ML19296C374

Unc Recovery Sys Statistical Control Manual, Revision 3

ML19296C374
Person / Time
Site:	Wood River Junction
Issue date:	10/01/1979
From:	Deluty J UNC RECOVERY SYSTEMS, UNITED NUCLEAR CORP. (SUBS. OF UNC, INC.)
To:
Shared Package
ML19296C372	List: ML19296C371 ML19296C374
References
14617, QAP-002, QAP-2, NUDOCS 8002250718
Download: ML19296C374 (23)

Text

.

5

.i unh,Unc OUALITY ASSURANCE PROGRAM f

RECOVERY 1dE779

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1 oi 23 63p. 002 SYSTEMS 5-*'g4ATISTICAL CONTROL MANUAL

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i UNITED NUCLEAR CORPORATION UNC RECOVERY SYSTEMS STATISTICAL CONTROL MANUAL eco2=a7 ' 3 PREPARED BY:

J.

Deluty Revision III October 1, 1979 146:L7 l

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10/2/79 NEW 2 of 2 3 STATISTICAL CONTROL MANUAL OAP 002 s

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TABLE OF CONTENTS 1.0 GENERAL 2.0 ASSAY PRODUCT SCALES 3.0 CHF'.

ASSAY o

4.0 WHULE BOTTLE GAM.N!A (WB) ASSAY 5.0 55 GALLON DRUM GAMMA ASSAY 6.0 FLUOROMETRIC ASSAY 7.0 FILTER GAMMA ASSAY 8.0 ISOTOPIC ASSAY 9.0 CONTROL CHARTS

e aue Dated Page No.

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10/1/79 NEW v3 of 2 ) STATISTICAL CONTROL MANUAL CAP 002 1.0 General This manual outlines the statistical procedures for calculating bias, systematic and random errors, and limits of error fer l

all measurements systems utilized for uranium accountability control.

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1.1 Measurement Systems Assay scales Chemical assay NDA - whole bottle gamma count for residues NDA - 55 gallon drums for gamma counts Fluorometrlc analyses for low level discards NDA - In place filter gamma counting Isotopic enrichment assays 1.1.1 Each of the above measurement systems has it s individual programs for the evaluation of errors.

All errors are computed at the 95% confidence level.

The limit of error for any individual system is generally takt.. at two standarc deviations, pro-vided a minimum of 16 data values are taken.

1.2 Limit of Error for Uranium and Enrichment Measurements The input values for a job are determined from dissolver solutions after introduction to the assay tanks.

A series of these assay tank samples are composited and analyzed for U and U-235.

1.2.1 Limit of Error of U L.E.(U)

(L.E. Assay)

+ (L.E. sampling)

+

=

(L.E. Weight) 1.2.2 Limit of Error of U-235 L.E.

(U-235)

(L.E. U)

+ (L.E. Isotopic

=

Assay) 1.3 Shipper / Receiver (S/R) Differences 1.3.1 When comparing shipper's and receiver's values for the same shipment, and when both report Limits of Error, if the S/R difference is equal to or less than the statistically combined Limits

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[

1.3.1 of Error (that is, the confidence interval contains

0) the S/R difference is not significant.

Example:

Shipper's U value = 88.15 t 0.05S Receiver's U value = 88.10 0.10%

(0.05)2 + (0.10)2 h

(s.0125)h =

0.11%

=

S/R difference of 0.05% is less than the statistically combined L.

of E.

total of + 0.11% and the S/R dif ference is not considered significant.

1.3.2 When comparing shipper's and receiver's values for the same shipment, and when only one Limit of Error is reported, the S/R difference is not con-sidered significant if it is equal to or less than twice the given Limit of Error.

Example:

Shipper's U value = 88.15%

Receiver's U value = 88.10%

0.10%

2 x.10

.20%

s/R difference of 0.05% is less than the Limit of Error of 0.20% and the S/R difference is not considered significant.

1.4 Physical Inventories 1.4.1 The limit of error of a physical inventory is calculated by compiling inventory data for each MBA into groupings of like materials.

Limits of error of each grouping may be combined as follows:

(L.E.1)

+ (L.E.2)

(L.E.n)

L.E.

=

+

1.4.2 ID is defined as the difference between physical inventory and book inventory af ter the latter has been adj usted for losses cr.d discards.

ID may be the result of measurement uncertainties, unrecognized or unusual losses, human or mechanical errors, or losses or gains from other unknown causes.

