SAFE-R and SAFE-D: Computer Codes for the Analysis of Failure Data, by J.K. Shultis, N.D. Eckhoff, D.E. Johnson, and G.A. Milliken, Report NUREG/CR-2375, US Nuclear Regulatory Comm., Washington, DC, Dec. 1981.

In an earlier companion report, NUREG/CR-2374 Use of Non-Conjugate Prior Distributions in Compound Failure Models, the theory and computational methods were described for application of a compound failure model to two types of commonly encountered attribute failure data. This report describes the computer codes which were developed from the theoretical and numerical investigation presented in the earlier report.

Two separate but similar FORTRAN computer codes have been developed for the analysis of component failure data with a compound statistical model: SAFE-D and SAFE-R. The SAFE-D code (Statistical Analysis for Failure Estimation: failure-on-Demand) analyzes data which gives the observed number of failures (failure to respond properly) in a specified number of demands for similar components that would change their condition upon demand. The second program, SAFE-R (Statistical Analysis for Failure Estimation: failure Rate) is to be used to analyze normally-operating components for which the observed number of failures in a specified operating time is given. In both these codes the failure parameter (failure probability per demand for SAFE-D or failure rate for SAFE-R) may be assumed equal for all similar components (the homogeneous failure model) or may be assumed to be a random variable distributed among similar components according to a prior distribution (the heterogeneous or compound failure model).

For the compound model analysis, the prior distribution may be chosen as one of several distribution families (e.g., lognormal, beta, gamma, Weibull, etc.). The parameters of the selected prior distribution are estimated from the failure data by any or all of the following methods: (i) matching the data mean and variance to those of the selected prior distribution, (ii) matching the data mean and variance to those of the marginal distribution, and (iii) maximizing the likelihood function of the marginal distribution. Both a chi-squared and/or a Kolmogorov-Smirnov goodness-of-fit test can be performed in order to see how well the resulting statistical models describe the given attribute data. Finally an analysis of the posterior distribution, estimated for each component, can be requested as well as various types of confidence intervals and tolerance intervals.

Both programs are multi-run semi-free format programs designed to give the user a great amount of flexibility in specifying program options and values of the program parameters. Each input command requests a particular calculation or analysis with either the homogeneous or compound model as is appropriate to the given failure data. A run consists of one or more commands which specify the particular statistical analyses desired by the user. SAFE-D and SAFE-R allow the user to build upon earlier runs or to reinitialize and start a completely separate analysis during a single load and execution of the program.

Section 2 describes the structure of the codes including input commands and options, and includes a flow diagram showing how separate parts of the codes are used. Finally in Section 3, an example is presented which illustrates the use of the codes.

SAFE-D and SAFE-R were originally written for an IBM mainframe computer. The versions distributed here have been converted to PC versions by Wilfried Hennings (W.Hennings@fz-juelich.de). The zipped packages include the source code, a PC .EXE executable file, example test input/output files, and the User's Manual NUREG-2375 in three formats (MicroSoft Word, PostScript, Adobe's PDF) and in US-letter and A4 paper sizes. The source code has been successfully run on a variety of other desktop machines.