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Introduction to Health Physics: Fourth Edition - Ruang Baca FMIPA UB

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572 CHAPTER 10<br />

Figure 10-22. Optimization of radiation protection. (Reproduced with permission from Basic Safety<br />

Standards for Radiation Protection. Vienna, Austria: International A<strong>to</strong>mic Energy Agency; 1982.)<br />

To optimize protection, X + Y must be minimized. If α = cost per unit radiation<br />

detriment and the detriment from a given procedure is S, then the cost of this<br />

detriment is<br />

Y = αS, (10.39)<br />

and the quantity <strong>to</strong> be minimized is<br />

X + Y = X + αS. (10.40)<br />

If the costs of protection and detriment are a function of a parameter Z (for example,<br />

increased shielding thickness or increased ventilation rate), the minimum in the<br />

curve of cost versus dose in Figure 10-26 occurs when<br />

dX<br />

dZ<br />

that is,<br />

dX<br />

dZ<br />

+ α dS<br />

dZ<br />

= 0, (10.41)<br />

dS<br />

=−α . (10.42)<br />

dZ<br />

If we wish <strong>to</strong> optimize a shield thickness, then the cost of the shield is<br />

X = CAt, (10.43)

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