1.4.3 The quantity of ID is determined by the equation:

ID = (BI + R) - (S + MD + EI)

BI equals becinning inventory R equals quantity of SNM material received during the period S equals SNM material shipped during the period MD equals quantity of measured SNM material that was discarded during the period EI equals ending inventory

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1.5 L.E.

(I.D.)

1.5.1 Assuming the measurement uncertainties associated with each component of the above equation for (I.D.) are independent of each other, the (I.D.)

limit of error may be calculated by the following equation:

L.E.

(I.D.)

=t (L.E. Additions)2 + (L.E. Remaining)2

+ (L.E. Removals)

See Figure 1.5.1 for individual factors utilized in computing the above equation.

1.5.1.1 Additions to process shall include any material removed from tamper-safe conditions for introduction into the process stream during the inventory period.

1.5.1.2 Material remaining shall include SNM within the process stream which had under-gone processing during the inventory period.

1.5.1.3 Removals from process shall include final product produced during the period, various measured waste streams, burials, environ-mental losses, and any other removal of SNM from the process stream.

1.6 Computation of L.E.

(ID) 1.6.1 Each specific category of measurements is grouped together to determine the L.E.

for that group.

For example, each individual lagoon discard sample will have a limit of error as determined in Sec-tion 6.

The limit of error for all.the lagoon dis-cards will be equal to the square root of the sum of the squares of each lagoon L.E. discarc measure-ment during the inventory period.

A similar pro-cedure is followed for each category as described on attached Figure 1.5.1.

The L.E.

(Removals),

for example, will be equal to (L.E. Product)

+ (LE. Lagoon)

+ (L.E. Burial) b (Environment)2 + (L.E. Analytical) 2 '

+ L.E.

1.6.2 The significance of the quantity (I.D.) is eval-utated by comparison with the calculated L.E.

(I.D.).

If the quantity (I.D.) is equal to or smaller than the confidence interval (I.D.)

L.E.

(I.D.), the quantity (I.D. ) is not significant.

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10/1/79 NEW 6/23 STATISTICAL CONTROL MANUAL O A P- 002

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l.6.3 This manual provides the procedures to be used by this facility for the statistical control of all systems used for the measurement of SNM.

No devia-tions nor changes are to be permitted except by recommendation of the Measurement Control Coordinator and with the approval of the Manager, Quality Assur-ance or the Manager, Nuclear Material Control.

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s w, 10/1/79 NEW 8/23 STATISTICAL CONTROL MANUAL OAP 002 2.0 STATISTICAL CONTROL PROGRAM FOR A3SAY AND PRODUCT SCALES 2.1 General Assay and product scales are checked daily using working standard weights which are calibrated against Class S weights during each inventory period.

2.1.1 A critrol graph is maintained for each assay scale, ind.cating upper and lower. control limits.

In the event the daily check exceeds an established limit, its cause shall be determined and corrected or the scale shall be removed from service until repaired.

2.2 Assay Scales: Statistical Calculations The data obtained from the daily standard measurements shall be used for determining the bias, and the systematic and random error variances.

2.2.1 Bias Calculation:

Calculated from B = (x - p )

g where x equals the mean of the standard weight measurements and p equals the value assigned to it.

g 2.2.2 Random Error Variance (V )

2

[~ (x )

_ {gx)2/n 2

2.2.2.1 Compute s

=

n-1 where x equals the daily check weighing.

/12 where 6 equals 2.2.2.2 Compute A1e s

-A the rounding error of the scale.

If Ay should be negative, set it equal to zero.

2.2.2.3 Net weight Random Error Variance 2

1+26j 2

V

= 2A 12 r

2.2.3 Systematic Error Variance (V )

s 2

2 2

2, j3 2.2.3.1 Compute s s /n + s

=

12 2

The value s is as calculated in para.

2.2.2.1.

s equals the uncertainty of the g

value assigned to the standard weight.

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b3II 10/1/79 NEW 9/23 STATISTICAL CONTROL MANUAL O A P-002 2

g 2.2.3.2 s

as computed provides the systematic t

variance for either the gross or tare weighing.

The net weight variance V will 2

equal 2s 2.2.4 Total Net Weight Variance V{ will equal the sum of 2

the random variance V and the systematic variance 2

V*s 2.2.5 The total net weight variance (Vt) is subsequently applied in determining the weighing error of a series of net weights as summed in an analytical composite.

The total composite net weight equals the sum of the individual batch net weights.

