engleski

Influence of Cumulative Distribution Function Approximations on Risk Assessment

The obtained measurement results of an item of interest must conform to specified requirements. The decision of whether a measured quantity is accepted as satisfactory is made based on a predetermined tolerance interval. Such a procedure is called conformity assessment decision. When assessing the conformity with specified requirements, there is a risk for both the producer and the consumer. The measured value may be within the tolerance interval, while the actual value is outside the tolerance interval. In that case, it is a mistake of false acceptance. This is an incorrect decision, whose probability is called consumer's risk. The costs associated with that kind of error often are borne by the consumer. Conversely, the measured value may be outside the tolerance interval while the actual value is within the tolerance interval. In this case, a false rejection error was made. This incorrect decision is called producer's risk and associated costs are borne by a producer. To avoid such decision-making errors, the consumer and producer risks are determined. The analytical term for calculating both risks, consumer and producer, includes the cumulative distribution function (CDF) of the standard normal distribution. The CDF of the normal distribution is the integral of the normal probability density function (PDF). Such integral cannot be evaluated in closed form. For that reason, several approximations for CDF of standard normal have been developed. These approximations will be applied for risk calculation.

Approximations to CDF of normal distribution, CDF, consumer risk, producer risk

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