Automated work sampling with unbiased variance estimates

Comput. & Indus Engng Vol 6, No 1. pp 39~.7. 1982

036~8352182]0100394D$03.0010

Printed in Great Britain.

Pergamon Press Ltd.

AUTOMATED WORK SAMPLING WITH UNBIASED VARIANCE ESTIMATES ELINOR S, PAPE Industrial Engineering,The University of Texas at Arlington,Arlington,TX 76019, U.S.A.

(Receivedfor publication 13 October 1981) Abstract--Work samplingis a work measurement tool that was over simplifiedduring the slide rule era by assuming a binomial distribution for observation data totals. The binomial variance was then used to calculate the variance of the proportion estimate(s)and to determinethe necessary number of observations needed to attain a certain accuracy. Now a variety of computer programs are being written to perform work sampling calculationsincorporatingthe same quick, easy, but often biased variance estimates. When a samplingstudy extends over a relatively long period of time better variance estimates for the proportions are available which are essentially sample variances constructed from observation-round proportions, work shift proportions, or daily proportions. These alternate variance estimates will yield different accuracy claims and different determinations of the number necessary additional study days, sometimes larger and sometimes smaller than the classic estimates. In the very practical case of unequal number of observations per round and/or per day these calculationsare extremely time consumingwithout a program but relatively simple in any computer language. A Fortran program is presented which calculates three different accuracies and numbers of additional study days (the classic estimates and two others), markingthe one prefered based on the amount of data in the system at that point. Properly operated the program will periodiallyupdate a data file with additional study data until the operator is satisfiedand terminates the work samplingstudy. Pace rating of work categories, when appropriate, can also be incorporated by the program to modify proportion estimates. INTRODUCTION Traditional variance estimation Work sampling data can be viewed as a large, multi-dimensional array of 0-1 data entries, the 1 indicating the occurence of the activity described by those dimensions and the 0 indicating the non-occurence. If an attempt is being made by the sampling technician to pace rate the observed work for leveling purposes the "1" data entries are accompanied by one, two or three digit rating numbers. Some dimensions of the data array are the worker, the work category, the observation round, and the observation day (or shift). Other dimensions could be identified but these are the only ones recognized by the Fortran program presented here. In an effort to determine the proportion of time, zr, occupied by a particular work category, or by a particular work category given a particular day, the O's and l's are added and divided by the total number of digits, N, to achieve, p, a generally unbiased estimate of the desired proportion. (Biases can be introduced into the proportion estimates by operator awareness of sampling schedule or by careless sampling procedures, such as regularly leaving early or arriving late.) If each of the O's and l's that go into the proportion estimate for the ith category, Pi, are assumed to be independent samples from the same process, the variance of Pi is estimated by S2/N, when S 2 is the sample variance. However an S 2 based on O's and l's reduces with very little manipulation to Npi(1 - p i ) / ( N - !) and hence the variance of pi is traditionally estimated by V1 = p i ( 1 - p g ) / ( N - 1 ) . When N is large and calculations are made by hand the estimator p~(1-p~)/N is commonly used. V1 can be recognized as a scaled variance estimate of a binomial random variable because the assumption of independent 0's and l's is one of the primary binomial assumptions. Two uses are made of the variance estimate construction of confidence intervals and determination of the number of additional observations, or days of observations, necessary to produce some desired accuracy, either absolute or relative. The program presented here calculates and displays in its final report p~ - A, p~, and p~ + A where P~ -- P I ( L A ) and A = ZX/(p~(1 - p i ) / N - l) -- Z V A L ( ( P I ( L A ) (1 - P I ( L A ) ) / ( T N - 1))05. 39

40

ELINOR S. PAPE

Z = Z V A L is a percentage point of a normal distribution defined to be 1.96 in one of the first statements of the program and S R K J is the counter used to determine the total number of worker observations during the study. The anticipated additional study days necessary to achieve a particular accuracy are found by equating that accuracy to A, solving for N, dividing by the average number of observations per day and subtracting the number of days of the study that have been completed. Where A C C is absolute accuracy, and D A Y is the number of days of study taken, the program calculates and displays AJ = ~

