**RSICC CODE PACKAGE PSR-432**

**1. NAME AND TITLE**

PHAZE: Parametric Hazard Function Estimation.

**2. CONTRIBUTORS**

Idaho National Engineering and Environmental Laboratory, Idaho Falls, Idaho, through the Energy Science and Technology Software Center, Oak Ridge, Tennessee.

**3. CODING LANGUAGE AND COMPUTER**

PHAZE was developed using FORTRAN 77 for an IBM PC (P00432IBMPC00).

**4. NATURE OF PROBLEM SOLVED**

Phaze performs statistical inference calculations on a hazard function (also called a failure rate or intensity function) based on reported failure times of components that are repaired and restored to service. Three parametric models are allowed: the exponential, linear, and Weibull hazard models. The inference includes estimation (maximum likelihood estimators and confidence regions) of the parameters and of the hazard function itself, testing of hypotheses such as increasing failure rate, and checking of the model assumptions.

**5. METHOD OF SOLUTION**

PHAZE assumes that the failures of a component follow a time-dependent (or non-homogenous) Poisson process and that the failure counts in non-overlapping time intervals are independent. Implicit in the independence property is the assumption that the component is restored to service immediately after any failure, with negligible repair time. The failures of one component are assumed to be independent of those of another component; a proportional hazards model is used. Data for a component are called time censored if the component is observed for a fixed time-period, or plant records covering a fixed time-period are examined, and the failure times are recorded. The number of these failures is random. Data are called failure censored if the component is kept in service until a predetermined number of failures has occurred, at which time the component is removed from service. In this case, the number of failures is fixed, but the end of the observation period equals the final failure time and is random. A typical PHAZE session consists of reading failure data from a file prepared previously, selecting one of the three models, and performing data analysis (i.e., performing the usual statistical inference about the parameters of the model, with special emphasis on the parameter(s) that determine whether the hazard function is increasing). The final goals of the inference are a point estimate and a confidence interval for the hazard function at any time.

**6. RESTRICTIONS OR LIMITATIONS**

PHAZE is limited to a maxima of 100 components and 40 failures per component.

**7. TYPICAL RUNNING TIME**

RSICC executed the sample problem in approximately 10 minutes.

**8. COMPUTER HARDWARE REQUIREMENTS**

PHAZE is designed for an IBM PC or compatible computer. A math coprocessor is required to run the executable module.

**9. COMPUTER SOFTWARE REQUIREMENTS**

DOS 3.0 or higher is required on an IBM PC.

**10. REFERENCES**

PHAZE, NESC No.1147, PHAZE Flexible Disk Cartridge Description, National Energy Software Center Note 92-13 (October 15, 1991).

C. L. Atwood, "User's Guide to PHAZE, A Computer Program for Parametric Hazard Function Estimation, EGG-SSRE-9017 (July 1990).

C. L. Atwood, "Estimating Hazard Functions for Repairable Components," EGG-SSRE-8972 (May 1990).

**11. CONTENTS OF CODE PACKAGE**

Included in the package are the referenced documents and one 3.5" diskette, which includes source code, executable, sample problem input and output, and auxiliary information written in a self-extracting compressed DOS file.

**12. DATE OF ABSTRACT**

September 1999.

** KEYWORD:** RISK ASSESSMENT