Data Centers Using Voltage Level Extrapolation and Chebyshev’s Inequality

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This paper will be published at Ashrae journal. For any questions please contact [email protected].

Dependence of ESD Charge Voltage on Humidity in Data Centers (Part-3 Estimation of ESD-Related Risk in Data Centers Using Voltage Level Extrapolation and Chebyshev’s Inequality) Xu Gao Atieh Talebzadeh Mahdi Moradian Yunan Han

David E. Swenson David Pommerenke

ABSTRACT

This paper is the third paper of a series that investigates the ESD-related voltages and risks in data

center. This paper analyses the risk of damage or upset under the following environmental conditions

. The main purpose of this study is to evaluate the

increase of ESD related upsets or failures caused by reducing the relative humidity from 25% to 8%. The

pattern-walking test, random walking test and the extrapolation method described in (Moradian 2014) are

also used in this paper. As the distribution function of the tribocharging induced voltage is not directly

k ow he hebyshev’s I equ li y is use o predict the upper bound for the probability of ESD-related

failures.

INTRODUCTION

A considerable amount of electric energy is consumed to control the environmental condition for

reliable operation of Information Technology (IT) equipments in data centers. Setting environmental

conditions is part of trade off between energy usage and reliability. At the lower end of humidity, the risk

of ESD induced failures increase. The American Society of Heating Refrigerating and Air Conditioning

Engineers (ASHRAE) has introduced guidelines for the recommended environmental condition shown in

Figure 1. (ASHRAE 2011). Several studies were performed to investigate the effects of humidity and

mailto:[email protected]



temperature on the risk of failures in data centers (Simonic 1981, 1982; Frei 1998; Fayu 2013; Moradian

2014). Using the measured voltage probability distribution functions and extrapolations to higher voltages

it is possible to estimate the risk of ESD problems (Moradian 2014). This method is applied to measured

tribocharging voltage data for different relative humidity (RH) at a temperature of . RH values of

45%, 25% and 8% are selected, Figure 1. The results of this study show that the risk does not increase

strongly if the relative humidity is reduced from 25% to 8%. However, a reduction from 45% RH to 25%

RH leads to strong increases. Further, a more extreme environmental condition of 8% RH at a temperature

of was selected as this combines rather higher absolute humidity with a low RH. The data indicate

that the risk is similar to the condition of The extrapolation is based on the estimation

of the distribution function beyond its measured range. The selection of the distribution function is not

unique causing uncertainties in the estimated probabilities. To provide confidence in the risk estimation an

upper bound of the probability is determined using the hebyshev’s inequ li y

Figure 1 ASHRAE Psychometric Chart. The stars indicate the four environmental conditions in

this study.




PATTERN WALKING TEST AND RANDOM WALKING TEST

The well defined walking pattern is based on the industry standard test method ANSI/ESD STM97.2

(Moradian 2014),. A person walks in a well-defined pattern on a floor sample, wearing a specific type of

shoes under different controlled environmental conditions while the induced electrostatic voltage is being

recorded. The general test setup is shown in Figure 2, and the well-defined walking pattern is shown in

Figure. 3. The person repeats the walking pattern a minimum of 10 times while holding an electrode to

record the static voltage during walking. The person waits for 2 seconds when he reaches the starting point.

The recording time for each walking test is at least 100 seconds. In addition Moradian (Moradian 2014)

introduced a random walking pattern. Here the walking is less controlled, faster and sideways movements

and dragging of shoes is included. While less repeatable, this reflects actual walking better.

Figure 2 Well-defined walking experiment setup (Moradian.al. 2014).




Figure 3 Well-defined walking pattern (Fayu.al. 2013, Moradian.al. 2014).

Table 1 lists the floor and shoe types used in this experimental series. Rubber 1 and Rubber 2 are

conductive, low resistance rubber floors, which we refer to as “ESD l ” he ein The speci ic high-

p essu e l min e l ( PLF) used is high esis nce l , e e ed he ein s “N n-ESD” l Als ,

Vinyl1 and Vinyl2 are low dissipative range floors, which can be considered medium-ESD floors. For each

combination of flooring and footwear, over 100 seconds of walking data (for both pattern walking and

random walking) were recorded at each environmental condition. This leads to more than 66 minutes of

recorded walking data for each environmental condition.

