MPXM2102AS datasheet(10/670 Pages) MOTOROLA

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frequencies of an event to established confidence intervals.

The relationship between failure rate and the chi-square

distribution is as follows:

L1 +

x2 a, d.f.

Where:

λ =

failure rate

lower one side confidence limit

χ2 =

chi–square function

α =

risk, (1–confidence level)

d.f.

degrees of freedom = 2 (r + 1)

number of failures

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

1.833

4.605

4.045

7.779

6.211

10.645

8.351

13.362

10.473

15.987

12.584

18.549

14.685

21.064

16.780

23.542

18.868

25.989

20.951

28.412

23.031

30.813

25.106

33.196

27.179

35.563

CUMULATIVE DEVICE HOURS, [t]

105

108

107

109

104

100

0.1

1,000

106

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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