1 DAY

unless

A J is negative in which case A J overflows the format printing asterisks. If the assumption of independent 0's and l's is valid, A J estimates the number of additional days of study, (with

number of observations per day equal to those days thus far observed) necessary to produce a confidence interval with end points p - A C C and p + A C C . The traditional variance estimate, V1, has some good qualities but foremost is its ease of computation. Only one statistic is needed, the sum of the 0's and l's. Because, in practice the 0's and l's are not generally independent V1 can be a biased estimate of the true variance. Alternate variance estimators can be obtained by reducing the theoretical 0-1 data matrix to row or column sums and essentially forming S2's sample variances, based on those sums. The motivation for this reduction[4] is to establish more nearly independent samples from a population of proportion estimates. Most notably data is reduced to observation round totals for given work categories and to day (or shift) totals for given work categories. These reductions produce two alternate variance estimates. These two estimators are essentially sample variances but their computation is made more complex by the fact that rarely, if ever, will equal amounts of data exist for each observation round and for each day due to absenteeism and a host of practical considerations. The advantages gained in terms of bias reduction would rarely be worth the computational complexity if calculations were to be performed by hand. These computations do not reduce any bias in p as an estimate of 7r, they merely produce less biased estimates of the variance of p. These variance estimates are used to establish alternate confidence intervals, to show how accurate the estimate may be and to determine alternate estimates of how many additional readings are necessary to produce any desired accuracy. V A R I A N C E E S T I M A T E BASED ON O B S E R V A T I O N ROUND TOTALS

When it is desired to produce proportion estimates, p's, by combining observations made of two or more operators on each observation round, the observation round totals are more nearly independent than are the individual readings because of positive or negative correlations in worker behavior. Even ignoring worker behavior patterns work category is often correlated with time of day, e.g. clean up and set up, and hence two workers observed at the same time are necessarily correlated. If observations on several workers are not combined (summed) then the work crew is taken as containing one worker and the program is run separately for each of those workers. It is important to distinguish between a sampling study done to determine the three proportions of idle time on three different operators performing possibly three entirely different jobs, crew size = 1 three times, and a study done on three workers performing the same type job to determine a single proportion of idle time, crew size = 3 one time. If crew size proportions are assumed independent from round to round, independence being achieved by random selection of times, then the sample variance of the observation round proportions for each work category can serve as an estimate of the variance of Pi. If the crew size stays constant during the study time this variance estimator of Pi, the sample proportion of time occupied by the ith category would be J

~(Pij - Pi)2 ( J - 1)J

(1)

Automatedworksamplingwith unbiased varianceestimates

41

where J is the total number of observation rounds and P0 is the estimate of ~ri based on the jth day's data. However in practice the crew size in the ]th round, Kj, almost never stays constant and the estimator should actually be constructed as J

V2=

( J - I)(N)

(2)

J

where N = E Kj, total number of worker observations made during the study. Computationally the program presented here forms the estimator as SYZ(I)- TN(PI) 2 V2 = ( S M ( I ) - 1)(TN)'

where P I ( L A ) = Pi, T N = N, S K P ( L A ) = E Kip ~, and S M ( I ) = J. The program displays Pi - B, Pl, and Pi + B where B = Z V A L ~ / ( V 2 ) . The additional study days required when V2 is a better estimator than V1 is estimated as

in a manner similar to AJ. Negative values of BJ are replaced by asterisks.

VARIANCE ESTIMATE BASED ON DAY (OR SHIFT) TOTALS Observation round data might not be considered independent for several reasons, because they occur clustered within strata (days) or because they are stratified across days if systematic stampling is practiced [2, 3]. Recognizing the possibility of pi's being influenced by day effects a more conservative approach to estimating the variance of each Pi rests on the day totals as the independent quantities. If each days' number of worker observations, Me, were constant the variance estimate of Pi would be D

Y . (Pie -- Pi) 2

( D - 1) D where Pie is the estimate of ~r,.based on the dth day's data and D is the total number of days thus far observed. However with variable Me the variance estimate is found by D

(pi~ - p i ) 2 (O- 1)N

Me

V3= computationally

( S M P ( L A ) - T N . PI(LA)2)/[(DA Y - 1)TN) °5, D

where S M P ( L A ) = E Mapif . Confidence intervals formed with V3 are displayed in the programs final report as Pi - C, Pi, and p + C where C = Z V A L (V3) °'5.

42

ELINOR S. PAPE

Estimates of additional days of study are found from

CJ = ( (A-~--C)2 I ) DA Y in the same manner as with VI and V2.

