Specification Setting: Setting Acceptance Criteria from Statistics of the Data - - BioPharm International

ADVERTISEMENT

Specification Setting: Setting Acceptance Criteria from Statistics of the Data


BioPharm International
Volume 19, Issue 11

APPENDIX

Calculation of two-sided multipliers (M UL ) by Howe's method and one-sided multipliers (MU/ML) by Natrella's method

Howe's method calculates a variable MUL to provide us with a level of confidence of C% that the limits (x mean – MUL * S) and (x mean + MUL * s) will contain D% of the distribution.

The sigma multiplier MUL is given by











in which N is the number of values in the sample, Z(1 – D)/2 is the critical value of the Normal distribution that is exceeded with probability (1 – D)/2 and X 2 (N – 1),C is the critical value of the chi-square distribution with (N – 1) degrees of freedom that is exceeded with probability C%.

Equation [1] looks complex, and the statement, "We are 99% confident that 95% of the measurements will fall within the calculated tolerance limits" requires a bit of thought, but it is not difficult to calculate MUL using Excel. For example, if cell J24 contains N, if C = 99% and D = 99.25%, the value of MUL is given by

= SQRT((J24 – 1)*(1 + (1 / J24))* (NORMINV(0.00375,0,1)^2) / (CHIINV(0.99,J24 – 1)))........... [2]

Some values of the sigma multipliers calculated by Howe's method appear in Table 1. The entries in Table 1 were calculated with C set to 99% and D set to 99.25%.

These values of C and D were selected by noting that the usual practice for specifications calculated from the mean (x mean) and standard deviation (s) is to set the limits at +/– 3 times the standard deviation either side of the mean. C and D were thus selected so that the two-sided tolerance interval limits would be (x mean – 3 * s) and (x mean + 3 * s) when the sample size is around 250.

Natrella's method for probabilistic one-sided tolerance intervals calculates variables MU and ML to provide us with a level of confidence of C% that D% of the values will be less than an upper limit of (x mean + MU * s) or that D% of the values will be more than a lower limit of (x mean – MU * s). The calculations are the same for MU and ML














and N is the number of values in the sample, ZD is the critical value of the Normal distribution that is exceeded with probability D and ZC is the critical value of the Normal distribution that is exceeded with probability C.

MU can be calculated using Excel. For example, if cell B4 contains N, if C = 99% and D = 99.625%, the values of a and b are given by:

a = 1 – (NORMINV(0.99,0,1))^2 / (2*(B4 – 1))........... [6]

and

b = (NORMINV(0.99625,0,1))^2 – (NORMINV(0.99,0,1))^2 / B4........... [7]


blog comments powered by Disqus

ADVERTISEMENT

ADVERTISEMENT

GPhA Issues Statement on Generic Drug Costs
November 20, 2014
Amgen Opens Single-Use Manufacturing Plant in Singapore
November 20, 2014
Manufacturing Issues Crucial to Combating Ebola
November 20, 2014
FDA Requests Comments on Generic Drug Submission Criteria
November 20, 2014
USP Joins Chinese Pharmacopoeia Commission for Annual Science Meeting
November 20, 2014
Author Guidelines
Source: BioPharm International,
Click here