# ALTA Example 6 - Stability / Shelf Life Study

Software Used: ALTA 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 or 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 the specimen is then disposed of). Measurements for each ingredient (A, B and C) and at each time period are given in the following tables.

The following table shows the acceptable range for each ingredient.

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 PRO.)

Step 1:The data for ingredient A are entered in ALTA PRO and the lognormal distribution, along with an untransformed generalized log-linear life-stress relationship, is used to calculate the parameters. The data and settings used in the ALTA standard folio are shown next. Several plots from this analysis follow.

Figure 1: The calculated data set for ingredient A in ALTA's standard folio.

The next figure shows the Life vs. Age plot with 90% 2-sided confidence intervals. (The y-axis range has been changed to 142-156.) 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 vs. Age plot for A with 90% two-sided confidence intervals on mean life.

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 next.

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 0.000166, or about 0.02%, as the above figure shows. The probability of ingredient A being above limit after 24 months (i.e., the reliability when stress = 24 and mission end time = 156) is 0.03%. (Note that although they have not been used here, confidence intervals can easily be employed in the QCP.)

Step 2: The data for ingredient B are entered in a new data sheet and the analysis is repeated. The data and settings used are shown next.

Figure 4: The calculated data set for ingredient B in ALTA's standard folio.

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

Figure 5: Life vs. Age plot for B with 90% two-sided confidence intervals on mean life.

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%.

Step 3: The data for ingredient C are entered in a new data sheet, and the analysis is repeated. The data and settings used are shown next.

Figure 6: The calculated data set for ingredient C in ALTA's standard folio.

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

Figure 7: Life vs. Age plot for C with 90% two-sided confidence intervals on mean life.

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%.

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.

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