PROGRAM OUTPUT Final Report The most important output of the program is its "Final Report" giving the three confidence intervals, p leveled by a rating factor, and the three versions of additional study days needed for the desired accuracy. The additional days must have the same number of observations as the average of those days observed thus far. A notation appears at the bottom of the report indicating which might be preferred on the basis of the number of days data. The criteria are admittedly arbitrary and can be modified on the basis of the practitioner's experience. With no more than 2 days data the traditional intervals are marked "preferred". From 3 to 14 days the observation round column is marked "preferred" and with 15 or more days the day effect column is "preferred". In general, the right most column is less biased but more inaccurate (higher variance). The left most column is most subject to bias but has low variance. The notation "Final Report" may seem a misnomer since additional days of data may be necessary. Provision may be made for the summations originally initialized to 0 by the DATA command at the beginning of the program to be stored and recalled so those quantities are not re-initialized to zero on subsequent runs of the program and the previously collected data need not be reanalyzed. Daily Data Sheets and Summary Reports The Data Sheet is no more than a copy of the work sampling form that might be used by a technician not using an electronic clipboard. The categories have been named in the FORMAT statements but, rather inconsistently, the STUDY NO. and STUDY TITLE have not. Regardless of the headings it is important to print out the data for error detection purposes. The formating of the data sheet would need to be modified for a crew of more than 10. The Summary Report reduces the data sheet by adding across workers and averaging ratings for each work category. The formating of this report would need to be modified for more than 5 categories. PROGRAM INPUT The READ statements and formats are all identical but are intended for three different types of data cards. The first card on any day will have only Month and Day in the first 4 columns. Subsequent cards will leave the first 4 columns blank, give sequential number, time, and the category number, and ratings for all workers. When a second card is read with a different data from the 1st, the daily summary reports are printed before reading subsequent cards. The final card bears the number 99 in "the first two columns which signals not only the daily reports but also the final report. On subsequent runs of the program it would be desirable to input final values from the previous run summations originally initialized to 0 under the DATA command at the beginning of the program. How the user will wish to do this will depend on the system being used. PROGRAM LIMITATIONS As written this program accommodates only 5 categories, 10 workers and 50 observation rounds per day. The most difficult part of expanding the program would be the formating of output of daily reports.

Automated work sampling with unbiased variance estimates

43

Certain specification such as category name, z value, and accuracy are included in the program rather than read in as data. The user might wish to modify these factors. PROGRAM

RESULT

INTERPRETATION

The engineer faced with three answers to the same question may not consider this program to be an improvement. However when the alternate estimators differ appreciably from the traditional estimators the binomial assumption of independence is being violated. The correlations can be positive or negative resulting in, respectively, more or less data being needed for the same accuracy level. With unequal numbers of workers per observation round and unequal numbers of observation rounds per day computations of anything except the traditional estimators are difficult by hand calculators. However with more and more computations of this sort being performed by computer it seems unnecessary to continue to settle for the quick, dirty, but biased results industrial engineers have used in previous years. REFERENCES I. R. E. Heiland & W. J. Richardson, Work Sampling. McGraw-Hill, New York (1957). 2. J. J. Moder, Selection of work sampling observation times: Part I. Stratified sampling. AIIE Trans. 12(1), 23-31 (1980). 3. J. J. Moder & H. D. Kahn, Selection of work sampling observation times: Part II. Restricted random sampling. AIIE Trans. 12(1), 32-37 (1980). 4. E. S. Pape, Work/activity sampling-contempary design analysis methodology and applications: Part II. Work sampling calculations revisited. AIIE, 1979 Fall Industrial Engineering Conf. Proc., pp. 371-375.

APPENDIX F O R T R A N IV G1

C* C*

R E L E A S E 2.0

WORK

DATE = 81130,

MAIN

(PERFORMANCE)

S A M P L I N G STUI:Y

C* C*

C* C* 0001 0002

0003 000~ 0005 0006 0007 0008 0009 0010 0011 0012 0013 0010, 0015 0016 0017 0018 0019 0020 0021

0022 0023 0020, 0025 0026 0027 0029 0029

0030

AUTHOR DATE

: :

DR.

ELINOR

15 AUG

1980

PAPE

15/23/02

*

8.

* *

9. 10.

