Example of a System Reliability Analysis

Diagram

Scenario A represents the current structure of the system as shown in the following image.

The physical model for Scenario A includes the following components:

• Water Source: Produces water that can be used in the water bottling process. For our example, we will assume that the Water Source is a naturally occurring spring. This component is represented by an Asset element in the Diagram for Scenario A.
• Water Pump: Pulls water from the Water Source and into the Buffer. This component is represented by an Asset element in the Diagram for Scenario A.
• Water Tank: Stores water and feeds it into the Bottling Subsystem. This component is represented by a Buffer element in the Diagram for Scenario A.
• Bottling Subsystem: Fills bottles and attaches labels and caps. This subsystem is comprised of three Asset elements (Bottling Line 1, Bottling Line 2, and Bottling Line 3) and a Link. This component is represented by a Subsystem element in the Diagram for Scenario A.
• Link: Combines and manages the production of the Bottling Lines within the Bottling Subsystem. The Link specifies that two of the three Bottling Lines must be running for the entire Subsystem to run. This component is represented by a Link in the Diagram for Scenario A.

Risks

When the Water Pump element fails due to a risk, the entire system will fail and accrue lost production costs. The following risks are assigned to the Water Pump element in Scenario A:

• Seal Failure.
• Bearing Failure.
• Impeller Failure.

Every time the Water Pump experiences an unplanned Bearing Failure, the correction will require the use of the Bearing, Mechanic, and Seal Resources. If the Water Pump requires a bearing replacement as the result of a planned correction, only the Bearing and Mechanic Resources will be needed. Therefore, the following Resources have been assigned to the Bearing Failure Risk:

• Unplanned Resources: Mechanic, Bearings, and Seal.
• Planned Resources: Mechanic and Bearings.

Actions

There are no actions defined for Scenario A.

Diagram

Scenario B represents the current structure of the system as shown in the following image.

The physical model for Scenario B is shown in this image. It is identical to Scenario A, but Actions and additional Resources have been assigned to the Water Pump in this Scenario to mitigate Risks.

Risks

The same Risks are defined for Scenario B as are defined for Scenario A. The same Resources are assigned to these Risks.

Actions

For Scenario B, the following Actions have been defined for the Water Pump:

• Replace Seal: A time-based maintenance Action that mitigates the Seal Failure Risk.
• Vibration Analysis: An inspection or periodic condition-based maintenance Action that mitigates the Bearing Failure Risk. The Vibration Technician Resource has been assigned to the Vibration Analysis Action.
• Redesign Impeller: A redesign Action that mitigates the Impeller Failure Risk.

Diagram

Scenario C represents the current structure of the system as shown in the following image.

The physical model for Scenario C is shown in this image. It is similar to Scenario A but contains the following additional components:

• Water Pump 2: Pulls water from the Water Source and into the Water Tank. Water Pump 2 serves as a backup or standby for Water Pump 1 and is represented by an Asset element in the Diagram for Scenario C.
• Sensor 1: Monitors Water Pump 1 for failure. When Water Pump 1 fails, Sensor 1 activates Switch 2, indicating that Water Pump 2 will start running, and deactivates Switch 1 to indicate that Water Pump 1 has stopped running. Sensor 1 is represented by a Sensor element in the Diagram for Scenario C.
• Sensor 2: Monitors Water Pump 2 for failure. When Water Pump 1 fails, Water Pump 2 will start running and will continue to run until it fails. When Water Pump 2 fails, Sensor 2 will activate Switch 1, indicating that Pump 1 is running, and will deactivate Switch 2 to indicate that Water Pump 2 has stopped running. Sensor 2 is represented by a Sensor element in the Diagram for Scenario C.
• Switch 1: Is initially set to On, indicating that Water Pump 1 is initially running. When activated by Sensor 1, connects the Water Source and Water Pump 1 so that Pump 1 will feed water into the Water Tank. When deactivated by Sensor 1, Switch 1 disconnects Water Source and Water Pump 1. Switch 1 is represented by a Switch element in the Diagram for Scenario C.
• Switch 2: Is initially set to Off, indicating that Pump 2 is not running initially. When activated by Sensor 2, connects the Water Source and Water Pump 2 so that Pump 2 will feed water into the Water Tank. When deactivated by Sensor 2, Switch 2 disconnects Water Source and Water Pump 2. Switch 2 is represented by a Switch element in the Diagram for Scenario C.

Risks

The same Risks are defined for Scenario C as are defined for Scenarios A and B. The same Resources are assigned to these Risks.

Actions

There are no Actions defined for Scenario C.

