Up/Down Plot

The system event log is shown in the figure below and is as follows (only blocks with failures are plotted):

1. At 46 hours, Block Wear_LR fails and brings down subdiagram Tire_LR. At the same time, it turns Block Puncture_LR OFF. Subdiagram Tire_LR goes down and activates Block Wear_SP and Puncture_SP, and subdiagram Spare is turned ON, too.
   
2. At 184 hours, Block Wear_LR is done with repair. According to the settings, it is always ON upon repair (is restored). The restoration of Block Wear_LR activates Block Puncture_LR and thus subdiagram Tire_LR is ON. The restoration of subdiagram Tire_LR deactivates Block Wear_SP and Puncture_SP, and subdiagram Tire_SP is turned OFF, too.
   
3. At 375 hours, Block Wear_RF fails and brings down subdiagram Tire_RF. At the same time, it turns Block Puncture_RF OFF. Subdiagram Tire_RF goes down and activates Block Wear_SP and Puncture_SP, and subdiagram Tire_SP is turned ON, too.
   
4. At 445 hours, Block Wear_RF is done with repair. According to the settings, it is always ON upon repair. The restoration of Block Wear_RF activates Block Puncture_RF and thus subdiagram Tire_RF is ON. The restoration of subdiagram Tire_RF deactivates Block Wear_SP and Puncture_SP, and subdiagram Tire_SP is turned OFF, too.
   
5. At 536 hours, Block Wear_LR fails again and brings down subdiagram Tire_LR. At the same time, it turns Block Puncture_LR OFF. Subdiagram Tire_LR goes down and activates Block Wear_SP and Puncture_SP, and the subdiagram Tire_SP is turned ON, too.
6. At 572 hours, Block Puncture_SP fails and brings down subdiagram Tire_SP. At the same time, it turns Block Wear_SP OFF. Subdiagram Tire_LR is already down at this time. Thus the system is down.
7. At 602 hours, Block Wear_LR is done with repair. According to the settings, it is always ON upon repair. The restoration of Block Wear_LR activates Block Puncture_LR and thus subdiagram Tire_LR is ON. The restoration of subdiagram Tire_LR should deactivate Block Wear_SP and Puncture_SP. However, Wear_SP is already OFF and Puncture_SP is already down at this time, thus nothing happens. The system is ON at this time due to the restoration of subdiagram Tire_LR.
8. At 617 hours, Block Puncture_SP is done with repair. According to the settings, it is always OFF upon repair.
9. At 686 hours, Block Puncture_LR fails and brings down subdiagram Tire_LR. At the same time, it turns Block Wear_LR OFF. Subdiagram Tire_LR goes down and activates Block Wear_SP and Puncture_SP, and the subdiagram Tire_SP is turned ON, too.
10. At 718 hours, Block Puncture_LR is done with repair. According to the settings, it is always ON upon repair. The restoration of Block Puncture_LR actives Block Wear_LR and thus subdiagram Tire_LR is ON. The restoration of subdiagram Tire_LR deactivates Block Wear_SP and Puncture_SP, and the subdiagram Tire_SP is turned OFF, too.