The total variance equals the number of net weighings 2

times V.

The limit of error at the 95% C.L will t

2 h

equal t2 nx (V )

where n equals the number of net weight weighings.

2.3 Froduct Scale The following calculations pertain to the determi'ation of n

the net weight variance for the product scale as both tare and gross weights are utilized on this scale.

2.3.1 Bias Calculated as per para.

2.2.1.

2.3.2 Random Error Variance (V ).

Daily check weighings are made at the 100 gram level representing a typical tare weight and at the 10 Kilogram level representing a typical gross weight.

2 2.3.2.1 Compute s from daily check weighing by 2

[(x)

- [(x) 2/n 2

f r both s

=

n-1 tare and gross weighings (s and s2) 2 14s17

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UbC 10/1/79 NEW LO/23 STATISTICAL CONTROL MANUAL O A P.a 02 2

2.3.2.2 Calculate A

=s A.

and g

12 A

=s

-A where O 9

9 12 equals the rounding error of the scale.

If A is negative, use A equal to zero.

2 2.3.2.2 Random error net variance V equals r

( ^ t + A I

• 2 b.2 g

12 or alternatively 2

2 V

= s

+s r

t g

2.3.3 Systematic Error Variance (V )

(5

- LL)

(E

-E)

V

=

g g

where E

= average gross weighing i

= average t re weighing t

E = standard weight value 2.3.4 Total Net Weight Variance (V )

V2,y2,y2 2'

h 2

V Units will be grams.

L.E.

=

Convert the L.E.

to a relative percent by

. (cr ms)

X 100 L.E.

(%)

=

10,000

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- b5 35 10/1/79 NEW 11/23 STATISTICAL CONTROL MANUAL Q A P-0 02 3.0 STATISTICAL CONTROL PROGRAM FOR CHEMICAL ASSAY 3.1 General A titrimetric procedure for uranium is utilized for the measurement of SNM in dissolver solutions and product for accountability control.

The titer of reagents used is standardized against National Bureau of Standards certified materials (950b or 960 metal).

3.2 Statistical Control A primary standard solution, prepared from NBS standards, is run with each group of samples being assayed.

The concentration range of this standard is selected to be in the general analytical range of the samples being analyzed.

A secondary standard, obtained from either of two "Round Robin" programs (GAE or SALE), may be used in addition to the above as a secondary standard prepared independent of this laboratory.

As these standards serve as a continuous evaluation of the titer of the analytical reagents used in the chemical analysis, the procedure is monitored for any bias that may develop, resulting in a minimal systematic error system.

3.2.1 The random error for chemical analyses is evaluated by the following program.

During each inventory period, samples are split and each split is assayed.

A minimum of sixteen paired analyses from sixteen sample populations is utilized.

The random error 2

variance (V ) as a relative percent is computed from this data using the relationship:

y - [(%di)

[(%di)2/n 2

2_

r 2 (n-1) where di equals the % difference between the pair.

See Figure 3.3 for format and method of computa-tion.

3.2.1.1 Sampling errors are computed in a similar e'

manner except that duplicate assay tank

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samples are used.

N Error (sampling) = Error (Analytical and Sampling)

- Error (Analytical) 3.2.2 The systematig errgr variance for chemical analysis is equal to sy + s where s equals the uncertainty q

o of the primary calibration materials (this vglue is cdrrently 0.02% for NBS 950b).

The term s r.epresents the variance of the standards.

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~ l3[l($ 10/1/79 NEW 12/23 STATISTICAL CONTROL f1ANUAL C A P.002 3.2.3 The t'otal variance for chemical assay equals the sum of the random error variance and the systematic error variance.

Two times the square root of this value equals the limit of error for chemical assay.

3.2.4 The bias is determined from the relationship B =

(R-E stanOa)r,ds and Uwhere R equals the average value of the equals the assigned value of the g

reference standard.

3.3 Limit of Error of Analytical Composite A series of assay tank samples are composited in propor-tion to their representative weights to prepare an analyti-cal composite.

The limit of error of the uranium repre-sented by the composite is dependent upon the following sources of error:

a)

Analytical Variance b)

Sampling Variance c)

Net Weighing Variance of the assay tanks 3.3.1 Each of these variances are determined independently by a measurement control program.

The limit of error of uranium represented by a composite is determined by the following relationships:

L.E.(U) =*

(L.E. Assay)

+(L.E.