The conductivity of a shoe is a core parameter for its ESD mitigating performance. Researchers have

shown a strong correlation between the shoe-floor resistivity and the charge voltage (Swenson.al.1995; Lim

2000), However, certain wax-like materials have been shown to reduce the tribo-charging strongly,

although they do not exhibit conductive properties. A wide range of popular shoes has been selected for

this investigation. The shoe column includes two low resistance shoes, which served as the ESD shoes in

this experiment. The other shoes are high resistance shoes not considered to have ESD-reducing properties.

Further information about footwear and flooring resistance in relation to ESD protection can be found in

(Gaertner.al.1997; Swenson.al.1995).




Table 1. Floor and Shoe Types

Floor Description Shoes Description

Rubber 1 ESD floor Mid-Range Dissipative

ESD Shoes ESD shoe

Rubber 2 ESD floor Low Range Dissipative

ESD Shoes ESD shoe

Vinyl 1 Medium-ESD floor Deck Shoes 1 Non-ESD shoe

Vinyl 2 Medium-ESD floor Deck Shoes 2 Non-ESD shoe

High Pressure Laminate

(HPLF) Non-ESD floor Deck Shoes 3 Non-ESD shoe

- - Plastic Shoes Non-ESD shoe

- - Leather Dress Shoes Non-ESD shoe

- - Running Shoe Non-ESD shoe

PROBABILITY DENSITY AND CUMULATIVE PROBABILITY

Although each walking tests recorded the voltage for more than 100 seconds , the operator could be

charged to higher voltage if the test would be repeated many times. This probability is estimated by the

method described in (Moradian 2014). It allows to estimate the probability of exceeding risk related voltage

thresholds which have been set to 500V, 4 kV and 8 kV. , Details of the extrapolation method are given in

(Moradian 2014).

The measurement was performed for three different relative humidity conditions, 45%, 25% and 8%,

at a temperature of ( F). Figure 4 shows the probability density curve for the measurement data

getting form the tests for all combinations of floors and shoes in Table 1. The discrete points in Figure 4

were obtained in the following manner. At first, the probabilities of the observing voltage in the each

quantized intervals (100 V) were calculated from the measured time-domain waveform in the pattern

walking test, and then the discrete probability values for each voltage intervals were normalized by the

length of the voltage interval to get the discrete probability density points. According to the extrapolation

method demonstrated in the paper (Moradian 2014), a two-part piecewise function was fitted on these

discrete density points for each environmental condition. The equ i ns i ed p b bili y densi y

unc i n (PDF) e e p essed in Equ i ns , nd he c ndi i ns , nd

, espec ively




Figure 4 Probability density obtained from measurements for all types of floors and all types of

shoe based on the defined pattern walking test.

F , the fitted piecewise PDF is given as

4 1.8

4 6.9

2.30 10 ( ) , 0 600600

( )

2.30 10 ( ) , 600600

vv

p vv

v

(1)

F , the fitted piecewise PDF is given as

4 1.4

4 3.7

1.80 10 ( ) , 0 10001000

( )

1.80 10 ( ) , 10001000

vv

p vv

v

(2)

F , the fitted piecewise PDF is

4 1.1

4 3.7

2.22 10 ( ) , 0 11001100

( )

2.22 10 ( ) , 11001100

vv

p vv

v

(3)




This fitted probability density function allows estimating the probability density for higher voltage. It

should be noted, however, that the fitted function is not unique. The data could suggest other slopes or

more complicated functional behavior. Following the discussion in [reference to the max esd event] and the

methodology of (Simonic 1981, Bodeau 2012, Mardiguian 2009, and another unpublished study performed

by Hewlett-Packard) a two-part piecewise fitted function was used. Thus, it is reasonable to make the

assumption that if the walking voltage in our test was recorded for a very long time, such as a year, the

measured probability distribution will converge to a two-piecewise function. Due to the limited recording

time in the pattern walking test, the measured discrete probability density points do not completely follow

the two-part piecewise distribution, as shown in Figure 4. There are uncertainties in selecting the breaking

points for the two pieces and in the selection of the fitting lines. These uncertainties in fitting process could

cause a difference in estimating the ESD-related risk. For example, in the Figure 4, for the 8% RH

condition, the last three measured discrete probability density point obviously deviate from the fitted line.

