Estimating Drive Reliability in Desktop Computers and Consumer Electronics Systems

1、ifrom: gerry coleseagate personal storage grouplongmont, coloradodate: november 2000number: tp-338.1estimating drive reliability in desktop computersand consumer electronics systemsintroductionhistorically, desktop computers have been the primary application for hard disc storage devices.however, th

2、e market for disc drives in consumer electronic devices is growing rapidly. this paper pre-sents a method for estimating drive reliability in desktop computers and consumer electronics devicesusing the results of seagates standard laboratory tests. it provides a link between seagates publishedreliab

3、ility specifications and real-world drive reliability as experienced by the end-user.definitionsseagate estimates the mean time between failures (mtbf) for a drive as the number of power-on hours(poh) per year divided by the first-year annualized failure rate (afr). this is a suitable approximationf

4、or small failure rates, and we intend it to represent a first year mtbf. the annualized failure rate for adrive is derived from time-to-fail data collected during a reliability-demonstration test (rdt). factoryreliability-demonstration tests (frdt) are similar but are performed on drives pulled from

5、 the volumeproduction line. for the purposes of this paper, we assume that any concept that applies to an rdt alsoapplies to an frdt.seagate reliability testsat seagate personal storage group in longmont, colorado, desktop disc drive reliability tests are nor-mally conducted in ovens at 42c ambient

6、temperature to provide accelerated failure rates. in addition,the drives are operated at the highest possible duty cycle (a drives duty cycle is defined by the numberof seeks, reads and writes it performs over a specific time period). we do this to discover as many fail-ure modes as possible during

7、the product development cycle. by fixing any problems we may see at thisstage, we can make sure that our customers wont see the same problems.estimating weibull parameterslets assume we have an rdt with 500 drives, all run for 672 hours at 42c ambient temperature.during this test, further assume tha

8、t we observe three failures (at 12, 133 and 232 hours). thismeans that, of the 500 drives tested, 497 ran the entire test without failing. to analyze and extrapolatefrom the test results, we perform weibull modeling using supersmith software from fulton findings.1specifically, we use the maximum lik

9、elihood method to estimate the weibull-distribution parametersbeta (a shape parameter) and eta (a scale parameter).in tests with five or fewer failures, the beta parameter cannot be well defined by the test data.because such cases are common in drive testing, we analyze the data using a weibayes2app

10、roach.this approach requires that we estimate the beta parameter using historical data. in the desktop-products lab, we are currently assuming that beta = 0.55. this value is based on the manufacturingdata shown in the following table, which includes all desktop products tested prior to march 1999.1

11、. supersmith, fulton findings, winsmith and winsmith weibull are trademarks of fulton findings, 1251 w. sepulveda blvd., #800,torrance, ca 90502, usa2. abernethy, dr. robert b., the new weibull handbook, second edition, published by the author, 1996, chapter 5.intelligencecorporate headquartersscott

12、s valley, california, usa +1-831-438-6550asia/pacific headquarterssingapore +65-488-7200europe, middle east and africa headquartersboulogne-billancourt, france +33 1-41 86 10 00 t e chnol ogy p a p e r from seaga tedesktop drive sitelongmontperaiwuzipooled desktop datadatabase37 rtd, 5 frdt2 rtd, 4

13、frdt1 rtd49 testsmean beta0.5460.6170.3880.552standard deviation of beta0.1760.068n/a0.167the graph below shows the results of both the weibull and weibayes analysis. the solid line in the figurebelow shows weibull beta and eta parameters (beta = 0.443, eta = 69331860) estimated using the maximumlik

14、elihood3(mle) approach on only 3 failures out of 500 drives. as mentioned before, these results are con-sidered less accurate than those of the weibayes method for small failure rates.the results of the weibayes method (with beta = 0.55) are shown as a dashed line in the figure below.because 672 tes

15、t hours at 42c should be a sufficiently long run time for an rdt, we use our internaltest exit confidence level4of 63.2 percent for the weibayes analysis. the weibayes calculations indicate that,at 42c, given a historical beta = 0.55, a reasonable value for eta is 3,787,073 hours.example of weibull

16、and weibayes analysis90 80 70 60 50 40 30 20 10 5 2 1 .5 .2 .1 w/mleweibayes fitobserved weibull fit via mleetabetan/s693318600.443500/49737870730.55wb c=-63.2yr2000mo2d22gfc10100100010000100000 10000001e+071e+081e+09test time at 42c (hours)the next step in the analysis is to convert the value for e

17、ta that was based on tests at 42c to a value thatreflects our specified operational temperature (25c). using the arrhenius model,5an acceleration factor of2.2208 can be used to account for this difference in temperature. therefore, the value for eta at 25c (eta25)is assumed to be equal to the value

18、for eta at 42c (eta42) times 2.2208, or 8,410,332 hours.3. abernethy, dr. robert b., the new weibull handbook, second edition, published by the author, 1996, appendix d.4. earlier in the rdt, a larger confidence level would be used to reflect the uncertainty in weibull parameter estimationdue to the

