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Dennis S/Methodologv for statist 'nwcmOD()LOGY FOR STATISTICAL

CONTROL OF THE ANECHOIC CHAMBER

FIELD GENERATION SYSTEM

Dennis S. Friday

National Bureau of Standards

U.S. Department of Commerce

Boulder, Colorado 80303

January 1986

RESEARCH INFORMATION CENTER 9 , j NBSIR 85-3033

> LL^

METHODOLOGY FOR STATISTICAL n

lr

CONTROL OF THE ANECHOIC CHAMBER

FIELD GENERATION SYSTEM

Electromagnetic Fields Division

Center for Electronics and Electrical Engineering

National Engineering Laboratory

National Bureau of Standards

Boulder, Colorado 80303

January 1986

U.S. DEPARTMENT OF COMMERCE, Malcolm Baldrige, Secretary

Dennis S. Friday

NATIONAL BUREAU OF STANDARDS, Ernest Ambler, Director

CONTENTS

Page

1. Introduction 1 2. Related microwave methodology 2 3. General considerations 3 4. Control charts for the M and S parameters 4

4.1 Location control charts (M) 4

4.2 Dispersion control charts 7 4.3 S Location and dispersion charts

5. Discussion of P net charts 8

5.1 A "rough" control chart for Pnet -location 9

6. Conclusions and comments 11

7. References 15

i i i

METHODOLOGY FOR STATISTICAL CONTROL

OF THE ANECHOIC CHAMBER FIELD GENERATION SYSTEM

Dennis S. Friday

The microwave anechoic chamber is a National Bureau of Standards

laboratory facility in which standard electromagnet!

- c fields are generated. The chamber enables special measurements and

electromagnetic compatibility tests to be conducted on antennas

and other devices. This paper is concerned with methodology for

assuring that the standard field patterns generated in the chamber

are repeatable. Procedures are proposed for developing a data

base from measurements obtained by placing the system, which

generates the fields, in certain relevant reference

configurations. Methodology is presented for developing

statistical control charts to monitor both the location and the

scale parameters of these data over time.

Key words: anechoic chamber; control charts; electromagnetic

fields; measurement assurance; standard fields; statistical

control

.

1. Introduction

The microwave anechoic chamber is a National Rureau of Standards (NBS)

laboratory facility in which standard electromagnetic fields are generated.

Extremely low reflection levels in the center of the chamber enable

specialized measurements and EMI or EMC tests to be conducted on antennas or other electronic devices. This paper is concerned with methodology for

assuring that the standard electromagnetic field patterns generated in the

chamber are consistent over time. Procedures will be developed to monitor the

system which generates the fields. Check-standard type historical data are obtained by placing the system in certain reference configurations and

measuring relevant parameters. We will refer to such procedures as "self

tests." These measurements will form the data base from which statistical

control is established.

Several control chart procedures are presented for maintaining

statistical control of the test system. This methodology will provide

statistical limits within which future anechoic chamber self test data should

fall. A systematic departure from these limits indicates that the system is

out of control and must be dealt with accordingly.

1
2. Related microwave methodology

The theory for the measurements upon which this paper is based is

presented in a paper by Kanda [1]. A brief summary will be sufficient for our purposes. Let Pj denote the power incident on the transmitting antenna and P

R be the power reflected. Then:

P R

S 34 .

—

1

CL.

1 | 1

CNI

S

1 3 (1 - M2

)

1

S

p

2 r2

l b 24 (1 -

1 r2 I 2

)

(la)

(lb)

where Pi and P 2 are respective powers at ports 1 and 2 of a directional

coupler, and ri and r 2 are the correspondi ng reflection coefficients (into the

power meters). The S^-'s are scattering parameters for ports i and j (port 4

is the input to the transmitting antenna and port 3 the output of the

transmitter). See [1,2] for details. The quantities ei and e 2 are known to

be near unity in magnitude (in general <1 percent error). The net power

delivered to the transmitting antenna is given by P Ret = Pj - P^ and is a crucial measurement for determining on-axis field intensity. Unfortunately,

practical constraints permit only one determination of P net in a self test.