*

11o

*

12. 13. 10,. 15. 16. 17. 18. 19. 20. 21. 22. 23. 20,. 25. 26. 27. 28. 29. 30. 31. 32. 33. 30,. 35. 36. 37. 38. 39. 0,0° 41. 0,2. 0,3° 40,° 0,5. v,O° ~7° °,8. o, 9 , 50. 51. 52° 53.

* *

C* • **************************************************************** I N T E G E R DATE, D A T E 1 , H O U E D I M E N S I O N IC ( I0), IR (I0) ,IIA (5,50), JCA {5,50), NO (50), Ill (50), MI {50) ,El IJ (50} ,KJ (5) ,X [5},YSQ ( 5 ) , S V ( 5 ) , S K P ( 5 ) , P J (5),RJ (5),SMP(5) ,SX'[(5} • 2PI {5),A (5),PAl {5),?A2 {5) ,AJ ( 5 ) , B ( 5 ) , P B I I 5 ) , P B 2 { 5 ) , B J (5) ,C (5) •PCI{ 35) , P C 2 { 5 ) , C J (5) ,PRT (51 ,XAV(5) ,XQJ (5) ,JC (5) ,JR (5} DATA S V,SM P,SKP, S X ~ / 2 0 * 0 . / , TN, SM, DA~//3*O./ ZVAL=I .96 Ace=0.02 • ************************** READ M O N T H AND DATE * * * * * * * * * * * * * * * * * * * * * * * * READ [5,100)MON,DATE 100 FURHAT (212) DATEI=DATE 2 DO 3 I N = I , 5 0 KIJ fIN}=0 DO 3 I ~ = 1 , 5 [~A (I[~,IN) =0. JCA (IM, IN)=0 3 CONTINUE DO ~ 6 = 1 , 5 ~J ( L ) = 0 EJ IL}=0. x [L) =0. YS~ {L) =0. CONTINUE DAY=DAY+I • ************************** P,~INT THE H E A D I N G * * * * * * * * * * * * * * * * * * * * * * * * * * 5 ;4RITE (6,200) 200 F O R M A T { I H I , 9 X / / 2 1 X , ' W O R K ~['ERFORMANCE) SA[IPLING STUDY DATA SHEET') W R I T E ( b , 300) MON, DATE 300 F O R M A T [IH+,20X,0,U, (' ')////5X,'CATEGORIES',5X,'CSSE~VER' ,35('_') ,'D 1ATE',/12,'/',I2,'/80','SHEET',0, { ' _ ' ) , ' O F ' , b ('_')) WRITE(6,30I) 301 F O R M A T (IH+, 66X, 8 ('_') ) ,/RITE (6,it00) W00 FORMAT (IH ,2X,'$I -- SET U P ' , 5 K , ' S T U D Y N O . ' , I 0 ('_'),'STUD~[ TITLE', IO,2('_')/3K,'#2 -- EIIN'/3X,'#3 -- AVOIDABLE'/JX,'I;t~ -- UNAVOII~ABLE' 2 / 3 X , ' # 5 -- PERSONAL'/) W R I T E (6,500)

CAIEVoL6. No. I--D

ELINOR S PAPH FORTPAN 0031

0032 0033 0034

0035 0036 0037 0038 0039 0040 0041 0042 0043 0044 0045 0046 0047 0048 0049 0050

0051 0052 0053

0054 0055 0056 0057 0058 O05g 0060 0061 0062 0063

0064 0065 0066

IV

GI

[,ELEASE 2.0

MAIN

DATE

= 81134

54. 55. 50. 57. 58. 59. o0. 61. b2. 63. 64, 65~

DO 31 J = 1 , 5 0 DO 8002 I N = I , 5 JC ( IN} =0 JR [I.~)=0 8002 C O N T I N U E N=N+I [
67. 68. 69. 70. 71. 72. 73. 74, 75. 76. 77. 78. 79. 80. 81. 82. 83. 84. 85. 86. ~7. 88. 89. 90. 91. 92. 93. 94. 95. 96. 97. 98, 99.

C*

C*

0070 0071 0072 007]

100.

