Douglas Stinson, Fred Ameli, and Nick Zaino
Digital & Applied Imaging
©1995 Eastman Kodak Company
Used by permission.
A figure-of-merit, BLERmax, provides a reasonable approximation to the customer's perception of the integrity of data stored on KODAK Writable CD and Photo CD Media. When determining data life, using the industry standard specification of BLERmax less than or equal to 220 requires extrapolation far beyond the range of the data. Consequently, we have used the criteria BLERmax less than or equal to 50. The change of the figure-of-merit has been found to follow an Arrhenius model. That model predicts (at the 95% confidence level) that 95% of properly recorded discs stored at the recommended dark storage condition (25°C, 40% RH) will have a lifetime of greater than 217 years.
The extremely low cost per megabyte, small size, and convenient handling of CD-ROM and CD Recordable (CD-R) discs has resulted in the explosive growth of their use as a data storage and distribution medium. With disc capacities around 680 MB, the user has a significant investment in the data on each disc, and wants assurance that the data will be retrievable in the future. Exceptional data life was a design criteria from the beginning of the project which resulted in the development of the KODAK Writable CD and KODAK Photo CD. It drove the choice of all materials used in the fabrication of the disc, in particular, the recording layer.
The purpose of this report is to assess the level of success which was achieved at meeting that goal and to provide users with a quantitative estimate of the useful life of data recorded on a KODAK Writable CD Media. Specifically, we estimate the lifetime of properly recorded KODAK Writable CD Media when stored under the recommended dark storage condition of 25°C, 40% RH. This lifetime will apply to 95% of the population at the 95% confidence level.
The natural aging of KODAK Writable CD Media was accelerated by exposure to elevated temperature. The functional form of the distribution of a customer perceived "figure-of-merit" was estimated and the 95% point of the distribution determined. The correct function for interpolating or extrapolating the 95% point to "end-of-life" at each temperature was found. After verifying the validity of the standard Arrhenius model for this situation, the model was used to extrapolate the data life time at 25°C. We attempted to conform as closely as possible to the evolving standards for optical media lifetime determination currently under development.
To the customer, end-of-life is determined by the inability to retrieve data in the customer's system. However, since a single uncorrectable error constitutes end-of-life, this figure of merit is binary: "good" or "bad". In order to determine the time to failure using this figure of merit, each disc must be tested until it fails; a binary figure of merit provides no visibility to pre-failure changes from which end-of-life can be extrapolated. Because of the longevity of this product, it is impractical to test to failure except under the most accelerated (harsh) conditions--where extrapolation to 25°C behavior is most prone to error. In addition, different CD readers use different strategies in the implementation of the industry standard error correction code (ECC). This, plus differences in the implementation of the analog front-end of the readers, cause discs which generate uncorrectable errors in one reader to perform without error in another reader.
To avoid these difficulties, we chose to measure a continuously varying parameter closely related to uncorrectable errors. A key performance parameter defined in Sony and Philips' Compact Disc Digital Audio System Description (the Red Book) and in IEC 908 is the number of data blocks per second in error at the entrance of the first level ECC decoder, averaged over any 10 seconds; the Block Error Rate (BLER). We have found that the maximum value of this parameter anywhere on the disc (BLERmax) correlates reasonably well with uncorrectable errors. This figure of merit is also being used by the ANSI working group on CD lifetime test methods. Consequently we adopted BLERmax as the figure of merit. The industry standard specification is that BLERmax must be less than or equal to 220. Over the course of our study, BLERmax did not approach this limit. Consequently, estimating the time to reach BLERmax = 220 required extrapolation far beyond the limits of the data. In one of the better determinations of CD-ROM lifetime, 3M faced a similar situation. They decided to predict what they called "middle of life", defined as BLERmax = 50. For the purpose of this study, we have adopted the same criterion.
In the optical media industry the highest temperature normally employed in accelerated testing is 80°C. Early experiments with small numbers of samples of KODAK Writable CD media showed negligible change in performance after 2000 hours at 80°C/85% RH. As a result, in this test we set teh maximum temperature to 100°C and incubated and tested discs according to the schedule shown in table I.