P ne t» however, is dependent on values of the scattering parameters and it is

possible to make repeated measurements of these in each test.

We introduce the following notation. Let

and

M =

s i 3 S 34

S = |S 24 |.

M is the scattering ratio in the matched load equation

(2a)

(2b)

( 3 )

(P 4 is the power at port 4, see [2]) and S is the scattering coefficient

which (given M) is obtained from the shorted termination equation.

2
where £3 and £4 are very close to unity.

Control chart procedures will be developed for P net , M, and S. The power

P net is monitored because of its basic relationship to field strength.

Parameters M and S are monitored not only because of their influence on P ne ^ and the possibility of repeated measurements for each self test, but for

engineering reasons. The nature of any unexpected changes in M and in S can

be used for diagnostic information and provide clues to the reasons for system

malfunction

.

3 . General considerations

No control chart procedure can be considered appropriate for a given

application until sufficient data have been obtained to validate the

assumptions on which the chart is based. The methods proposed herein are based on a careful study of the system and its theory but not on test data.

Only one preliminary measurement was possible at the time of this writing. It

is therefore possible that as the data base for this system is developed, some

of these procedures will have to be modified or extended. As more is learned

about the system, procedures will be "tuned" appropriately. The methods we present, however, provide a good basis from which to begin.

Frequency and frequency band considerations will be not be addressed

directly at this stage of development. A single important central frequency

should be chosen initially and used for these tests. The procedures will

apply to any single frequency. If possible, three or five equally spaced

frequencies covering the band of interest should be monitored. Clearly, the

practical consideration of system downtime for these tests will be a limiting

factor. The system must serve its primary function of test and calibration.

The parameters M and S are defined to be the unsquared magnitudes since

they are likely to be less skewed than M

2

, S

2

, etc. This is conjecture,

however, until sufficient data are available. It may be necessary to choose

some other function of M or S for improved control.

3
Given these considerations and reservations we now propose some control

chart procedures. To illustrate the methodology we will initially discuss

only the M parameter.

4. Control charts for the M and S parameters

If the system is functioning properly, the statistical laws governing the

fluctuations in the M parameter will not change over time. In particular the

first two moments E(M) and V(M), the theoretical mean and variance,

respectively, will be constant over time. We will develop control charts to

monitor both of these quantities based on measures of location and dispersion.

4.1 Location control charts (M)

Assume that k repetitions of the measurement sequence for determination

of M are done in each self test of the system. If possible, a good compromise

is k=10. This would result in a confidence interval about 15 to 20 percent

larger than the limiting interval (as k-*»). About six or seven repetitions

should be considered minimum since the size of the confidence region increases

rapidly below this value. It is best to choose a reasonable k then stay with

it for all the tests. It will be assumed that k is constant here. If it

changes, however, the procedure can be generalized.

Let n denote the number of self tests conducted up to the current time;

i.e., M(i,j); i=l,...,k; j=l,...,n is the ith measurement of M in the jth self

test of the system.

M(l,l)

M ( k , 1

)

v

n different tests

Given the data compute:

M(l,n)

M(k,n)

repeated measurements

of M in each test

1 kv

l M(1,j)

i =1

(self test averages) (5a)

n (pooled average) (5b)

4
1 (6a)

kl

i =1

(pooled variance). (6b)

Then the control chart for the location of the M parameter is constructed by

pi otti ng

freedom, and subscript p is the control level chosen for the chart. The value

(1-p) is commonly known as the type 1 error level associated with the chart.

Tables in references [2] and [3] give the t values for p

= 0.95 and p = 0.99

for selected degrees of freedom. It is possible to have two sets of limits,

an inner "warning limit" and an outer "action limit."

An illustration of how the t statistic is obtained is illustrated in

figure 1.

*Since we use S for one of the parameters monitored we use the symbol 0 for

standard deviation. This is common in statistical literature since it is a measure of dispersion.

M. vs j=l

J

The upper and lower control limits respectively are

where t

p is a percentage point of a t distribution with n(k-l) degrees of

Figure 1: Illustration of how P and t p are related.

