9 Report Layer

9.1 Preliminary Discussion

The report layer is populated with constructs to save results of calculations. These constructs fall into two categories:

  • Constructs to tell which software, algorithm(s), and option(s) were used to produce the results
  • The results themselves

It is almost impossible and probably not even desirable to normalize fully the report layer. Tools are very different from one another and produce a wide variety of results. New calculation methods are regularly proposed. To normalize everything would lead to a huge and anyway incomplete format. Moreover, the way results are arranged into reports depends on the study. It is also, at least to some extent, a matter of taste.

If the Model Exchange Format cannot give a formal structure for the report layer, it can at least suggest a style to describe what has been calculated and how it has been calculated. It can also provide a check-list of what should be included as information to make results truly exportable and importable. The existence of such report style would be very useful for reporting tools (whether they are graphical or textual): it would be much easier for these tools to extract the information they need from the XML result files.

9.2 Information about calculations

Here follows a non-exhaustive list of information about how the results have been obtained that can be relevant and other special or unique features of the model.

  • Software

    • Version
    • Contact organization (editor, vendor, etc.)
    • ...
  • Calculated quantities

    • Name
    • Mathematical definition
    • Approximations used
    • ...
  • Calculation method(s)

    • Name
    • Limits (e.g., number of basic events, of sequences, of cut sets)
    • Preprocessing techniques (modularization, rewritings, etc.)
    • Handling of success terms
    • Cutoffs, if any (absolute, relative, dynamic, etc.)
    • Are delete terms, recovery rules or exchange events applied?
    • Extra-logical methods used
    • Secondary software necessary
    • Warning and caveats
    • Calculation time
    • ...
  • Features of the model

    • Name
    • Number of: gates, basic events, house events, fault trees, event trees, functional events, initiating events
  • Feedback

    • Success or failure reports
    • ...

9.3 Format of Results

PSA tools produce many kinds of results. Some are common to most of the tools, e.g., probability/frequency of some group of consequences, importance factors, sensitivity analyses. They fall into different categories. The following three categories are so frequent that is it worth to normalize the way they are stored into XML files.

  • Minimal cut sets (and prime implicants)
  • Statistical measures (with moments)
  • Curves

9.3.1 Minimal Cut Sets

A first (and good) way to encode minimal cut sets consists in using the representation of formulae defined by the Model Exchange Format. However, it is often convenient to attach some information to each product, which is not possible with the formulae of the Model Exchange Format. An alternative XML representation for sums of products (sets of minimal cut sets are a specific type of sums of products) is given in Listing 9.1. More attributes can be added to tags “sum-of-products” and “product” to carry the relevant information.

Listing 9.1 The RNC schema for the XML representation of sums-of-products
sum-of-products =
  element sum-of-products {
    attribute description { text }?,
    attribute basic-events { xsd:nonNegativeInteger }?,
    attribute products { xsd:nonNegativeInteger }?,

product =
  element product {
    attribute order { xsd:positiveInteger }?,

literal =
  element basic-event { name }
  | element not { element basic-event { name } }

9.3.2 Statistical measures

Statistical measures are typically produced by sensitivity analyses. They are the result, in general, of Monte-Carlo simulations on the values of some parameter. Such a measure can come with moments (mean, standard deviation), confidence ranges, error factors, quantiles, etc. The XML representation for statistical measure is given in Listing 9.2.

Listing 9.2 The RNC schema for the XML representation of statistical measures
statistical-measure =
  element measure {
    attribute description { text }?,
    element mean {
      attribute value { xsd:double }
    element standard-deviation {
      attribute value { xsd:double }
    element confidence-range {
      attribute percentage {
        xsd:double { minExclusive = "0" maxExclusive = "100" }
      attribute lower-bound { xsd:double },
      attribute upper-bound { xsd:double }
    element error-factor {
      attribute percentage {
        xsd:double { minExclusive = "0" maxExclusive = "100" }
      attribute value {
        xsd:double { minExclusive = "0" }

quantiles =
  element quantiles {
    attribute number { xsd:positiveInteger },

quantile = element quantile { bin-data }

bin-data =
  attribute number { xsd:positiveInteger },
  attribute mean { xsd:double }?,
  attribute lower-bound { xsd:double }?,
  attribute upper-bound { xsd:double }?

9.3.3 Curves

Two or three dimensional curves are often produced in PSA studies. A typical example is indeed to study the evolution of the system unavailability through the time. The XML representation of curves suggested by the Model Exchange Format is given in Listing 9.3.

Listing 9.3 The RNC schema the XML representation of curves
curve =
  element curve {
    attribute name { xsd:NCName }?,
    attribute description { text }?,
    (attribute X-title { xsd:string },
     attribute Y-title { xsd:string },
     attribute Z-title { xsd:string }?)?,
    (attribute X-unit { unit },
     attribute Y-unit { unit },
     attribute Z-unit { unit }?)?,
    element point {
      attribute X { xsd:double },
      attribute Y { xsd:double },
      attribute Z { xsd:double }?

unit = "seconds" | "hours"