Larry George, revised December 16, 2005, pstlarry@cal.berkeley.edu
Note April 21, 2019: The following 2005 design specification will be replaced by "User Manual for Credible Reliability Prediction." Popular MTBF predictions (MIL-HDBK-217, Telcordia TR332, and commercial software and standards equivalents) compare with credible reliability prediction like fake news vs. facts, because credible reliability prediction is based on observed field reliability. www.asqrd.org published my monograph "Credible Reliability Prediction" (CRP) from 2003 to 2014 then lost it. I asked for permission to republish my mongraph. ASQ RD management decided to publish it and asked me for a copy. So I decided to publish "User Manual for CRP." The original CRP monograph contained spreadsheet screen shots that showed recommendations. The "User Manual for CRP" (MS Word *.docx) will include live spreadsheet images ready for use, and will be accompanied by an Excel workbook (*.xlsm) containing entire spreadsheets, workbooks, and VBA code, ready to use. Please stay tuned or contact me for preview (pstlarry077@gmail.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