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SEMI E89-1104 E © SEMI 1999, 2004 11 Ballard, D. H., McCormack, D. W. , Jr., Moore, T. L., Pore, M., Pr ins, J., Tobi as, P. A. (1998). “A Comparison of Gauge Study Practices,” Proceedings from the 1997 Joi nt Statistica…

SEMI E89-1104

8.7.6.3 Under the assumption of no lack of fit, the ratio

LOF

follows Fisher’s F distribution. Calculate the

probability associated with this ratio.

NOTE 21: This probability can be calculated using the Excel

function: FDIST(F

LOF

,nJ,J2).

8.7.6.4 Reject the assumption of no lack of fit if this

probability is small (e.g., 0.01 or less). In this case,

nonlinearity is probably present in the MS.

8.7.7 If there is no evidence of lack of fit, calculate the

approximate 95% confidence interval for a

111

/( )

()

ijk j

ijk

SS n J











(24)

where:

= (mean) value of the reference parameter from

reference wafer j.

8.7.7.1 If the interval contains the number one, a

is not

statistically different from one. If this is the case and

also b

is significantly different from zero, b

is the

estimate of the bias.

8.7.7.2 If the interval does not contain the number one,

is significantly different from one and bias is not

constant with parameter level.

8.7.7.3 If

is not significantly different from zero, the

estimate of bias is zero.

8.8 Matching Tolerance

8.8.1 Determine the bias of two MSs of the same kind

under conditions of reproducibility.

8.8.2

If the results give a stable bias determination for

each MS and if each MS has acceptable linearity,

subtract the two biases to obtain the matching tolerance,



biasbias





(25)

where:

bias

= bias of the first MS and

bias

= bias of the second MS.

9 Procedure to Determine P/T Ratio

9.1 Estimate the precision of the MS, P, as 6s

if the

specification is symmetrically two-sided or as 3s

if the

specification is asymmetrical or one-sided.

9.2 Take the tolerance, T, as follows:

9.2.1 The difference between the USL and the LSL for

a symmetrical two-sided specification,

9.2.2 The smaller difference between the USL (or LSL)

and the target value for an asymmetrical two-sided

specification, or

9.2.3 The difference between the USL (or LSL) and the

median of the expected distribution for a one-sided

specification.

NOTE 22: If a symmetrical two-sided specification is given

Target  Tolerance,

double the stated tolerance to obtain the correct value.

9.3 Calculate the P/T ratio, in percent, as follows:

100(%)/ 

(26)

rounding to the nearest percent.

NOTE 23: Generally, a P/T ratio should be 30% or less.

10 Procedure to Determine SNR

10.1 Estimate the precision of the MS, P, as 6s

if the

process distribution is two-sided or as 3s

if the process

distribution is asymmetrical or one-sided.

10.2 Estimate the population standard deviation of the

process distribution from process data as



process

Because it is difficult to directly measure the standard

deviation of the product without including variation due

to the MS, 

process

is generally defined as:

RTotalprocess

 (27)

where:

Total



= variance obtained by measuring a large

representative sample of the product and



= variance determined from the reproducibility

(see Section 7).

NOTE 24: Detailed procedures for obtaining the process

distribution and the associated standard deviation are outside

the scope of this guide.

10.3 Calculate the SNR, in percent, as follows:

100(%) 





process

SNR (28)

rounding to the nearest percent.

NOTE 25: In general, an SNR of 10 or more generally means

the MS is suitable for measuring the product, while an SNR of

less than 3 or 4 may be a concern in a particular measurement

process.

11 Related Documents

11.1 The following documents describe MSA

methodologies similar to those advocated in this guide.

SEMI E89-1104

Ballard, D. H., McCormack, D. W., Jr., Moore, T. L.,

Pore, M., Prins, J., Tobias, P. A. (1998). “A

Comparison of Gauge Study Practices,” Proceedings

from the 1997 Joint Statistical Meetings of the

American Statistical Association, Quality and

Productivity Section.

John, Peter, “Alternative Models for Gauge Studies,”

International SEMATECH technology transfer

document 93081755A-TR (February 24, 1994); PDF

file can be downloaded from International

SEMATECH’s public web site at http://www.

sematech.org/docubase/wrappers/26.htm.

Montgomery, D.C. and Runger G. C. (1993), “Gauge

Capability and Designed Experiments. Part I: Basic

Methods,”

Quality Engineering 6(1), 115–135.

Montgomery, D.C. and Runger G. C. (1993), “Gauge

Capability and Designed Experiments. Part II:

Experimental Design Models and Variance Component

Estimation,” Quality Engineering 6(2), 289–305.

Potter, R.W. (1991), “Measurement System Capability

Analysis,” IEEE/SEMI Advanced Semiconductor

Manufacturing Conference, pp. 121–125.

---, Measurement Systems Analysis Reference Manual,

Third Edition, (2002); Daimler Chrysler Corp., Ford

Motor Co, and General Motors Corp. Automotive

Industry Action Group (AIAG);

http://www.aiag.org.

---, “NIST/SEMATECH e-Handbook of Statistical

Methods,”

http://www.itl.nist.gov/div898/handbook.

SEMI E89-1104

RELATED INFORMATION 1

MEASUREMENT UNCERTAINTY CALCULATIONS

NOTICE: This related information is not an official part of SEMI E89. It was derived from task force deliberations

during the revision of SEMI E89-0999 in 2001-2003. This related information was approved by full letter ballot

procedures and was approved for publication by the NA RSC on August 16, 2004.

R1-1.1 Measurement uncertainty depends on the

repeatability of the MS, the reproducibility of the result

over time, the number of measurements in the test

result, and all sources of random and systematic error

that could contribute to disagreement between the mea-

surement result and its reference value.

R1-1.2

Determine the measurement uncertainty

according to the following rules:

 Expressing Uncertainty — Each uncertainty com-

ponent is quantified by a standard deviation.

 Bias — All biases are assumed to be corrected and

any uncertainty due to bias is the uncertainty of the

correction.

 Standard Uncertainty — All uncertainty compo-

nents (standard deviations), whether Type A or

Type B (see Section 5.3.41), are combined as an

RSS sum to arrive at a “standard uncertainty,” u.

This standard uncertainty is the standard deviation

of the reported value, taking into account all

sources of error, both random and systematic, that

affect the measurement result.

 Extended Uncertainty — If the purpose of the

uncertainty statement is to provide coverage with a

high level of confidence, an expanded uncertainty

is computed as U = ku, where k = 2 is typically

chosen for an approximate 95% coverage.

 Uncertainty Interval — If Y is the reported mea-

surement value, then the symmetric interval from



U to Y + U is the uncertainty interval associ-

ated with the measurement value.

R1-1.3 The measurement result for which an

uncertainty is required must be completely specified as

 the number of repetitions that were averaged,

 the test method,

 the environmental conditions,

 the operating conditions over which the repetitions

were made, and

 any calibration uncertainty.

R1-1.4 Obtain Type A uncertainty for a particular

measurement from a determination of reproducibility

(see Section 7) conducted according to the same

specifications as the particular measurement and

including all relevant components of reproducibility.