*

PRINT

OUT

'WORK

SAMPLING

STUD][

SUMNARY

REPORT'

C*

0067 0068 0069

15/23/02

500 F O R H A T ( I H , 4 0 X , ' W O R K E R N U M B E H ' / 2 X , ' O ~ S ' , 4 X , ' T I ~ E OF'/2X,'NO. OBSER IVATION' ,2 X,' I ' ,6X,' 2',6X,' 3 ' , 6 X , ' 4' ,6X, '5' , 6X, t 6',bX,' 7' ,6%,'8' ,OX 2 , ' 9 ' , 5 X , ' 10'/18X, IO('CA ET ')/2X,3 {' ' ) , 1 X , 1 1 ( ' _ ' ) , I 0 (' . . . . . ')) EKJ=O. SPL=O. N=O C • ~*~******~******** *****~******* ******************* *********~*** C" * C* NAIN L O O P FOR DATA I N ~ U T ~ g A D D I N G W OF WCRKERS DOING E A C H * C" C A T E G O R I E S g I~EQUIEED DATA C A L C U L A T I O N * C* * C * ¥ * * * * * * ~** **~' *** ** *** ******* *** * * * * * * * * * * * * * * * * * * * ** * * * * * * * * * * *

*

101.

*

102.

C * * * * * * * * * * * * * * * * * * * ***** * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * * 40 D A T E I = D A T E W H I T E (6,2000) 2000 F O R N A T ( 1 H I , 3 O X , ' W O R K (PERFORNANCE) SAMPLING STUD¥'/4OX,'SUMMAR¥ RE IPORT') W R I T E (6,2001) 2001 F O R M A T (III+,39X, 14 ('_')/) ~RITE (6,2002) 2002 F O R N A r [IH , 4 0 X , ' C A T E G O R I E S ' / 2 X , ' O B S ' , 4 X , ' T I N E OF'/2X,'NO. OHSERVAT IION.,6X,' I' , 13X,' 2', 13X, ' 3' , 13X, ' 4', 13X, ' 5 ' / 1 8 X , 5 ['NO ~I' ,4X) 2 , ' K I J ' / 2 X , 3 ('_'), IX, 11 ('_') , I X , 5 ( 1 2 ( ' _ ' ) , 2 X ) , ' _ ' )

M=N-1

0074 0075 0076

DO 52 K = I , H W ~ I T E ( 6 , 2 O O 3 ) NO (K) ,IH (K) ,NI (K) , J C A ( I , K ) , R A ( I , K ) , J C A

114, (2, K) ,RA (2, K) ,J

1CA {3,K) ,RA [3,K} ,JCA [ 4 , K ) , R A [4,K) ,JCA [ 5 , K ) , RA [ 5 , K ) , K Z J (K) 0077 0078 0079 0080 0081 0082 0083

0084 0085 0086 0087 0088 0089 0090 0091 0092 0093 0094 0095 0096

2003

F O R M A T {2X, I 2 , 5 X , I 2 , ' : ' , I 2 , 4 X , 5 ( I 2 , 2 X , F 8 . 2 , 2 X ) ,I2) R K J = R K J + K I J (K) 52 C O N T I N U E XT=O. KJT=O DO 56 I I = I , 5 K J T = K J T + K J {If) XQJ (II)= [KJ ( I I ) * * 2 ) / R K J PJ(IS) = K J ( I I ) / R K J IF ~ K J { I I ) . E Q . O ) GO TO 5 W XAY ( I I ) = X ( I I ) / K J [II) SO T O 56 54 XAV ( I I ) = O . 56 C O N T I N U E WRITE (6,3001) 3001 F O R M A T [IHO,88X) W R I T E (6,3002) 3002 FORMAT(IH*,15{'_'), IX,6(13('_'),IX)) W R I T E (6,3003) RKJ, H 3003 ~ORNAT ( I H O , 3 X , ' K J ' , 8 O X , F 5 . 0 / I H ,3X,'IJ',81X,13)

103. I0~. 105. I06, I07. 108. 109, 110. 111, 112, 113. 115. 116.

117, 118. 119. 120. 121. 122. 123. 124. 125, 126. 127. 128, 129. 130.

