The rule of the 3 sigmas ---- how many times multiply the sigma to get 85%?

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$\sigma c=\sqrt{\overline{R}(\sigma S)^{2}+\overline{S^{2}}(\sigma R^{2})}$ where,

$\sigma c$ --- the buffer stock --- needed for maintaining the risk of stockouts, is used by logistitians

$\overline{R}$ --- the mean of the reserves

$\overline{S^{2}}$ --- the mean of the production

$(\sigma S)^{2}$ --- the square of the std. deviation of the production series

$(\sigma R^{2})$ --- the square of the std. deviation of the reserves

With this value of the stock buffer i am able to assure 84% of the stockouts. If i wanted 97.6% of the cases i would calculate for the value of 2 sigmas instead of one like in the equation. Now these percentages are given values......but what if i wanted to have the stock buffer to cover a custom percentage not only the cases where sigma is 1, 2 or 3....but 1.2 for example. The problem is i need to get how many times i have to multiply the sigma in order to get 85% of the stockouts covered by the possible stockouts.

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I'm not sure what type of underlying probability model you are using, but those percentiles look a lot like the values given by the normal distribution. In that case, if you wanted a custom percentage (p), you would find the value of $\sigma$ such that the probability that a standard normal variable is less than $\sigma$ equals p.