The TI was also calculated with α=0.027 and γ=0.95 for each time point. To compare the two methods for each TI value, a corresponding
z-value was calculated (see Table IV).
Table IV: The by-time-point method limits from the tolerance interval (TI) and z-values for the corresponding TI values.
. The slope-control-chart method is commonly used when it is necessary to compare the results between several tested batches
or between the currently tested batch and other batches from the historical database. For the purpose of this experiment,
control limits were defined from the historical data and then used to test Batch 10 for the presence of OOT results. For each
time point, a least-squares regression line that includes all data up to that time point was constructed. The regression line
was constructed from the data of 0, 3, and 6 months, and the slope of that line was calculated. The procedure was repeated
until the last tested time point of the ongoing stability study. The mean and standard deviation of the slopes for the given
time intervals were calculated. The slope-control chart was then constructed (see Table V).
Table V: Slope-control chart and the z-values for Batch 10.
To identify the present OOT result, the z-score test was used to calculate the z value for the slope at each time period of
Batch 10. The value of z was limited to -2 < z <+2, provided that 95.45% of the future values will enter the interval of
these limits. Unlike the previous two methods for identification of OOT results, where the absolute value of the result was
analyzed, in this method, the authors analyzed the values for the slope. Because small changes in the slope value cause a
significant change in the regression line (and in this case it would mean the kinetics of degradation), for this model, narrower
limits for the z-value were chosen.
Additionally, the TI also was calculated from the slope values at each time interval. In this case, however, the TI was calculated
with defined α=0.045 and γ=0.95, for proper comparison with the limits determined by the z-score test (7). In order to compare
the two methods for each TI value, a corresponding z-value was calculated (see Table VI).
Table VI: The slope-control chart method limits from tolerance intervals (TI) and z values for the corresponding TI values.