131, 132. 133, 134, 135. 136 137,

45

Automated work sampling with unbiased variance estimates FORTRAN

0097 0098 0099 0100 0101 0102

RL'tEAS]'; 2 . 0 "

IV G1

0103 0104 0105 0106 0107 0108 0109 0110 0111

SUmmATION

CALCULATE P-C, P*C,

9001

9902 9003 4004 4005

9010

0146 0147

0153 0159 0155 0156 0157

A, JA, B, JB, C, JC, P, P-A, AND RATING A D J U S T M E N T

E-B,

P~B,

DO 66 L A = I , 5 PI (LA)=SY {LA)/T~ A ( L A ) = Z Y A L * ( ( P I (LA)* {I.-PI (LA))/(TN-I.)) **0.5) PAI(LA)=PI (LA)-A(LA) PA2 {LA) =HI (LA) +A {LA) AJ (LA) = ( ( ( A ( L A ) * * 2 ) / A C C * ~ 2 ) - I . ) * D : Y B ( L A J = Z Y A L * ((SKP ( L A ) - T N * P I ( L A ) * * 2 ) / ( ( S ~ - I . ) * T N ) ) s * 0 . 5 ~'BI {LA)=PI {LA)-B {LA) P B 2 ( L A ) = P I ( L A ) +B(LA) BJ (LA) = ( ( ( B ( L A ) * * 2 ) / A C C * * 2 ) -I.) *DAY C {LA} = Z V A L * { (S~P [LA)-TN*PI ( L ~ ) * ~ 2 ) / { ( D A Y - I . ) * T N ) j * * O . 5 PCI (LA)=PI (LA)-C (LA) PC2(LA) =HI (LA) +C(LA) CJ (LA)= (( (C (LA)**2)/ (~%CC**2))-I.)*DAX P~T {LA)= [PI (LA)* {SXT (LA)/S£ (LA)))*0.01 I F ( A J ( L A ) . G E . O . ) GO TO 62 AJ {LA)=9999. 62 IF[BJ {LA}.GE.O.) GO TO 5~, BJ (LA) =9999. 64 I F ( C J [ L A ) . G E . O . ) ;0 T O 66 CJ {LA) =9999. 66 C O N T I N U E C* C* C*

0148 0149 0150 0151 0152

* * *

DO 60 L=1,5 SV (L)=SV(L) +KJ (i) SKP(L~ = S K P ( L ) + Y S Q ( L ) S M ~ (L) = S M ~ [n)+x~J (L) SXT (n) =SXT ( L ) + X (n) 60 C O N T I N U E IF (MON.NE.99) GO TO 2

0112 0113 0114 0115 0116 0117 0118 0119 0120 0 121 0122 0123 0124 0125 0126 0127 0128 0129 0130 0131 0132 0133

014~ 0145

OF EACH D A Y ' S R E S U L T S

TN=TN+RKJ

C• C* C* C*

0136 0137 0138 0139 0140 0141 0142 0143

15/23/02

DATE = 8 1 1 3 4

WRITE (6,3004) (KJ(IB) ,1B=I,5) ,KJT 3004 F O R M A T {IH , D X , ' X L . , 1 1 X , 6 { 1 3 , 1 1 X ) ) WRITE(6,3005) (PJ(IB),IB=I,5) 3005 F O R M A T ( I H , 3 X , ' P J ' , I 2 X , 5 ( F 6 . 3 , R X ) , ' 1.000') WRITE (6,3006) (XAV(IH),IB=I,5) 3006 F O R ~ A T ( I H ,3X,'AVE. R T ' , 6 X , 5 { F 6 . 2 , R X ) ) C* C* C~

0134 0135

~AIN

9011 4012 4013 67 7001

* * * *

138. 139. 140. 141. 1~2. 143. 144. 145. 146. 147. 148. 149. 150. 151. 152. I~3. 15~. 155. 156. 157. 158. 159. 160. 161, 102, 103.

105. 166. 167. 168. 169. 170. 171. 172. 173. 174. 175, 176. 177. 17R. 179, 180. 181 . 182. ls3. 1B4. 185i

186, 1d7i P ~ I N T OUT FINAL E E S U I T G * 18~, 189 190 WE ITE (6,900 I) 191 FORPiAT [IH1 ,50X, lq {~ ~') /5 I%, '*' , 16X, '*' ,/51X, ' * FINAL a E 2 O P ~ *'/5 192 11X,'*', 16X,'*'/51X, 18 ['*'}/) 193 W5 ITE (6,4002) 194 FOH[IAT {IH ,' NO. OF WeRK~HS I N V O L V E D ' , g x , ' 9 ' ) 195, W H I T E (6,o,003) 196 FORMAl" (IH ,'NO. OF CA'IE;O~
46