By comparing Scenario A, Scenario B, and Scenario C, we will be able to view each scenario's reliability and cost and identify the scenario that has the highest reliability and lowest cost associated with it. Scenario A represents the current design, and both Scenario B and Scenario C represent modifications to the original design. These modifications support different hypotheses about modifying our current system:

• Scenario B proposes that by implementing certain Actions that mitigate Risks associated with the Water Pump, we may be able to increase the reliability and decrease the cost of the system.
• Scenario C proposes that by introducing an additional Water Pump, which will prevent a full system failure when Water Pump 1 fails, we may be able to increase the reliability and decrease the cost of the system.

By modeling and comparing the three different Scenarios, we should be able to draw conclusions and make recommendations about changes that should be implemented to improve the reliability of the system.

This is a simple example and is limited to three scenarios only. As you develop a System Reliability Analysis, you may want to develop additional scenarios that model other variations to the system. As we continue to use this example throughout the System Reliability documentation, we will provide suggestions for where you might modify or extend our example to take advantage of the System Reliability features to create a more complex, in-depth analysis.

This example contains one root System Analysis record. The following values exist in the fields of that record:

Fields	Values
Name	System Reliability Analysis Example
Currency	$
Start Date	1/1/2010 12:00:00 AM
Period	7 Years
Iterations	1000
Time Analysis Type	Yearly
Confidence (%)	90
Histogram Bins	20
Enable Event Log	False
Random Seed	True

The following table shows the data stored in the System Scenario records in this example:

Scenarios	Values Specified
Scenario A	Name: Scenario A Description: Current Structure
Scenario B	Name: Scenario B Description: Current Structure With Actions
Scenario C	Name: Scenario C Description: Redesigned Structure With Backup Pump

Each Scenario in this example contains two System Subsystem records. One System Subsystem record contains the Diagram structure for each Scenario, and the other System Subsystem record contains the Bottling Lines, which are used in all three Scenarios. The following table lists the data that exist in each record.

Subsystem	Values Specified
Diagram for Scenario A	Name: Diagram for Scenario A Production Contribution: 100 Fixed Cost: 0 Variable Cost: 0 Variable Cost Units: Per Day Lost Production Cost: 100000 Lost Production Cost Units: Per Day
Diagram for Scenario B	Name: Diagram for Scenario B Production Contribution: 100 Fixed Cost: 0 Variable Cost: 0 Variable Cost Units: Per Day Lost Production Cost: 100000 Lost Production Cost Units: Per Day
Diagram for Scenario C	Name: Diagram for Scenario C Production Contribution: 100 Fixed Cost: 0 Variable Cost: 0 Variable Cost Units: Per Day Lost Production Cost: 100000 Lost Production Cost Units: Per Day
Bottling Subsystem	Name: Bottling Subsystem Production Contribution: 100 Fixed Cost: 0 Variable Cost: 0 Variable Cost Units: Per Day Lost Production Cost: 0 Lost Production Cost Units: Per Day

The following table shows the data stored in the System Asset records in this example. The light blue row identifies the Scenario(s) in which each Asset element is used.

Asset	Values Specified
All Scenarios
Water Source	Name: Water Source Production Contribution: 100 Fixed Cost: 0 Variable Cost: 0 Variable Cost Units: Per Day Lost Production Cost: 0 Lost Production Cost Units: Per Day
Bottling Line	Name: <Bottling Line 1, Bottling Line 2, or Bottling Line 3> 1All Bottling Lines use the same data with the exception of the Name field, whose value is different for each Asset element. Production Contribution: 40 Fixed Cost: 0 Variable Cost: 0 Variable Cost Units: Per Day Lost Production Cost: 0 Lost Production Cost Units: Per Day
Scenario A
Water Pump	Name: Water Pump Production Contribution: 100 Fixed Cost: 5000 Variable Cost: 50 Variable Cost Units: Per Hour Lost Production Cost: 0 Lost Production Cost Units: Per Day
Scenario B
Water Pump	Name: Water Pump Production Contribution: 100 Fixed Cost: 5000 Variable Cost: 50 Variable Cost Units: Per Hour Lost Production Cost: 0 Lost Production Cost Units: Per Day
Scenario C
Water Pump 1	Name: Water Pump 1 Production Contribution: 100 Fixed Cost: 5000 Variable Cost: 50 Variable Cost Units: Per Hour Lost Production Cost: 0 Lost Production Cost Units: Per Day
Water Pump 2	Name: Water Pump 2 Production Contribution: 100 Fixed Cost: 5000 Variable Cost: 50 Variable Cost Units: Per Hour Lost Production Cost: 0 Lost Production Cost Units: Per Day