A different slope for the second piece of line can be obtained if putting more weight on these three points.

Here the uniform weights are used for all discrete points in the fitting method. The uncertainties associated

with this fitting method results from the limited information in the measured data. Although for each test,

over 100 seconds time-domain waveform was recorded, the voltage recording time is not enough to

illustrate the accurate distribution of the walking voltage. This extrapolation method provides us an

approach to approximately estimate the probability distribution function from limited information.

The pattern walking test was also done under 8% RH at temperature The c mp is n he

p b bili y densi y nd s sh n in Figu e is sh n in Figu e h he

envi nmen c ndi i n , nd h ve simil p b bili y densi y dis ibu i n

The similar analysis was performed on the random walking test as well. Figure 6 show the probability

density of random walking he h ee envi nmen c ndi i ns, , nd Similar

with the results for pattern walking, the probability density curves for 25% and 8% are close.




Figure 5 Comparison of probability density for 8% RH at and 38 C (all types of floors and

all types of shoe, pattern walking test).

Figure 6 Probability density for 45%, 25% and 8% RH at (all types of floors and all types

of shoe, random walking test).




In order to evaluate the risk of ESD-related failure or upset, it is necessary to obtain the probability of

observing a voltage exceeding a certain voltage value. This probability can be calculated by performing

integration on the probability distribution function, which is the cumulative probability as given by

Equation 4.

0

( 0) ( ) , 0 0V

P V V p v dv for V

(4)

Figure 7 shows the cumulative probability curve calculated by integrating the fitted probability density

function in Figure 4 and Figure 5 for the pattern and random walking voltage under three environmental

conditions. Here the 10000 V is used as the up bound for the integral instead of infinite. From Figure 7, it

can be seen that the integral of the fitted probability density function over the whole voltage range (from 0

V to 10000 V) is approximately equal to 1 (in the Figure 7, it shows that P(V>=1) is close to 1), which

satisfy one of the requirement for the probability density function. Due to the uncertainty within this

extrapolation method and the limited information getting form the measured data, the estimation of the

cumulative probability might not be accurate in the absolute sense. This estimation method, however, is

still reasonable to be applied for evaluating the change of ESD risk when the environmental condition is

changed in the relative sense. The similar uncertainty in extrapolation method was also analyzed and

reported in paper (Bodeau 2012). From Figure 7, it can be seen that the random walking has larger

probability to reach the high voltage level than the pattern walking. This is because in the random walking

test, people walks with many activities but without standing during the recoding of the walking voltage,

while in the pattern walking test, people stands for 2 seconds when reached the start points, as explained in

the previous section. In reality, people will in most case pause (standing) for a moment before they touch

something. Therefore, we believe that the pattern walking data base is the better base for the ESD-related

risk estimation.




Figure 7 Cumulative Probability for 45%, 25% and 8% RH at (all types of floors and all

types of shoe, pattern walking test).

X FACTOR

X factor is used to evaluate the relative effect due to the environmental change on the failure rate. It

informs about the risk increase if a data center changes its environmental conditions but maintains the same

flooring and footwear combination and user activity. The X factor used in this paper is defined as

P( 0) under environmental condition A

X factorP( 0) under environmental condition B

V V

V V

(5)

where P(V>=V0) is the cumulative probability for voltage exceeding threshold voltage V0. In this paper,

three threshold (500 V, 4 kV, and 8 kV) voltage values are used. The 4 kV and 8 kV thresholds were

selected based on the I IEC 61000-4-2 (2008) test levels. The 500 V threshold was selected as an assumed

robustness during service of IT equipment (Moradian 2014). During service, shielding panels maybe

removed, the operator may handle hard drives or other plug-in devices.