Sampling)

+(L.E. Weight) 3.3.2 Based upon experience to date, the sampling errors and the net weight L.E. are insignificant when com-pared to the assay L.E., which is over 10 times greate: than either error.

Data to date ind3Eates l~1 W d' sampling errors to be of unmeasureable mag-nitude and net weight L.E.

to be of the order of 0.01 to 0.03%.

As the limit of error of the chem-ical assay may be in the range of 0.1 to 0.25, this item will be the predominate factor for the evalua-tion of the uranium L.E. as represented by a com-posite.

3.4 Chemical Analysis of Low Level Calciner Ash Residues The random error variance for low level residues is obtained from a series of paired analyses.

Sampling errors are minimized by milling and riffle-splitting to insure homogeneity and true representation of the material.

3.4.1 The limit of error is determined from a minimum of sixteen paired analyses.

The method of compu-tation is similar to that for paired analyses for chemical assay as described in paragraph 3.3 of this section.

3.5 Limit o" Error for Product Analyses

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10/1/79 NEW 13/23 STATISTICAL CONTROL MANUAL OAP 002 3.5.1 Sampling All product shall be milled and riffled in order to obtain a representative sample.

No further evalua-tion of this sampling technique is required as per para.

4. 3.1.1 o f th e FNMC.

3.5.2 Chemical Analyses for % Uranium Product is chemically analyzed by the Davies and Grey titrimetric procedure.

Three sub-aliquots of the submitted sample are analyzed.

3.5.3 Determination of Limit of Error of Product Analysis The L.E. of product analysis will depend upon:

a)

Analytical Random and Systematic Variance b)

Net weight weighing variance c)

Sampling errors - (ref. para. 3.2.1.1).

3.5.3.1 Method of Computation a)

From data of triplicate analyses, compute 2

(

~

random error variance (V ) by V

• r b)

Obtain systematic error variance (V }2 s

as determined in para.

3.2.2.

c)

Obtain product scale net wt. variance (V2 in %) from para.

2. 3. 4.

d)

Total Variance = (V2+V +YI r

b 2

2 e)

Limit of Error = 2 V

V

+V r

Page 14 of 23 QAP-002 PAIRED ANALYSES Inventory Period DATE JOB #

SAMPLE X

.X

(

1 2

2 x = assay data

[(%di)

% di = t*1 - *2 X 100 r

Average 2 (n-1) n=

2 2

2 y = s /n + s (from stds data)

[%di=

y2,y2 2

+y

[(%di)2/n =

q L.E. = 2x (V{}

Figure 3.3 14617

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.O 10/1/79 NEW 15/23 STATISTICAL CONTROL MANUAL O A P- 002 4.0 WHOLE BOTTLE GM1MA COUNTING 4.1 A single channel analyzer is utilized by counting the 185 KEV peak of U-235.

This measurement system is only utilized for residues being stored in one gallon plastic bottles.

4.2 Calibration The instrument is calibrated (in accordance with Section 4.2.3.2 of the FNMC), by measurements of standards encom-passing the concentration range commonly encountered.

Daily checks are made to verify calibrations and instru-ment functioning.

Additionally, a standard is measured by Operations personnel after every ten samples have been measured to verify instrument functioning.

4.3 Statistical Program 4.3.1 Bias and Systematic Error Variance are calculated using the daily replicate measurements of two standards (e.g. 10 g and 50 g).

4.3.1.1 Bias % B=

(R - p ) where x equals the average of the da!1y measurements and po equals the assigned value of the standard.

4.3.1.2 Systematic Error Variance (V )

= [(x ) - [(x)

/n, s

n-1 where n = no.

measurements 2

Systematic Error Variance (V )

=

3 2

2 s /n + sg where s equals the uncertainty of the o

assigned value of the standard.

(Vf) 4.3.1.3 Random Error Variance Data obtained from replicate measurements of typical process material.

variance = V2" [(x2)

_ [(x)2/n r

n-1 4.3.1.4 Calculation of L.E.

for Whole Bottle Counting The total variance will equal the sum of the systematic and random error variances.

2 2

V

" Y"s (4.3.1.2)

+V

( 4. 3.1. 3 )

t 2(V )h 2

The L.E.

equals

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so.,.c UOC 10/1/79 NEW 16/23 STATISTICAL CONTPOL MANUAL O A P.002 4.3.1.5 As this program utilizes two different process material samples, measured on alternate days, there will be some differ-ence in the L.E. calculated for each due to different concentration ranges.