19、 limited run time.5. nelson, wayne, applied life data analysis, john wiley & sons, 1982.2 c u m u la ti ve p e rc e n t fa il u reapplying the estimated weibull parameters to estimate first-year mtbfusing the temperature-adjusted estimated values of the weibull beta and eta parameters, we can calcul

20、ate thecumulative-percent-failure rate at any time. by subtracting the cumulative-percent-failure rates for two differ-ent times (t1 and t2), and using appropriate values for beta and eta25, we can estimate the percent of drivesthat are likely to fail at 25c during any time interval from t1 to t2.to

21、 estimate the afr for the first year of drive operation in a desktop computer setting, we assume that thedrive is used at a rate of 2,400 power-on-hours (poh) per customer year. in addition, we assume that drivesare subjected to a 24-poh integration period by the device manufacturer. because any dri

22、ves that fail duringthis period are returned to seagate and are not shipped to the end-user, they are not counted in the first yearafr and mtbf.based on these assumptions (100% duty cycle, eta25 = 8,410,332 hours, beta = 0.55, and 2,400 poh peryear) the percent failure rate in the first customer yea

23、r after integration can be calculated as the percent fail-ure rate between 24 hours (t1) and 2,424 hours (t2). the results of this calculation are shown in the tablebelow, which derives a first-year mtbf from the rdt data.input area:weibull shape factor (beta):weibull scale factor (eta):2,400 hours

24、per year0.558,410,332p(fail), 0 to 2,424 poh per year:1.123%p(fail), 0 to 24 hours:first-year afrpoh per year:first-year aft:first-year weibull mtbf 0.089%= 1.0338%(before rounding)2,400 0.010338= 232,140accounting for actual user conditionsthe calculations above suggest that if a customer were to u

25、se our drive at 25c and 2,400 poh per year, theexpected customer mtbf in the first year would be 232,140. however, these conditions may not always applyto the consumer electronics environment. for example, in some consumer devices, the drive may be poweredon almost 100 percent of the time and yearly

26、 usage rates may be much higher than 2,400 poh. in otherdevices, such as video game players, the poh per year may be relatively low. the following section describeshow we can adjust the calculated mtbf so that it applies to various usage levels, duty cycles and ambienttemperatures.usage levelsadjust

27、ed mtbf as function of expected poh per yearto account for variation in mtbf due todifferent levels of usage, we may use themtbf adjustment curve shown at right.for example, to adjust an mtbf from2,400 poh per year to a maximum usagerate of 8,760 poh per year, the mtbfwould be increased by 1.8 times

28、.conversely, for low-usage environments, asin some video games, the mtbf may bedecreased by as much as a factor of two.2.001.501.000.500.00expected poh per year3 49 2 11 28 17 64 24 00 30 36 36 72 43 08 49 44 55 80 62 16 68 52 74 88 81 24 87 60 m t b f s p e c . m u lt ip li e rtemperaturenext lets

29、look at the effects of elevated operating temperature. the same arrhenius model that we used todevelop an acceleration factor may also be used to generate an mtbf temperature derating-factor (df) curve.the following table shows the decrease in first-year mtbf (at 100% duty cycle) as ambient temperat

30、ureincreases above 25c.temp (c)25263034384246505458626670acceleration factor1.00001.05071.27631.54251.85522.22082.64653.14013.71034.36645.11865.97796.9562derating factor1.000.950.780.650.540.450.380.320.270.14adjusted mtbf232,140220,533181,069150,891125,356104,46388,12374,28462,67853,392

31、46,42839,46432,500from the table above, it is clear that as the ambient temperature rises, the derating factor and the adjustedmtbf become significantly smaller. for example, at 42c, we find the 2.2208 acceleration factor referred topreviously in this analysis. its reciprocal, 0.45, is the df value,

32、 which indicates that the mtbf at 42c is lessthan half as long as the mtbf at 25c.duty cyclemost disc drives in pcs are operated at duty cycles of 20 percent to 30 percent. however, consumer electronicsdevices may have lower or higher duty cycles. seagate has measured average daily data-transfer rat

33、es on existingconsumer electronics devices and found duty cycles as low as 2.5 percent.to compare the effect of a 2.5 percent duty cycle with that of a 100 percent duty cycle (used in rtd test-ing), we can examine the effect of duty-cycle-dependent components in the drive relative to other compo-nen

34、ts. the number of duty-cycle-dependent components in a hard disc drive is proportional to the number ofdiscs in the drive. the relationship between disc count and afr is shown in the following figure. in this graph,the area below the dotted line indicates the “base” or nonduty-cycle-dependent failur

35、e rate for a hypotheticaldrive with no discs (or a drive that is not reading, writing or seeking). the solid line indicates estimated failurerates as a function of the number of discs present.effect of disc count on total and base afr1.0total afr0.2base afr40012disc count (4 is max

36、)34 n o rm a li ze d a frfrom the previous graph it is clear that reducing a drives duty cycle reduces only the duty-cycle-dependentfailures (those between the dotted and solid line). using the ratio between duty-cycle-dependent and totalfailures, we can estimate the effect of duty cycle on afr. for

