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MPXM2102AST1 Datasheet(PDF) 10 Page - Motorola, Inc |
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MPXM2102AST1 Datasheet(HTML) 10 Page - Motorola, Inc |
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10 / 670 page  1–4 Motorola Sensor Device Data www.motorola.com/semiconductors frequencies of an event to established confidence intervals. The relationship between failure rate and the chi-square distribution is as follows: l L1 + x2 a, d.f. 2t Where: λ = failure rate L1 = lower one side confidence limit χ2 = chi–square function α = risk, (1–confidence level) d.f. = degrees of freedom = 2 (r + 1) r = number of failures t = device hours Chi-square values for 60% and 90% confidence intervals for up to 12 failures is shown in Table 1. As indicated by the table, when no failures occur, an estimate for the chi-square distribution interval is obtainable. This interval estimate can then be used to solve for the failure rate, as shown in the equation above. If no failures occur, the failure rate estimate is solely a function of the accumulated device hours. This estimate can vary dramati- cally as additional device hours are accumulated. As a means of showing the influence of device hours with no failures on the failure rate value, a graphical representa- tion of cumulative device hours versus the failure rate measured in FITs is shown in Figure 1. A descriptive example between two potential vendors best serves to demonstrate the point. If vendor A is introducing a new product and they have put a total of 1,000 parts on a high temperature storage test for 500 hours each, their corresponding cumulative device hours would be 500,000 device hours. Vendor B has been in the business for several years on the same product and has tested a total of 500,000 parts for 10 hours each to the same conditions as part of an in-line burn-in test for a total of 5,000,000 device hours. The corresponding failure rate for a 60% confidence level for vendor A would be 1,833 FITs, vendor B would have a FIT rate of 183 FITs. Table 1. Chi-Square Table Chi-Square Distribution Function 60% Confidence Level 90% Confidence Level No. Fails χ2 Quantity No. Fails χ2 Quantity 0 1.833 0 4.605 1 4.045 1 7.779 2 6.211 2 10.645 3 8.351 3 13.362 4 10.473 4 15.987 5 12.584 5 18.549 6 14.685 6 21.064 7 16.780 7 23.542 8 18.868 8 25.989 9 20.951 9 28.412 10 23.031 10 30.813 11 25.106 11 33.196 12 27.179 12 35.563 CUMULATIVE DEVICE HOURS, [t] 105 108 107 109 104 100 10 1 0.1 1,000 106 1 10 100 1,000 104 105 106 107 108 109 Figure 1. Depiction of the influence on the cumulative device hours with no failures and the Failure Rate as measured in FITs. Freescale Semiconductor, Inc. For More Information On This Product, Go to: www.freescale.com |
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