Tolerance distribution model, risk

Tolerance Distribution Model. This model assumes that each member of the population at risk has an individual tolerance below which no response will be produced and that these tolerances vary in the members of the population according to some probability distribution (F). The probability distribution is also assumed to involve parameters of location (a) and scale (0 > 0) and can be generally denoted by F (a + 0 log z), where z is the tolerance level to a particular toxic agent. The probability, P(d), that a random individual will suffer a response from a dose, d, is P(d) = F (a + 0 log d) = dF(x). 

The continuously analysis and control of the manufacturing process is the precondition for the obtaining of excellent products. The two established methods are quality control charts and the relayed process capability indices. Quality Control Charts (QCC) can be used without an exact knowledge of the characteristic distribution model and are useful in the analysis of manufacturing risks. QCCs show the mean and scattering of each product characteristic in relation to the given tolerance areas. Furthermore, alert and intervention limits can be adapted inside QCC, if needed. This method is an industrial standard, further explanations can be found in (Timischl 2002). It is possible... 

All the models are based upon standard statistical distributions. The Multi-Hit model is based upon a Poisson distribution. The Probit model is based upon a normal distribution, and the One Hit, Multistage and Weibull models rely upon linear probabilities. Such distributions have proven applicability in dealing with substantial percentages of the population (up to 1 in 20). However, the models lose precision when they are pushed to extremes such as 1 in 10, such as encountered in risk assessment. Furthermore, homeostatic mechanisms such as DMA repair and immunological survellance may be poorly evaluated in risk assessment. Such high doses are administered to achieve the siaximum tolerated dose, that these mechanisms are surely overwhelmed in the animal studies. Additionally it should be noted that a risk of one in a million does not mean one tumor in the lifetime of a million people, it means that each individual has one chance in a million of developing a tumor in a lifetime. 

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