Table 2 lists the cumulative probability of the pattern walking voltage with all types of floors and all

types of shoes under the three different environmental conditions. According to these cumulative

probability values, the X factors were calculated using the Equation 5. The results of X factor are listed in

Table 3. The X factor shows the effect of environmental condition change on the probability of voltage

exceeding a threshold voltage. For example, as shown in Table 3, the probability of voltage exceeding 4 kV

is become 224,000 times higher if the relative humidity changes from 45% to 25% at 2 C, while this

probability only goes up by 3.6 times if the relative humidity changes from 25% to 8% at 27 C. Therefore,

from Table 3, it clearly indicate that there is a strong effect on the cumulative probability when relative

humidity changes from 45% to 25% while if the relative humidity is changed from 25% to 8 %, the effect

on cumulative probability is much weaker. This conclusion can also been derive from Figure 1, in which

the probability density curve of 25% RH are very close to the curve of 8% RH, but far away from the curve

of 45%. These results indicate that a data center might potentially save lots of energy by reducing the

relative humidity from 25% to 8%, but without strongly increasing the probability of ESD-related failure.

To determine if a cumulative probability value will be risky or not for data center, the threshold

probabilities are given in paper (Moradian 2014), as shown in Table 4. The derivation of these threshold

probabilities is introduced in paper (Moradian 2014). In this paper, the upper threshold probabilities in

Table 4 are adopted. The cumulative probability values which are larger than the corresponding threshold

probability will be considered as high risk. In the following tables for cumulative probability, the high risk

values are indicated with grey while low risk is indicated by white.

Table 2. Cumulative Probability P(V>V0) with All Floors and All Shoes,

Pattern Walking

Environmental Condition V0 = 500 V V0 = 4 kV V0 = 8 kV

45% RH at 0.19% 1.36e-6% 2.35e-8%

25% RH at 3.79% 0.03% 0.0048%

8% RH at 11.0% 0.11% 0.017%

To illustrate the meaning let us select the example of 0.11% indicated by bold font. If a person would

walk in a data center having any of the shoes included in the study on any of the floors included in the




study at 8% RH and 27C the voltage on his body would exceed 4000V for 0.11% of the time. If the

person randomly touches servers he would have a 1 to 1000 chance to touch a server at a level of >

4000V. Here 4000V is used as limit, as it is one test limit in the IEC 61000-4-2 test that is used to

ensure ESD robustness of electronic equipment.

Table 3. X Factor with All Floors and All Shoes, Pattern Walking

Condition Change V0 = 500 V V0 = 4 kV V0 = 8 kV

A: 25% RH at 27

B: 45% RH at 27

o

o

C

C 19.6 2.24e5 2.04e5

A: 8% RH at 27

B: 25% RH at 27

o

o

C

C 2.9 3.6 3.6

Table 4. Threshold Probabilities for different ESD Threshold Levels

Threshold Voltages

V0 = 500 V V0 = 4 kV V0 = 8 kV

Upper threshold probability 0.003% 0.1% 0.005%

Lower threshold probability - 0.01% 0.002%

The X factors in Table 3 are getting from the analysis to the all data set (all the combinations of

different types of floors and shoes in Table 1) to obtain the overall and general effect of the relative

humidity change to the ESD-related risk. To further evaluate the effect of relative humidity on different

types of data center, the same analyses were performed for the following three categories with selected data

sets:

Non-ESD Floors and Non-ESD shoes

ESD Floors and Non-ESD shoes

ESD Floors and ESD shoes

Table 5 and Table 6 list the cumulative probability and the X factors with data set of Non-ESD floors

and Non-ESD shoes, which is the worst category for ESD-related risk among the three categories above.




As shown in Table 6, similar observation is obtained for the X factor values with the X factor values in

Table 3 for all floors and all shoes. The c v lues C e much sm lle h n

v lues C.

Table 5. Cumulative Probability P(V>V0) with Non-ESD Floors and Non-ESD Shoes,

Pattern Walking


45% RH at 4.7% 0.013% 0.0018%

25% RH at 23% 1.13% 0.27%

8% RH at 48.8% 2.28% 0.43%

Table 6. X Factor with Non-ESD Floors and Non-ESD Shoes,

Pattern Walking


A: 25% RH at 27

B: 45% RH at 27

o

o

C

C 4.8 87 153.7

A: 8% RH at 27

B: 25% RH at 27

o

o

C

C 2.1 2.0 1.6

Table 7 and Table 8 show the cumulative probability results and X factors for the category of ESD

floors and non-ESD shoes. In this case, because the floor types are ESD floors, the probability of voltage

exceeding 4 kV and 8 kV are very low for all three environmental conditions. Although in this category,

the X factors for 25% to 8% R C show large values (33.3 for 4 kV and 14.2 for 8 kV), the large X

factor does not show a risk because the very low probability values for 4 kV and 8 kV.