The following table shows the data stored in the System Buffer record for this example:

Field	Value
Name	Water Tank
Production Contribution	100
Initial Quantity in Percentage	50
Time to Empty	0.5
Time to Empty Units	Days
Time to Refill	5
Time to Refill Units	Days

The following table shows the data stored in the System Link record for this example:

Field	Value
Name	Link
Minimum Predecessors:	2

The following table shows the data stored in the System Sensor records for this example:

Sensor	Values Specified
Sensor 1	Name: Sensor 1 Monitored Elements: Water Pump 1 Activated Switches : Switch 2 Deactivated Switches: Switch 1
Sensor 2	Name: Sensor 2 Monitored Elements: Water Pump 2 Activated Switches: Switch 1 Deactivated Switches: Switch 2

The following table shows the data stored in the System Switch records in this example:

Element	Values Specified
Switch 1	Name: Switch 1 Is Initially On: Yes Production Contribution: 100 Fixed Cost: 0 Variable Cost: 0 Variable Cost Units: Per Day Lost Production Cost: 0 Lost Production Cost Units: Per Day
Switch 2	Name: Switch 2 Is Initially On: No Product Contribution: 100 Fixed Cost: 0 Variable Cost: 0 Variable Cost Units: Per Day Lost Production Cost: 0 Lost Production Cost Units: Per Day

The following table shows the data for the Risks used in this example:

Note: The Source column identifies the entity family name of the record in which the associated data is stored. The data from all source records is combined to create the comprehensive Risk data.

Risk	Assigned To	Source	Values Specified
Water Source Failure	Water Source Asset in all Scenarios	System Risk Record	Name: Water Source Failure Last Failure: 1/1/1999 12:00:00 AM Fixed Unplanned Correction Cost: 0 Variable Unplanned Correction Cost: 0 Per Day Planned Correction Cost: 0 Planned Correction Duration: 0 Hours Is Active: True Is Latent: False Failure Without Replacement: False Number of Subcomponents: 1 PF Interval: 0 Days Repair Immediately: True Percentage of PF Interval to Wait(%): 0
		Exponential	Name: TTF Distribution Distribution Type: Exponential Time Unit: Years MTBF: 20 Enable Distribution Association: No
		Exponential	Name: TTR Distribution Distribution Type: Exponential Time Unit: Weeks MTBF: 2 Enable Distribution Association: No
Bottling Line Failure	Bottling Line Asset in all Scenarios	System Risk Record	Name: Bottling Line Failure Last Failure: 1/1/1999 12:00:00 AM Fixed Unplanned Correction Cost: 0 Variable Unplanned Correction Cost: 0 Per Day Planned Correction Cost: 0 Planned Correction Duration: 0 Hours Is Active: True Is Latent: False Failure Without Replacement: False Number of Subcomponents: 1 PF Interval: 0 Days Repair Immediately: True Percentage of PF Interval to Wait (%): 0
		Exponential	Name: TTF Distribution Distribution Type: Exponential Time Unit: Months MTBF: 12 Enable Distribution Association: No
		Normal	Name: TTR Distribution Distribution Type: Exponential Time Unit: Days MTTR: 1 Enable Distribution Association: No
Seal Failure	Water Pump Asset in Scenario A and B Water Pump 1 and Water Pump 2 Assets in Scenario C	System Risk Record	Name: Seal Failure Last Failure: 1/1/1999 12:00:00 AM Fixed Unplanned Correction Cost: 1500 Variable Unplanned Correction Cost: 1000 Per Day Planned Correction Cost: 1000 Planned Correction Duration: 4 Hours Is Active: True Is Latent: False Failure Without Replacement: No Number of Subcomponents: 1 PF Interval: 30 Days Repair Immediately: True Percentage of PF Interval to Wait (%): 0
		Weibull	Name: TTF Distribution Distribution Type: Weibull Time Unit: Years Beta: 4 Eta: 3 Gamma: 0 Enable Distribution Association: No
		Normal	Name: TTR Distribution Distribution Type: SingleValue Time Unit: Hours Value: 12 Enable Distribution Association: No
Bearing Failure	Water Pump Asset in Scenario A and B Water Pump 1 and Water Pump 2 Assets in Scenario C	System Risk Record	Name: Bearing Failure Last Failure: 1/1/1999 12:00:00 AM Fixed Unplanned Correction Cost: 2000 Variable Unplanned Correction Cost: 1000 Per Day Planned Correction Cost: 1000 Planned Correction Duration: 4 Hours Is Active: True Is Latent: False Failure Without Replacement: False Number of Subcomponents: 1 PF Interval: 6 Weeks Repair Immediately: True Percentage of PF Interval to Wait (%): 0
		Exponential	Name: TTF Distribution Distribution Type: Exponential Time Unit: Months MTBF: 60 Enable Distribution Association: No
		Exponential	Name: TTR Distribution Distribution Type: Exponential Time Unit: Hours MTTR: 8 Enable Distribution Association: No
Impeller Failure	Water Pump Asset in Scenario A and B Water Pump 1 and Water Pump 2 Assets in Scenario C	System Risk Record	Name: Impeller Failure Last Failure: 1/1/1999 12:00:00 A.M. Fixed Unplanned Correction Cost: 1500 Variable Unplanned Correction Cost: 1000 Per Day Planned Correction Cost: 1000 Planned Correction Duration: 4 Hours Is Active: True Is Latent: False Failure Without Replacement: False Number of Subcomponents: 1 PF Interval: 0 Days Repair Immediately: True Percentage of PF Interval to Wait (%): 0
		Exponential	Name: TTF Distribution Distribution Type: Exponential Time Unit: Months MTBF: 24 Enable Distribution Association: No
		Normal	Name: TTR Distribution Distribution Type: Single Value Time Unit: Hours Value: 12 Enable Distribution Association: No

