Larry George, revised December 16, 2005, pstlarry@yahoo.com

- Design Considerations
- Assumptions and Dependencies
- Constant failure rates and exponential reliability functions for all parts
- Independence
- Infinite mission time
- hot standby (active redundancy)
- General Constraints
- No more than eight parts in a parallel subsystem. Parts are assumed to be on hot standby (active redundancy).
- No more than five parallel or series subsystem in series. (Failure rates may be added to combine any number of series subsystems into a single series subsystem.)
- Entire subsystems may be replicated in parallel. Each is assumed to be in hot standby
- This is not for general networks, finite mission time, or cold standby. Please contact me for software for all-terminal network reliability, cold standby, or hysterecal standby.
- Inputs
- User shall enter data in cells representing reliability block diagram, or the user can run an input VBA macro program that requests information and pastes data in appropriate cells.
- Input program asks user to specify number of subsystems in series
- Input program asks user to specify reliability block diagram in the form of n1k1n2k2… where nj is the number of parts in the j-th parallel subsystem, and kj is the number required for subsystem function, kj<nj<9.
- Input program asks for FITs for each subsystem’s components. All components are assumed to have the same FITs. Please contact me if your requirements differ.
- Input program asks user to specify the age for reliability computation
- Input program asks user to specify the number of simulation iterations. The spreadsheet contains 1000 replications, but the input program will accept any reasonable number.
- Excel workbook spreadsheets or the input program shall compute system MTBF, reliability, and cost from user’s data
- Computation Methods
- Excel spreadsheets shall represent reliability block diagrams
- Exact formulas are used for all reliability computations and for MTBF computations whenever possible.
- Use recursive formula for MTBF of k-out-of-n given 1-out-of-n formula
- VBA macro programs shall implement input and simulation. To run the VBA macro program, select the Tools menu, Macro command, Macro subcommand. Excel will show the macro dialog box. Select the macro called “Sheet1.SP” or “Sheet1.PS” and choose the Run command.
- The VBA macro program takes a hardly noticeable time to run 10,000 iterations.
`Outputs`- Table 1 shows the reliability block diagram. If you use the VBA macro program, please make sure the RBD looks like what you intended. If not, simply rerun the macro program or type the data directly into table 1 to used the spreadsheet simulation.
- Table 2 contains
subsystem MTBF and reliability predictions, to your specified operating
age. The first section of the table lists the
*part*reliability and MTBF predictions. The second section lists*subsystem and system*reliability, MTBF predictions, and MTBF standard deviations. The subsystem MTBF standard deviations are those from the spreadsheet simulation with 1000 iterations. Compare the system MTBF standard deviations for the VBA macro program with those from the spreadsheet simulation. If you run the VBA macro program with more than 1000 iterations, the system MTBF standard deviation for the VBA macro program should be less than that of the spreadsheet system MTBF simulation. Table 2 also computes the FITs of the subsystems and system as inverses of the MTBFs. - Table 3 provides a tool for reliability allocation. Enter per unit part costs, and the table computes system cost. Run the spreadsheet or the VBA macro program with alternative parts, FITs, costs, and RBDs to find the optimum allocation. Optimum may be either the minimum cost design for at least a specified reliability or the maximum reliability design for a specified cost.
- Table 4 simulates system reliability. No entries are needed.
- Bibliography
- Klion, J., “A Redundancy Notebook,” RADC-TR-77-287, ADA050837, 1977
- George, L. L., “MTBF
Prediction for Redundant Systems,” ASQ
*Reliability Review,*Vol. 21, No. 4, pp 5-9, Dec.2001