5
The p is the probability that the M.'s will fall within the limits if the

J process is in control and the limits are centered so that half of the error probability is allocated to each tail. The underlying theory is described in

most elementary statistical texts and will not be repeated here.

A graphical illustration of an M-location chart is given in figure 2.

j

Figure 2: Illustration of an M-Location Chart

All three lines shift (since M shifts) for each new set of observations (but

less as more tests are done). If sample sizes must be different for each test

then the formula

D2 =

i M

(k r

D

lo-i

k .-n

J

D2

J

( 7 )

replaces the previous D

2 where kj is the size of the sample for the jth test

n (the number of measurements of M). The degrees of freedom are then ( J k.-n)

i=l J for finding the t

p value. J

6
4.2 Dispersion control charts (M)

These charts monitor the short term precision of the measurements of M.

The points plotted on the control chart are the D-'s (see eq (6)) (assuming k

is the same for each test). If k is different, use the D defined in eq (7).

Since we are only concerned about increases in variation we need only

have an upper control limit. This is found by using the F tables which can be

found in references [3] and [4] or in any standard statistics text. These two

references provide a complementary set of degrees of freedom. Let the limit

be

D /F (k-1, n (k-1)

)

P

where D is defined previously, p is the error probability, and (k-1) and

(n(k-l) ) are the degrees of freedom used in the F Tables.

The M-dispersion chart is illustrated in figure 3.

Figure 3: Illustration of M-Dispersion Chart

7
Again, the control limits shift with each new observati on--l ess so as n increases. It would be good to have the M-location and M-dispersion chart

displayed one above the other. This will enable the joint interpretation of

the resulting graphs.

4.3 S Location and dispersion charts

These

titles and

statistics

are identical to the corresponding M charts. Just change data and

all other theory follows through for S charts. Equivalent

for S charts are:

5,i = v I S(i ,j)

J k A

Plot the three lines

§ = ± Is. n j=i J

D

i = A l (S(i ,j) - S ) 3 K 1 1=1 J

D

2 = I J D

2

n j=l J

S ± Dt (n(k-l) ) n"

1/2

and the points S .

.

(8a)

(8b)

(9a)

(9b)

5. Discussion of P Ret charts

P net charts are different from the other two (M and S) charts in several

ways:

i. P net charts can only be based on one measurement per test. It is not

reasonable to completely disassemble then reassemble the entire test

system several times. This would be required to ensure that the repeated

P net measurements are independent statistically and to perturb all factors

that would affect its measured values.

8
A consequence of this is that we cannot depend on central limit

theory to statistically determine the error bounds as we did for M and

S. Information on the distributional behavior of P net is necessary. We

must therefore obtain data from controlled experiments and analyze the

data. It will then be possible to develop proper P net control procedures.

ii. P net is functionally dependent on the random variables M and S, the

objects of the previous control charts. Pj_ and P

2 , for example, are also

involved in determining P Ret . Statistical dependence is obvious. M and S may be dependent but we will ignore this for now. Little is understood

about the nature of this relationship until data can be obtained.

The end result of this dependence is that the control charts are not

independent and therefore the joint error probabilities cannot be treated

as such. This should not be an impediment, however. It is possible to

develop more complex control charts to monitor M, S, and P net rigorously

and simultaneously. This can be done when more information on their

statistical properties is obtained.

Initially, an assumption will be made that P net measurements are Gaussian

and a preliminary chart will be developed. As data become available,

assumptions can be checked and the procedures refined. Proceed as follows.

5.1 A "rough" control chart for P net -location

* * Define Pi, P 2 , • • • P to be the successive values of P net 5 • • • determined by

, . . . , n ( 10 )

where Pjj (= Pj) is the measured power at port j for the ith test.

Then the chart should be constructed as follows:

Let ( 11 )

( 12 )

9
Plot the individual P.'s vs i.

The upper bound for control is P* + t(n-l) D*.

The lower bound for control is P* - t(n-l) D*.