# of Discs
100°C / 40% RH
0, 24, 48, 72, 96, 120, 168, 264, 360, 528 hours
90°C / 40% RH
0, 84, 168, 336, 504, 672, 840, 1008, 1512, 2016 hours
80°C / 3% RH
0, 84, 157, 325, 565, 750, 1008, 1512, 2016 hours
60°C / 40% RH
0, 68, 336, 504, 672, 840, 1008, 1512, 2016 hours
23°C / 50% RH
Sample sizes were chosen to compensate for the fact that fewer failures are expected at the lower temperatures. A larger sample of discs was included in the 100° condition to allow for a better estimation of the functional form of the population of BLER values in a condition we expected to cause failure within the course of the experiment. The 80° condition was run at 3% RH rather than 40% RH so that, in a future study, the data generated by this experiment could be combined with 80°/85% data to estimate the impact of relative humidity.
All discs were fully recorded using a KODAK PCD Writer 200 under expected customer use conditions. Prior to incubation and after each test interval the performance of each disc was evaluated using an industry-standard test device.
After testing, discs were returned to the environmental chambers for continued incubation. Chamber ramp profiles were set so as to not cause condensation within the polycarbonate substrate or excessive sorption-gradient induced substrate deflection.
Of the three distributions, normal, log-normal, and Weibull, the log-normal distribtution was found to best describe the BLERmax data at each time/temperature point. Using this distribution, the value of BLERmax which encompassed 95% of the population could be estimated. Good linear fits to the log of this value vs. exposure time coud be readily obtaned. An example for the 100°C case is shown in figure 1. From these regressions the time to end-of-life at each temperature could be estimated. There was no statistically significant change in BLERmax at 60° over the 2000 hour course of the experiment. All parameters measured on the discs stored at ambient (25°C/50% RH) for the course of the experiment were within the normal range of values obtained from freshly manufactured discs.
The estimated lifetimes at elevated temperature are shown in the standard Arrhenius form of log(lifetime) vs. 1/Temperature in figure 2. As can be seen, the data are accurately fit by a straight line, suggesting the validitiy of the Arrhenius model for this data. As there was no change in BLERmax at 60°C, this data was not included in the regression. This regression was used to estimate the lifetime at 25°C.
The uncertainty of the lifetime was estimated using a bootstrapping technique. At each time and temperature, a different estimate of the population of BLERmax values was obtained by choosing n samples, with replacement, from the data, where n equals the total number of data points at that time and temperature. The procedure described above for estimating end-of-life at each temperature, and for extrapolating to 25°C was carried out with these new estimates of the population. This entire process was repeated 1000 times. The error bars in figure 2 contain 95% of these estimates. Therefore, figure 2 showsthat with 95% confidence, 95% of the population of KODAK Writable CD Media will have a data lifetime of greater than 217 years if stored in the dark at 25°C, 40% Relative Humiditiy after being recorded in a KODAK PCD Writer 200.
The fit the the Arrhenius model can also be used to predict the change in BLERmax as a function of time at 60°C. This prediction (solid line), along with the measured data, is shown in figure 3. The model accurately predicts the observed lack of change over the course of the experiment. This lends further support to the validity of the model, and to the room temperature lifetime prediction.
Some sources prefer to plot percent change in BLER vs. time rather than the absolute value of BLER. The 60° data is re-plotted in this manner in figure 4. Also plotted in the figure is the percent change in BLER of some CD-ROM discs after incubation at 80°C/85% RH. This data was obtained from figure I of reference 3. As can be seen, the aging characteristics of KODAK Writable CD Media compares favorably with the best CD-ROM discs. It will also be noted that the lifetime of CD-ROM discs vary considerably from manufacturer to manufacturer. Likewise, the lifetime determined for CD-R discs from one manufacturer are not necessarily predictive of the lifetime of discs from other manufacturers.
The official position on the lifetime of KODAK Writable CD and Photo CD Media is "We predict the lifetime of KODAK Photo CD, and KODAK Writable CD Media with InfoGuard Protection System, under normal storage conditions in an office or home environment, should be 100 years or more." In our opinion, the official KODAK statement is well within the legitimate interpretation of this study. Under controlled conditions, our best estimate of the data life of these products is 217 years, which provides room to incorporate reasonable differences of opinion as to what constitutes "normal storage conditions."
All lifetime predicitons are subject to the following caveats:
Several people greatly assisted in the execution of this work. Herb Brew coordinated the exposures to accelerated conditions and the measurements. The CD Production testing Group performed most of the measurements. Dave Nunez maintained and operated the environmental chambers.