The following table shows the data used in the Actions in this example. This information defines the properties of the Actions associated with the Water Pump element in Scenario B.

Note: The Source column identifies the entity family name of the record in which the associated data is stored. The data from all source records is combined to create comprehensive Action data.

Action	Mitigated Risk	Source	Values Specified
Redesign Impellers Impeller Failure		System Special Action Record	Name: Redesign Impellers Action Cost: 1600 Interval: 2 Years Duration: 2 Days Shutdown Required: True One Time Action: True Replace Failure Consequence: True Replace TTF Distribution: True
		System Risk Assessment	Mitigated Unplanned Correction Cost: 10001 Note: When you associate a Risk to an Action that is represented by a System Special Action record, and select the hyperlinked Action name in the Actions pane on the System Reliability Scenarios - Actions page, the Mitigated Unplanned Correction Cost field appears in the New Failure Consequence section on the Mitigated Risks tab and is labeled Fixed Unplanned Correction Cost.
		Weibull	Name: New TTF Distribution Distribution Type: Weibull Time Unit: Months Beta: 4 Eta: 48 Gamma: 0
Replace Seals	Seal Failure	System Preventive Maintenance Record	Name: Replace Seals Action Type: Time-Based Maintenance (Preventive) (PM) Action Cost: 2000 Interval: 2 Years Duration: 4 Hours Shut Down Required: True One Time Action: False
Vibration Analysis	Bearing Failure	System Inspection Record	Name: Vibration Analysis Action Type: Condition-Based Maintenance (Predictive) (CM) Condition Monitoring Type: Periodic Action Cost: 0 Interval: 3 Weeks Duration: 1 Hours Shut Down Required: False One Time Action: False Detection Probability(%): 90

The following table shows the data stored in the System Resource records in this example:

Resource	Values Specified
Bearing	Name: Bearing Fixed Cost: 200 Variable Cost: 0 Per Day Count Occurrences: True
Mechanic	Name: Mechanic Fixed Cost: 0 Variable Cost: 100 Per Hour Count Occurrences: False
Seal	Name: Seal Fixed Cost: 250 Variable Cost: 0 Per Day Count Occurrences: True
Vibration Technician	Name: Vibration Technician Fixed Cost: 0 Variable Cost: 100 Per Hour Count Occurrences: False

The following table shows the data stored in the System Resource Usage records in this example:

Resource	Linked To	Values Specified
Vibration Technician	Vibration Analysis Action	Resource: Vibration Technician Quantity: 1 Duration: 1 Duration Units: Hours
Mechanic	Bearing Failure Risk	Planned Resource Usage Resource: Mechanic Quantity: 1 Duration: 4 Duration Units: Hours   Unplanned Resource Usage Resource: Mechanic Quantity: 1 Duration: 8 Duration Units: Hours
Bearing	Bearing Failure Risk	Planned Resource Usage Resource: Bearing Quantity: 2 Duration: 0 Duration Units: Hours   Unplanned Resource Usage Resource: Bearing Quantity: 2 Duration: 0 Duration Units: Hours
Seal	Bearing Failure Risk	Unplanned Resource Usage Resource: Seal Quantity: 1 Duration: 0 Duration Units: Hours