Obtain t(n-l) from the t tables as done in M and S location charts.

This is a special case of the earlier charts for location when k=l. It

is not possible to develop dispersion charts for P net corresponding to those

for M and S dispersion.

CAUTION: It is important to interpret this P net -1 ocati on chart

with discretion since the bounds in this case are directly

dependent on the distributional assumption. Use it as a rough tool

only until assumptions can be verified or modified appropriately.

Figure 4 illustrates the format of the P net -1 ocati on chart.

Test Number (one measurement per test— Normality assumed)

Figure 4: Illustration of Pnet -Location Chart

10
Given the lack of distributional knowledge it is reasonable to choose two sets

of limits with t = 2 and 3. Under the Gaussian assumption and n large, these

would correspond approximately to p = 0.95 and to p = 0.99. This suggests a less artificial reliance on the p's, etc.; just a reasonable set of bounds.

Figure 5 illustrates this chart.

U.C.L.

U.W.L.

L.W.L.

L.C.L.

Figure 5- ^net -Location Chart with Warning Limits

Given more information, it is possible to improve on this and also possibly to

develop dispersion charts or a more specialized chart.

6. Conclusions and Comments

This is only a proposal for a good beginning. Control charts cannot be

finalized without data. Control chart methodology also contains more than is

discussed here. More specialized methods sensitive to particular types of

failures may be developed as more is understood about these measurements.

We clearly need data to continue. Attached are two control charts

(figures 6,7) for location of the S parameter based on simulations. The first

is for 10 self calibrations, each based on 10 measurements. The second is a continuation of 20 more self calibrations. The changing nature of the upper

and lower limits and grand mean is apparent. The parameters used for the

simulation were obtained from some preliminary measurements of the anechoic

chamber field generation system.

11
S-parameter

value

-i 1 1 1 1

I 1 Y niv. .26106F-02 AND 1 X D1V- .90000F-01

69.5*66 " U

II

II

I1

I

II 6*. 5607 -

II

I

I

I

II

I

I 69. 5*06 -

II

I

I

X H

I

I

I

I 69. 5125 -

I

I

I

I

I

I

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I1 6 9. * 8 A A -

I

I

II

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I 69. *563 - L

I _1

1 . UUCO

-I- ISTARPAC OS / STATUS 3.31 - AUGUST 22

1 I 1 II u u u u

-

•I- -r. I- -I- •I- I1.90CC 2. 8000 3.7000 *.6000 5.5000 6. *000 7.3000 8.2000

t t -

I -I 1- 9.1000 10.0000

Successive self tests of system

Symbols: U; upper limit

M; pooled mean for n=10 (eq (8b))

L ; 1 owe r limit

*; average S value for each test (eq (8a))

Figure 6. Simulated S-location chart, n=10

12
S-parameter

value

69.5972

-i

i 1 r d i v*

- u u u

ix

ii

ii

i

i

STARPAC OS / STAUIB 3.31 - "I 1 1 -I 1 1 1 1 1

. 2690OE-G2 AND l * DiV- .29000

u U 0 t U UUU Ult u u u u u u uuu u u uu u u

69.5702 -

I1

1

I

II

I

II 69. 5 A3 3 -

II

I

II M

I

III

H H H h 2 H M * H N h M M K R N MN« MU HA H N

*

* 69.5163 -

1

II

11

I

I

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I 69. *893 -

69. *623

I

I1

I

I

1

1I1-LI

1 l.OOCu

LL LL LL LLl LL LL LL LL LLL LL LL LL

I I I 1 1 1 x x x 3.9000 6.8000 9.7000 12.6C00 15.5000 16.9000 21.3000 29.2000 27.1000

Successive self tests of system

Symbols: U; upper limit

pooled mean for n=30 (eq (8b))

L ; 1 owe r 1 i mi

t

*; average S value for each test (eq (8a))

Figure 7. Simulated S-location chart, n=30

AUGUST 22 1-

1 u u

-

h n

l L -

1 1- 30.0000

13
To obtain good data the test procedure is important:

Choose one frequency band--a relevant one in terms of equipment,

test methods, calibration requirements, etc.