An average weighted L.E.

can be calculated as follows:

(ni-1) (L.E.1) 2+ (n2-1) (L.E.2)

Average L.E.

=

(n; + n2)

-2 G

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' l)[lE 10/1/79 NEW 17/23 STATISTICAL CONTROL MANUAL QAp.002 5.0 55 GALLON DRUM COUNTER 5.1 A single channel gamma spectrometer is utilized for NDA of U-235 by counting the gamma activity at the 185 KEV peak for low level residues stored in 55 gallon drums.

The drums are rotated on a turntable in order that all surfaces of the drum are equally scanned.

5.2 Calibration

The instrument is calibrated by introducing various quan-tities of U-235 into a drum and by plotting the instru-ment response as a function of SNM introduced.

The calibration range encompasses the range commonly encount-ered by process requirements.

5.3 Statistical Program 5.3.1 Instrument response is measured prior to any sample measurements by means of a standard pre-pared drum.

As this serves to verify the calibra-tion, systematic errors are effectively minimized.

5.3.2 Calculatien of Systematic and Random Error Variances and Limit of Error The method of calculation is similar to that des-cribed in paragraph 4.3.

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,., 10/1/79 NEW 18/23 STATISTICAL CONTROL MANUAL O A P. 002 6.0 STATISTICAL CONTROL PROGRAM FOR FLCOROMETRIC ASSAY 6.1 General Fluorometric analysis is utilized for the low level measure-ment of uranium in discard solutions.

These concentra-tions are generally within the range of 0 to 25 mg uranium per liter.

6.2 Statistical Control 6.2.1 The systematic error of this procedure is auto-matically adjusted to zero by the calibration of the instrument against a prepared standard.' The primary standard solution used for calibration is prepared by the Plant Chemist, utilizing National Bureau of Standards primary standard material.

The calibration of the instrument is performed by the chemical operators, and evaluated by the Plant Chemist by a program described below.

6.2.2 The random error and limit of error is de te rmined by a program of replicate analysis of process solution.

This test solution taken from the pro-cess stream, is " Spiked" by the Plant Chemist to adjust uranium concentration to the desired range.

This test solution is identified by a code number only, and each shift analyzes this solution three times weekly for a total of six analyses per week.

After each series of tests is completed, the test solution is replaced to provide new test data covering a different concentration range.

6.2.3 The standard deviation is calculated by the formula:

[](x)

_ {}(x)2/n 2

s_

n-1 J

The limit of error is taken as equal to 2s.

This value is converted to a relative percent by cal-culating the coefficient of variation in percent as follows:

s X 100

% L.E.

=

6.2.4 This percent L.E.

is applied to the analysis of sarples of the discard tank as the error in the assigned value of uranium discards.

The volume of the tank is measured by the height of the liquor in a sight glass, and this value is con-verted to volume of tank by a calibration curve for the subject tank.

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so.m 10/1/79 NEW 19/23 STATISTICAL CONTROL ?1ANUAL OAP 002 7.0 STATISTICAL CONTROL PROGRAM FOR IN-PROCESS FILTER ASSAY 7.1 General As most in process filters remain installed over several inventory periodr, a measurement procedure is necessary to determine the change, if any, of the uranium accum-mulation within each filter, and its associated limit of error of measurement for each intervening inventory period.

7.1.1 Measurements are made by gamma counting at the 185 KEV peak for U-235 utilizing a portable gamma counting system.

Each filter is counted on two opposite sides at five pre-selected points, provid-ing ten measurements per filter.

An average net count value is calculated and assigned as the net count value for that particular filter.

7.1.2 In the event no significant change occurs in the net average count for a particular filter, it is assumed that no change in the uranium content of the filter has occurred and the inventory value of that filter is the same as the previous inventory value, with zero limit of error for the current measurement.

In the event of an increase in the average net count value, the new value, based upon the instrument calibration, shall be assigned to the filter with its associated limit of error.

7.2 Calibration Calibration is, of necessity, a dual program of immediate and long-term calibration.

The long-term calibration is dependent upon the removal and ashing of a gamma measured filter and evalution of the uranium content of the resultant ash by chemical analysis.

As most filters remain in use for fairly long periods of time, ashing and chemical analysis for calibration data requires a fairly long time interval.

7.2.1 Immediate calibration, subject to correlation of data by ashing and analysis, when available, is done as follows:

Dummy filters, similar in size to filters, are constructed.

