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==ALTA Example 6 - Stability / Shelf Life Study ==
Software Used: ALTA 7 PRO

===Background===
A specific consumer product (e.g. a mouthwash, shampoo, etc.) is made up of three main ingredients (ingredients A, B and C) that have a characteristic (e.g. concentration) that may or may not change with time. A quantitative measure of a characteristic can be obtained, and this measure must be within a specified range for compliance. If any measure is outside its specified range, then the product is out of compliance and considered failed. There is no known dependency among these ingredients, and thus they are assumed to be statistically independent.

===Objective===
The product has a shelf life of 24 months. Determine the probability that a given specimen will be out of compliance at/after this time period.

===Experiment and Data===
For this study, 40 random products (specimens) are stored at normal use conditions. At 3, 6, 9 and 12 months, 10 specimens are removed and measured. The measurement process is a destructive test (i.e. once the specimen is opened for testing, the required readings are taken and that specimen is then disposed of). Measurements for each ingredient, and at each time period are given in Tables 1 through 4.

Table 1   
  
Table 2   
  
 
Table 3  
  
Table 4  
  
 

Table 5 shows the acceptable range for each ingredient.

{|align="center" border="1"
|-
|col span="4" style="text-align:center"|Table 5     
|-
|col span="4" style="text-align:center"|Acceptable Range
|- 
| || A|| B|| C 
|-
|Low|| 142|| 155|| 110 
|-
|High|| 156|| 185|| 135
|}

===Analysis===
If viewed from a "traditional reliability" perspective, the test in this example is not an accelerated test. However, its analysis will require that we employ the fundamental principles of ALT. The measured value of each characteristic (as measured after each holding period) can be viewed as the random variable (the time value in standard ALT) affected by the aging process (the stress value). In other words, the stress on each sample is the time in the holding cell and the random variable (what we traditionally think of as time-to-failure) is the value of the measured characteristic. With this approach, the analysis can be easily performed independently for each component in the ALTA software. In the analysis, the lognormal distribution is assumed, along with a general log-linear model. (See discussion on model settings for more details, as well as for a data entry example in ALTA 7 PRO.).

===Analysis Step 1===
The data for ingredient A are entered in ALTA 7 PRO and the lognormal distribution along with an untransformed generalized log-linear life-stress relationship are used to calculate the parameters. Figure 1 shows the data and settings used in the ALTA 7 Standard Folio. Several plots from this analysis follow.

Figure 1: The calculated data set for ingredient A in ALTA's Standard Folio.

Figure 2 shows the Life Characteristic vs. Age plot with 90% 2-sided confidence intervals. As can be seen from this plot, no increase or decrease in the characteristic is noted. In other words, age (at least up to the 12 months of observation) does not affect the characteristic for this ingredient.


Figure 2: Life Characteristic vs. Age for A, w/ 90% 2S Confidence Intervals

The last step in the analysis for this data set is to determine the probability that ingredient A will be outside the limits. This is easily done in ALTA's QCP, as shown in Figure 3.

Figure 3: The probability of Ingredient A being below limit at 24 months, calculated in ALTA's QCP.

The probability of ingredient A being below limit after 24 months is 0.02% and the probability of ingredient A being above limit after 24 months is 0.03%. (Note that although they have not been used here, confidence intervals can easily be employed in the QCP.).

===Analysis Step 2===
The data for ingredient B are entered in ALTA 7 PRO, and the analysis is repeated. Figure 4 shows the data and settings used.

Figure 4: The calculated data set for ingredient B in ALTA's Standard Folio.

Figure 5 shows the Life Characteristic vs. Age plot with 90% 2-sided confidence intervals. As can be seen from this plot, there is a noticeable decrease in the characteristic.


Figure 5: Life Characteristic vs. Age for B, w/ 90% 2S Confidence Intervals

Using the QCP, the probability that ingredient B will be outside the limits is found to be:

•Probability of being below limit after 24 months = 0.23%
•Probability of being above limit after 24 months = 0.00%


===Analysis Step 3===

The data for ingredient C are entered in ALTA 7 PRO, and the analysis is repeated. Figure 6 shows the data and settings used.

Figure 6: The calculated data set for ingredient C in ALTA's Standard Folio.

Figure 7 shows the Life Characteristic vs. Age plot with 90% 2-sided confidence intervals. As can be seen from this plot, there is a noticeable increase in the characteristic.


Figure 7: Life Characteristic vs. Age for C, w/ 90% 2S Confidence Intervals

Using the QCP, the probability that ingredient C will be outside the limits is found to be:

•Probability of being below limit after 24 months = 0.00%
•Probability of being above limit after 24 months = 17.83%


===Conclusion===

The probability of failure (i.e. the probability of the characteristic being outside the limits) can now be easily computed from the individual probabilities [assuming independence PS=1-{(1-PA)*(1-PB)...}]. In this case, the main contributing factor will be the probability that ingredient C exceeds the limits, which is significantly high. Having isolated the fact that ingredient C is the main cause of failure, appropriate corrective actions may be required.