Annex 1 5.9.2.1 Statistic Models

Statistische Modelle

Statistic Models are based on an estimation of values based on available information about software errors.

Statistic Models can be differentiated in models based on the time between the detection of two errors, and in models based on the number of errors (/Goel, 1985/).

Models based on the time between the detection of two errors are, e. g.:

When assuming that errors are corrected right after its detection, the probable time between the detection of errors tends to increase.

Models based on the number of errors might be:

When assuming that errors are corrected right after its detection, the number of errors tends do decrease.

Since the models are probability models, they are based on a number of assumptions. The most important assumption certainly is that the errors occur independent of each other. Also, it is usually assumed that the error correction will be successful. The disadvantage of the statistic models is that reasonable, probability-theoretical information can only be obtained after a certain application period. These statistic models cannot be used to define the reliability of software prior to its application.

In /Musa, 83/, the following criteria are suggested for the selection of statistic reliability models:

• precision of the prediction
• usefulness
• quality of the assumptions
• simplicity
The "precision of the prediction" refers to the ability of the model to predict future failures.

"Usefulness" refers to the ability of the model to estimate values. Such values are, e. g.:

• the mean time between failures (MTBF)
• the date a preset MTBF is reached
• resource and cost requirements in order to reach a preset MTBF.
The "quality of the assumptions" refers to the extent the assumptions can be confirmed by available data.

The "simplicity" can refer to several aspects. First, it should be simple to collect the data required for the model. Furthermore, the model concept should be simple enough for the user to understand this model without a comprehensive knowledge of the mathematical background.

#### 5.9.2.1.1 Model by Goel and Okumoto5.9.2.1.2 Execution Time Model by Musa5.9.2.1.3 Logarithmic Poisson Execution Time Model by Musa and Okumoto5.9.2.1.4 Jelinski-Moranda Model5.9.2.1.5 Model by Schick and Wolverton

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