Shown in Figure D.15 is a general four-state Markov model of piping reliability. All failure processes of this model can be evaluated using service data, assuming that such a data collection is of sufficient technical detail and completeness. This model is used in Section D.6 to develop time-dependent LOCA frequencies.

Figure D. 15 Four-State Markov Model of Piping Reliability[4]

In this and subsequent report sections, a pipe failure (F) is defined as a through-wall defect resulting in a non­active leak or small, active leak. The frequency of a large leak (L) in excess of Technical Specification limits is estimated using the following simple model:

Fl = Л X Plf (d.1)

Frequency of a large leak [1/Reactor-year].

Failure frequency [1/Reactor-year. Extension]; where ‘extension’ refers to the piping component boundary definition. Depending on the intended application and type(s) of degradation mechanism, the extension could be formed by counts of bends, pipes, tees, welds or length of piping. In Equation (4.2), the exposure term reflects the total component population in the data survey.

Exposure time (or reactor operating years)

Conditional probability of a large leak given a through-wall defect. Section D.5 includes a technical basis for estimating conditional failure probabilities.

The parameter estimation uses a Bayes’ update process that begins with the development of prior distributions for each of the terms in equation (D.1). These prior distributions are shaped by our knowledge about the susceptibility of different piping systems to degradation. The input to the Bayes’ update process comes from a small subset of PIPExp after it has been subjected to screening for pipe failures that meet certain selection criteria. A software tool (Bayesian Analysis Reliability Tool — BART™) is used to perform the updates.[5]

Piping reliability is a function of pipe size (diameter and wall thickness), and metallurgy, process medium, environment and design requirements; or attributes and influences, respectively. The purpose of data processing and data reduction is to extract from the total PIPExp database those subsets of service data that correspond to the attributes and influences of the Base Case definitions.

D.4.1.1 Informative versus Noninformative Prior Distributions — The type, extent and quality of applicable service data will determine the actual implementation of the Bayesian update process. Where sufficient service data is available an empirical Bayes approach is used. In this case classical estimation techniques are used to fit a prior distribution to the available data. When no or sparse service data is available a non-informative prior is defined. Relative to the five Base Cases the following approaches are used to determine the prior failure rates distributions:

• BWR Base Case — RR Loop B. There is ample service data on IGSCC. Our prior state-of-knowledge consists of service data before implementation of IGSCC mitigation strategies (mid-1980s). A prior failure rate is derived through classical statistical estimation.

• BWR Base Case — FW Loop B. Given the scarce service data, a lognormal distribution with a mean value of 1.0E-06 per weld-year and range factor (RF) equal to 100 is used. This is a noninfomative prior distribution.

• PWR Base Case — RC Hot Leg. The only available service data involves axial cracks in RPV nozzle-to-safe-end welds at three PWR units. A point estimate for the failure rates is calculated for

the period 1970 through 2000. This point estimate is approximated by a lognormal distribution with range factor of 100; i. e., essentially a noninformative prior.

• PWR Base Case — RC Surge Line. For the pressurizer surge line there is no service data including non-through wall or through-wall cracking. Again, a lognormal distribution with a mean value of 1.0E-06 per weld-year and RF = 100 is used.

• PWR Base Case — HPI/NMU Line. Service data exists, which is directly applicable to this base case. To account for design changes that have been implemented post-1997, a non-informative prior is combined with B&W-specific failure data and exposure data through end of calendar year 1997. The resulting failure rate represents a prior distribution, which is applicable to this Base Case.