The filters have various quantities of U-235 introduced into them.

These are counted in a manner similar to an on-site measurement.

A calibration graph is pre-pared for each size filter.

These calibrations will be re-evaluated as filters become ashed and analyzed in the future.

7.3 Statistical Control 7.3.1 The instrument is evaluated against prescribed standard conditions before and after use to ensure that instrument functioning is equivalent from one

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10/1/79 NEW 20/23 STATISTICAL CONTROL MANUAL O A P- 002 7.3.1 time period to another.

Adjustment of the instru-mentation to reproduce standard conditions effec-tively minimizes systematic errors in the system.

7.3.2 Random errors for filter measurements, assuming the stability of the instrumentation, depend to a great degree upon the distribution of the uranium within the filter, and even this variability differs from filter to filter.

It is assumed that the actual distribution of SNM within any filter lies within the extrece conditions of even distri-bution and one area concentration.

Therefore, the random error at any particular concentration for a particular size filter is determined by intro-ducing the SNM material into the " Dummy Filter" at the two extreme conditions of distribution as described above.

The variability of the measure-ments at these two conditions is an indication of the random error obtained due to distribution.

7.3.3 The random e':ror variance due to instrumental and unknown vari <bles is determined by the measurement of two typical filters on a twice weekly basis.

These filters are ones that have been removed from typical service and stored for this purpose.

Replicate analyses of these filters provide data for random error variance determination.

7.3.4 The bias and systematic error variance are deter-mined by the replicate measurement of a standard filter.

This standard consists of a constructed typical sized filter shell which is spiked with an accurately known quantity of U-235.

Replicate measurements cr this standard yield data for the determination of bias and systematic error variance.

7.3.5 Limit of Error The limit of error equals two times the square root of the sum of the scuares of the systematic error variance, random error variance, and variance due to distribution within the filter.

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NW STATISTICAL CONTROL MANUAL O A P. 002 10/1/79 21/23 8.0 STATISTICAL CCNTROL PROGRAM FOR ISOTOPIC ASSAY 8.1 General The isotopic enrichment is determined for each job pro-cessed and for each shipment of product.

Samples for this analysis are prepared by the Plant Chemist and are shipped to a contractor laboratory for analysis.

8.2 The Manager, Quality Assurance, or his designated repre-sentative, at intervals not exceeding one year, audits the contral procedures for any outside laboratory perform-ing services for this facility.

8.3 Statistical Control As this facility utilizes outside laboratory services for enrichment analyses, no control program for this measurement is necessary, outside of that described above.

The limit of error and bias for the isotopic analyses are provided to UNC-RS by the contractor laboratory.

3.4.E7 7

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r.. u so,.u 10/1/79 NEW 22/23 STATISTICAL CONTROL MANUAL QAP 002 9.0 CONTROL CHARTS 9.1 Simple Control Chart A simple control chart provides a graphic comparison of process performance data to computed control limits, which is visible as limiting lines on the chart.

Control limits are established at the 0.05 1*el of significance v

using past data to establish the limits for a new inven-tory period.

Data points which fall outside the esta-blished control limits require a response and correction by those responsible for the system involved.

9.1.1 Control limits for scales and balances may be established at a value which is equal to the read-ability of the device.

9.2 X-Bar and R Charts These charts are established and maintained for those measurement systems requiring such charts.

9.2.1 These charts are prepared utilizing three consecu-tive data points to a sub group.

9.2.2 control Limit Determination (a)

List all data points consecutively (b)

Calculate average of data 1, 2,

3 Ey Calculate average of data 2, 3,

4 E2 Calculate average of data 3, 4, n EN (c)

Calculate average of E, E '

by y

2 N

N

• 1 N

(d)

Do same as (a) and (b) above except calculate Range (minimum-maximum) for each three conse-cutive data points, R,

R R*

y 2,

N (e)

Compute average Range (E) by

{" R N

(f)

For X-bar chart, control limits equal k

A 2 A, equals 1.023 for three data points per sub-group at the three sigma level, and 0.682 at the two sigma level.

- n

'UCC 1d',l[79 NdkE 23 23 Sh$fISTICALCONTROLMANUAL O A P-002 9.2.3 (g)

For R-chart:

Upper control limit = D R 4

Lower control limit = D 3 where D

= 2.574 and D3 = 0 for 3 point 4

sub group at the three sigma level, and

}

= 0 at the two sigma level.

l D4 = 2.049 and D3 I

I s

9 9

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