37、 example, consider a four-disc drive with a totalafr of 1.4 percent and a base afr of 0.6 percent. reducing the duty cycle would reduce the failures by thefactor (1.4 0.6)/1.4 = 57 percent. in accounting for reduced duty cycle on a four-disc drive, therefore, wecan only reduce 57 percent of the fail

38、ures; the remainder are treated as independent of duty cycle.the resulting mtbf multipliers for drives with different numbers of discs are shown in the following figure.mtbf multiplier vs duty cycle and platter count2.201-disk minimumcapacity mtbf2.001.801.601.401.201.00100%90%80%70%60%50%40%30%20%1

39、0%duty cyclemultiplier2-disk mtbfmultiplier3-disk mtbfmultiplier4-disk maximumcapacity mtbfmultipliercombining multiple factorsto continue the analysis, we combine a range of duty cycles and temperature derating factors (df) for severaldifferent drives. the figure on the left shows mtbf multipliers

40、at a variety of duty cycles and temperatures fora high-capacity, 4-disc drive. the figure on the right shows the same multipliers as applied to a drive with onlyone disc. as shown in these figures, depending on the duty cycle and the ambient temperature of the drive inthe customers pc, the first-yea

41、r effective mtbf may be greater than, equal to, or less than the mtbf that weestimate based on in-house testing. for the one-disc drive, the effects of varying duty cycles are less signifi-cant and the mtbf multipliers tend to be significantly smaller.2.502.001.501.000.500.00thermal derating for a r

42、ange of duty cycles(for maximum capacity, 4-disc drive)df 100% duty cycledf 30% duty cycledf 20% duty cycledf 10% duty cycledf 5% duty cycledf 1% duty cycle1.401.201.000.800.600.400.200.00thermal derating for a range of duty cycles(for minimum capacity, 1-disc drive)df 100% duty cycledf 30% duty cyc

43、ledf 20% duty cycledf 10% duty cycledf 5% duty cycledf 1% duty cycle263034384246505458626670ambient temp c263034384246505458626670ambient temp c5 m t b f m u lt ip li e r m t b f m u lt ip li e r (d f) m t b f m u lt ip li e r (d f)reliability after the first yearthe weibull distribution of time-to-

44、failure, with a beta less than one, is a distribution of decreasing failureprobability over time. because of this, mtbf values for a drives first year in the field are likely to be lowerthan for subsequent years. what would the failure rate or mtbf look like if averaged over the entire usefullifetim

45、e of the drive? three possible methods for estimating reliability over a drive lifetime are listed below: we could use the weibull beta, eta25 analysis to estimate failures after the first year. however, thiswould require extending the rdt test results up to an order of magnitude beyond the duration

46、 of thetest. this would not be a very conservative practice. we could use data from the seagate warranty-return database, from which we may estimate the returnsin the second and third years relative to the number of drives returned in the first year. this data is onlyapplicable to the first three ye

47、ars, which is the limit of most current seagate desktop-drive warranties,but it has the advantage of being based on only seagate desktop products. we could assume a model that would “flatline,” or maintain a constant failure rate after the end of thefirst year. in other words, we could assume that a

48、fter the first year, all yearly failure rates would all beequal to the second-year failure rate. since failure rates would, if anything, decline over time, this wouldbe a conservative estimate of averaged mtbf for the life of the drive.these models are compared in the table below.model:yearcumulativ

49、eyearlyweibullcumulativewarranty data (oem only)yearlycumulativeflatline modelyearlycumulative1power-on hoursfailure ratefailure rate2,4001.20%1.20%failure ratefailure rate1.20%1.20%failure ratefailure rate1.20%1.20%623456789104,8007,2009,60012,00014,40016,80019,20021,60024,0000.55%0.43%0.37%0.33%0.

50、30%0.28%0.26%0.24%0.23%1.75%2.18%2.55%2.88%3.18%3.46%3.72%3.96%4.19%0.78%0.39%1.98%2.37%0.55%0.55%0.55%0.55%0.55%0.55%0.55%0.55%0.55%1.75%2.30%2.86%3.41%3.96%4.51%5.06%5.62%6.17%to further illustrate the differences between these models, lets look at the cumulative percent failure rates forthe three

51、 different models, each assuming a 200,000-hour first-year mtbf:cumulative yearly failure rate by customer year,weibull and flatline models compared to warranty returns7.00%weibull analysis6.00%5.00%4.00%3.00%2.00%1.00%0.00%“flatline” modelmodel based on oem drive warranty data12345678910customer ye

52、aras the graph above shows, the “flatline” model is less aggressive than the pure weibull model, and comesclose to the model based on seagate warranty returns in the first three years. for simplicity, and to providea conservative estimate, we have chosen to use the flatline model for our calculations.using the flatline model, the results of lifetime-averaged mtbf compared to first-year mtbf may be summarizedas follows:average values for years 1 through 3:failures per yearmtbfimprovement over noncorrected mtbf (232,140 hours)average values for years 1 through 5