PRODUCT STABILITY--PART I Table Suggested Stability Storage Temperatures (Tootill) Series 145 1 2 3 4 øC øF øC øF øC øF øC øF 39 102 42 108 52 126 60 140 63 145 63 145 64.5 148 69 156 91 196 87 189 78 172 78.5 173 Table iV Suggested Stability Test Design (Kennon) Tc•nperature Assay or Sampling Times (Months) o C øF 1st 2nd 3rd 4th 60 146 1 3 4 .. 45 113 3 4 6 8 37 99 6 8 12 .. RT RT 8 12 18 24 Table V Suggested Stability Test Design (Lordi and Scott) Temperature Assay or Sampling Times (Months) ø C øF 1st 2nd 3rd 41.5 107 0.84 2 5 60 140 0.35 0.84 2 46 115 0.43 1.3 4 70 158 0.14 0.43 1.3 thermore, the time scales to get the same amount of breakdown at each temperature will also be in geometric progression in the opposite direc- tion from the temperatures (as the higher temperatures require less time). The times are set on the basis of an estimate of the slope ratio. Thus, one needs an estimate of the slope ratio to start the experiment. This may be obtained from literature data or from a preliminary study. The experimental design will then result in approximately the same amount of degradation at the times samples are withdrawn and assayed regard- less of temperature. The design calls for samples to be withdrawn at two times for each of three temperatures, with the second time being set for 50% decomposition. Tootill has shown that, following this arrangement, each individual degradation curve is estimated with approximately equal precision and

146 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS that this simplifies both the statistical analysis and the task of judging the degree of conformity of the results to the Arrhenius equation. Table III shows four series of suggested storage temperatures which fit Toot- ill's design. Times and temperature set chosen would be determined depending on the degradation rate, to get the length of the experiment to a manageable or convenient length. Kennon (11) illustrated the utility of mathematical models in deter- mining chemlcal,stabfi•ty. The construction of the reference reaction paths he used was based on considerations involving heats of activation and shelf-life goals. From these paths a logical assay schedule arose. The schedule is actually based on the temperatures chosen for sample storage and would change if another set of storage conditions were used. An example of a set of suggested storage conditions and an assay schedule are shown in Table IV. Lordi and Scott (12) reported on their development of nomographic stability charts which were designed to facilitate the analysis and en- hance the utility of data obtained from stability tests. In connection with these efforts, they also suggested a stability program design based on probable heats of activation and t90's. They suggest the times and temperatures shown in Table V. Normally only one of the sets (either the 41.5-60 øC or the 46-70 øC) would be used. Two additional--and untraditional--types of stability testing proce- dures are also worthy of note. These methods of "placement" are quite different from those discussed so far. Eriksen, Pauls, and Swintosky (13) investigated the accuracy of heating-time measurements as they are affected by time lags during the heating and cooling of samples during a stability study. They developed an equation relating sample heating or cooling rate, storage time and temperature, and the heat of activation. This provided the ETTE or "equilibrium temperature time equivalent," and this information en- abled one to get better data for kinetic calculations. These techniques may not appear to be especially useful for our purposes, but they are most valuable when one works with high temperatures for short times, or with very large bulks, or when heat conductivity factors are not ideal. In a subsequent paper these authors (14) presented some additional infor- mation concerning applications of this technique in a tablet stability study. Some years later Eriksen and Stelmach (15) devised and illustrated with appropriate data a "one step" method of implementing a kinetic study. The technique uses a "reciprocal heating machine" to make a