Table 7. Cumulative Probability P(V>V0) with ESD Floors and Non-ESD Shoes,

Pattern Walking


45% RH at 0.15% 7.44e-9% 1.17e-11%

25% RH at 5.8% 7.14e-9% 2.12e-8%

8% RH at 12.2% 2.38e-4% 3.01e-7%




Table 8. X Factor with ESD Floors and Non-ESD Shoes,

Pattern Walking


A: 25% RH at 27

B: 45% RH at 27

o

o

C

C 37.8 958 1807

A: 8% RH at 27

B: 25% RH at 27

o

o

C

C 2.1 33.3 14.2

Table 9 and Table 10 show the cumulative probability results and X factors for the category of ESD

floors and ESD shoes. The cumulative probability values under all the environment conditions are very low

in Table 9. There is no risk for 4 kV and 8 kV under all three relative humidity. The X factor values in this

category do not contain too much meaning although larger X factor values get in Table 10, because there is

no ESD-related risk anyway for 4 kV and 8 kV threshold voltages.

Table 9. Cumulative Probability P(V>V0) with ESD Floors and ESD Shoes,

Pattern Walking


45% RH at 1.47e-9% 1.69e-17% 3.82e-20%

25% RH at 9.74e-3% 3.05e-7% 9.61e-9%

8% RH at 3.76e-4% 6.80e-10% 8.30e-12%

Table 10. X Factor with ESD Floors and ESD Shoes,

Pattern Walking


A: 25% RH at 27

B: 45% RH at 27

o

o

C

C 6.6e6 1.8e10 2.5e11

A: 8% RH at 27

B: 25% RH at 27

o

o

C

C 0.03 0.002 8.6e-4




Table 11 and Table 12 show the cumulative probability results and X factors for random walking

voltage with all combinations of floors and shoes. For the random walking, the similar phenomenon was

bse ved he c i h p e n l ing The c ch nging m C

is small. Although the Table 11 indicates that the risks are all high for random walking, the random

walking voltage, however, overestimate the voltage level, because people will in most cases pause for a

moment before they touch something.

Table 11. Cumulative Probability P(V>V0) with All Floors and All Shoes,

Random Walking


45% RH at 3.1% 0.017% 0.002%

25% RH at 25% 1.17% 0.3%

8% RH at 48.7% 2.07% 0.39%

Table 12. X Factor with All Floors and All Shoes, Random Walking


A: 25% RH at 27

B: 45% RH at 27

o

o

C

C 8.3 67.5 130.0

A: 8% RH at 27

B: 25% RH at 27

o

o

C

C 1.9 1.8 1.3

ESTIMATION FOR UPPER BOUND OF CUMULATIVE PROBALIBITY USING CHEBYSHEV’S

INEQUALITY

As discussed above, there are several uncertainties when using two-part piecewise fitting method to

extrapolate the probability density distribution. The reason is that only partial information about the

probability density distribution is obtained from the measured data. This uncertainty of extrapolation

method cause the cumulative probability results can be different when different extrapolation lines were

selected to fitting the measured discrete probability density points. This is the limitation of this




extrapolation method. To mitigate this limitation to some extent, a method to estimate the upper bound of

he cumul ive p b bili y is p p sed by using he hebyshev’s nequ li y Wi h his es im ed uppe

bound, we could draw the conclusion that although the estimated cumulative probability using the

extrapolation method has some uncertainty in its result, the cumulative probability will not exceed the

estimated upper bound.

Acc ding hebyshev’s nequ li y, nd m v i ble i h ini e me n v lue μ nd ini e v i nce

σ2,

2

2( )P x a

a

(6)

where a is a positive number, and P() means probability.

