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Software Used: Software Used: ALTA PRO
Download Example File for Version 10 (*.rsgz10) or Version 9 (*.rsr9)
Consider a chemical solution (e.g., ink formulation, medicine, etc.) that degrades with time. A quantitative measure of the quality of the product can be obtained. This measure (QM) is said to be around 100 when the product is first manufactured and decreases with product age. The minimum acceptable value for QM is 50. Products with QM equal to or lower than 50 are considered to be “out of compliance” or failed.
Engineering analysis has indicated that at higher temperatures the QM has a higher rate of decrease. Assuming that the product’s normal use temperature is 20ºC (or 293 K), determine the shelf life of the product via an accelerated degradation test.
For the purpose of this analysis, “shelf life” is defined as the time by which 10% of the products will have a QM that is out of compliance.
For this experiment, 15 samples of the product are tested, with 5 samples in each of three environments: 323 K, 373 K and 383 K. Once a month, and for a period of seven months, the QM for each sample is measured and recorded. The data set obtained is given in the table below.
Since all of the readings are above the critical QM threshold of 50, none of the samples tested in this experiment have gone out of compliance (or “failed”) by the end of the test. However, there is sufficient data for the degradation of each sample to extrapolate a failure (i.e., the month at which we expect each sample to be at QM=50).
Using ALTA’s degradation analysis folio, the data for all samples are entered and individually fitted to multiple exponential curves. From each respective curve, a failure time (i.e., the time the product is expected to go out of compliance) is automatically extrapolated and fit to the selected ALTA model (in this case, Arrhenius-Weibull).
Figure 1: Degradation analysis folio.
The following plot shows the exponential curves for six of the tested samples (with the scaling adjusted to Y= 40 to 100 and X= 0 to 20).
Figure 2: Degradation vs. Time plot for 6 of the tested samples.
A Use Level Probability plot is shown next.
Figure 3: Use Level Probability plot.
A Reliability vs. Time plot for this product, also at the use stress level, is shown next.
Figure 4: Reliability vs. Time plot.
A Life vs. Stress plot, where the green line represents the time by which 10% of the units are expected to be out of compliance (at a given temperature), is shown next.
Figure 5: Life vs. Stress plot.
A Standardized Residual plot of the data and fitted model to ascertain adequacy is shown next.
Figure 6: Standardized Residuals plot.
Based on this analysis, the projected shelf life of this product is 15.6 months. The desired result can also be obtained from the QCP, as shown next.