Test at one center frequency in this band or, if possible, a center

and the two band edge frequencies.

Technicians should obtain the data using careful and typical test

procedures. The importance of following all steps using realistic

lab procedures, dismantling and reassembling equipment, cannot be

overemphasized. These self tests should be interspersed with other

work and calibrations.

Choose k between 7 and 10 and for each setup of the test system

replicate the M and S measurements. They must be spaced in time

and interspersed with enough real hardware manipulation

(engineering judgement must determine this) to ensure independence

of the successive measurements. Lab practices are crucial to good

realistic data.

Perform about 10 tests, i.e., 10 P pet measurements. These include

10 groups of (say 7) M measurements and 10 groups of (say 7) S measurements; 140 data points in all.

More tests should be performed if possible. Twenty five would

provide adequate data, for example, but might be costly in terms of

time required and loss of the system for measurements.

These procedures will give a reasonable assessment of anechoic chamber system

performance in one frequency band. If this proves to be typical of other

frequency bands, methods could be developed for those bands with less initial

data.

14
7. References

[1] Kanda, M. The methodology for evaluating microwave anechoic chamber

measurements. Proceedings of the 1985 EMC Symposium and Exhibition; 1985

March; Zurich, Switzerland.

[2] Kanda, M.; Orr, R. D. A radio-frequency power delivery system:

Procedures for error analysis and sel f-cal i brati on. Nat. Bur. Stand.

(U.S.). Tech. Note 1083; 1985 August.

[3] Natrella, M. G. Experimental statistics. Nat. Bur. Stand. (U.S.) Handb.

91; 1963.

[4] Croarkin, C. Measurement assurance programs, part II: Development and

implementation. Nat. Bur. Stand. (U.S.) Spec. Publ. 676-11; 1984.

15
NBS-1 14A (REV. 2-90

U.S. DEPT. OF COMM.

4.

BIBLIOGRAPHIC DATA

SHEET (See / n struction s) TITLE AND SUBTITLE

PUBLICATION OR

REPORT NO.

2. Performing Organ. Report No. 3. Publication Date

NBSIR 85-3033 January 1986

METHODOLOGY FOR STATISTICAL CONTROL OF THE ANECHOIC CHAMBER FIELD GENERATION SYSTEM

5. AUTHOR(S)

Dennis S. Friday

6. PERFORMING ORGANIZATION (If joint or other than NBS, see in struction s) 7. Contract/Grant No. NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE 8. Type of Report & Period Covered

WASHINGTON, D.C. 20234

9. SPONSORING ORGANIZATION NAME AND COMPLETE ADDRESS (Street. City. State, ZIP)

10. SUPPLEMENTARY NOTES

Document describes a computer program; SF-185, FIPS Software Summary, is attached.

11. ABSTRACT (A 200-word or less factual summary of most significant information. If document includes a significant

bi bl iography or literature survey, mention it here)

The microwave anechoic chamber is a National Bureau of Standards laboratory facility

in which standard electromagnetic fields are generated. The chamber enables special

measurements and electromagnetic compatibility tests to be conducted on antennas

and other devices. This paper is concerned with methodology for assuring that the

standard field patterns generated in the chamber are repeatable. Procedures are proposed for developing a data base from measurements obtained by placing the system,

which generates the fields, in certain relevant reference configurations. Methodology

is presented for developing statistical control charts to monitor both the location

and the scale parameters of these data over time.

12. KEY WORDS (Six to twelve entries; alphabetical order; capitalize only proper names; and separate key words by semicolons)

anechoic chamber; control charts; electromagnetic fields; measurement assurance;

standard fields; statistical control

13. AVAILABILITY

[Xj Uni i mi ted

| | For Official Distribution. Do Not Release to NTIS

| Order From Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402.

[X] Order From National Technical Information Service (NTIS), Springfield, VA. 22161

* U.S. GOVERNMENT PRINTING OFFICE: 1986-677-898/45123 REGION NO. 8

14. NO. OF

PRINTED PAGES

20

15. Price

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