The Equation 6 can be written as

2

2( )P x a x a

a

(7)

Since in our case, the random variable is the absolute voltage value of human during the walking, the

random variable is non-negative. When 0u a , the Equation 7 can be write as

2

2( ) , for P x a a

a

(8)

Let b a , then

2

2( ) , for 2

( )P x b b

b

(9)

It can be seen that the left side of Equation 9 has the same form for the cumulative probability. The

hebyshev’s inequ li y indic es h n m e h he dis ibu i n unc i n is, s l ng s he me n nd

the variance are known, an upper bound for the cumulative probability can be given by Equation 9.

Although in our case, the mean value and the variance can only be estimated with the limited measured

data, the Equation 9 can be also used to predict the upper bound for the cumulative probability with the

mean value and the variance calculated from the measured data. The Figure 8 shows the predict upper

bounds of the cumulative probability and the predicted cumulative probability using the extrapolation




method for the data set with all types of floors and shoes. It is seen that the calculated cumulative

probability curves for different environmental conditions are below the predicted upper bound using the

hebyshev’s nequ li y, hich is in e pec i n The Figu e 9 shows the predict upper bounds of the

cumulative probability and the predicted cumulative probability using the extrapolation method for the data

set with non-ESD floors and non-ESD shoes. In this case, the calculated cumulated probability curves for

25% RH and 8% RH are close to their predict upper bounds, but still not exceeding the predict upper

bounds. From Figure 8 and Figure 9, it can be seen that the upper bound curves for 25% RH and 8% RH

are close relative to the curves for 45% and 25%, which indicate that the effect of relative humidity change

from 25% to 8% at C on ESD-related risk is not very strong in another perspective.

Figure 8 Estimated upper bound of cumulative probability for data set with all types of floors

and shoes.




Figure 9 Estimated upper bound of Cumulative Probability for data set with Non-ESD floors

and Non-ESD shoes.

Figure 10 shows the predict upper bounds of the cumulative probability and the predicted cumulative

probability using the extrapolation method for the data set with ESD floors and ESD shoes. In this case, as

shown in Table 9, there is no risk for 4 kV and 8 kV thresholds for all the three relative humidity at

empe u e C, which is estimated from the results using the extrapolation method. The upper bounds of

cumulative probability estimated by Chebyshev Inequality are shown in Table 13. It can be seen from

Table 13 that even for the upper bound values estimated by the Chebyshev Inequality, the probability

values are below the threshold probabilities for risk of 4 kV and 8 kV, which ensure that there is no risk for

the case with ESD floors and ESD shoes under environmental conditions of 45%, 25% and 8% RH at

temperature 2 C.




Figure 10 Estimated upper bound of Cumulative Probability for data set with ESD floors and

ESD shoes.

Table 13. The upper bound of Cumulative Probability P(V>V0) with ESD Floors and

ESD Shoes, Pattern Walking


45% RH at 0.06% 9.08e-4% 2.26e-4%

25% RH at 0.9% 0.01% 0.003%

8% RH at 0.5% 0.006% 0.002%

CONCLUSION

The effect of reducing the relative humidity at on the increasing of the ESD-related risk in data

center is investigated in this paper. From the results getting from this study, the X factor for reducing the

relative humidity from 25% to 8% at is about 1 to 3, which mean the relative humidity change from

25% to 8% will increase the probability of ESD-related failure in data center by 1-3 times. While the X

factor for reducing the relative humidity from 45% to 25% at is much larger than the value for




reducing the relative humidity from 25% to 8%. The small X factor value for relative humidity reducing

from 25% to 8% indicates that a data center might potentially save lots of energy by reducing the relative

humidity from 25% to 8%, but without strongly increasing the probability of ESD-related failure.

The contents presented in this paper is a continuous work of the paper (Moradian 2014), in which the

extrapolation method was used to estimated the probability of ESD-related failure. This accuracy of

extrapolation method, however, was limited by several uncertainties. To mitigate this problem to some

extent, in this paper, a method to predict the upper bond for the probability ESD-related failure using

Chebyshev’s nequ li y is p p sed

ACKNOWLEDGMENTS

We thank ASHRAE TC 9.9 for supporting this work.

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Data Centers Using Voltage Level Extrapolation and Chebyshev’s Inequality

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