ELINOR S. PAPE

FORTRAN

IV

0158 0159 0160 0161 0162 0163 0164 0165 0160

GI

RELEASE 70

7002 71 7003 7000 9000

2.0

,~AIN

DATE

IF (DAY.~';E.15) GO TO 71 W~ITE(6,7002) FORMAT (///40X,'PfEFEBRED GO T O 7 0 0 0 W R I T E (6,7003)

i,~ETHOD : C O [ ~ E L A I E D

~OEK

FOHMAT(///~4OX,'RrEFZRRED

[~ETHOD

EFF~uTb')

W R I T E (6,9000) FORMAT(/51X,'~*~ END

E~D

~ [ ~ - i ~ [ ~ g ~

SAMPLING

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30

7:20 7:31 7:3b 7:52 7:58 8:19 8:35 8:43 9:15 9:30 9:50 9:53 10 : 16 10:21 10:41 10:52 11:50 12:22 12:38 12:44 12:50 13 : 15 13:26 13:39 14:15 14:35 14:46 14 : 51 15:23 15:39

I CA 3 2 3 2 2 5 5 2 2 2 5 5 2 2 2 3 2 2 I 2 3 5 1 3 3 1 2 2 2 3

STUDY

DATA

SHEE%

STUDY

NU M B E R

3 RT C A

~ RT CA

£T

5 CA

RT

6 CA

~T

7 CA

0 80 0 85 85 0 0 85 30 S5 0 0 85 90 90 0 35 d5 60 90 0 0 lO 0 0 o0 85 90 85 0

70 70 70 0 70 0 75 0 70 50 0 0 50 60 70 50 70 70 60 60 80 0 70 60 0 0 0 0 0 0

d5 80 90 80 0 80 90 85 85 90 90 90 85 90 60 0 80 80 85 80 80 85 0 95 0 90 gO 85 85 85

0 75 80 85 70 0 85 75 70 70 0 O 0 0 70 80 75 80 0 80 0 0 75 b0 75 75 70 0 60 0

2 2 2 5 3 2 2 5 2 3 5 5 2 2 ~ 3 2 3 4 2 3 2 2 3 2 2 2 3 2 2

80 80 80 0 0 80 90 0 75 0 0 0 75 85 0 0 80 0 u d5 0 dO 80 0 90 80 85 0 60 70

2 ~ 3 2 2 2 2 2 2 2 2 2 2 2 2 3 2 5 I 2 2 2 2 3 2 2 2 2 5 3

70 0 0 80 85 90 80 80 90 85 dO 80 80 d5 90 0 85 0 60 80 80 70 70 0 b0 70 60 70 0 0

2 2 2 2 2 5 2 2 ~ 3 5 5 5 ~ 3 2 2 2 2 2 2 2 2 2 2 2 2 2 1 I

2 2 2 2 5 2 2 2 2 2 2 2 2 2 2 5 2 2 2 2 2 2 3 2 3 2 2 2 2 2

3 2 2 2 2 5 2 2 2 2 5 5 3 ~ 2 2 2 2 ~ 2 3 5 2 2 2 2 2 5 2 4

OF

TITLE

2 RT CA 2 2 2 3 2 4 2 5 2 I 5 5 2 2 2 1 2 2 I I 1 5 2 2 3 3 3 3 3 3

C£E~')

*~***')

WORKER T I M E OF OBSERVATION

: ~,ANDOM DAY

2z2. 223,, 22q., 225, 22t), 227 228, 229~ 2.~0,

DATE_6/13/_,~OSHEET

CATEGORIES OBSERVEa #1 -- S E T UP S T U D Y NO. #2-RUN #3 -- A V C I D A B L E #4-UNAVOIDABLE #5 - - P E R S O N A L

OBS ~O.

lb/2J/02

= 8113~

8 E~ CA 85 d5 80 70 50 0 70 70 0 0 0 O 0 0 0 80 85 85 70 U0 80 80 75 80 85 85 75 75 80 70

0 0 0 0 0 0 0 0 O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

9 RT CA 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 U 0 0 O 0 0 0 0 0 0 0 0 0 0 0

R~

10 CA

~T

0 0 0 0 0 0 0 d 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 O 0 0 0 0 0

0 0 0 0 0 0 0 O 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0

OF OF OF OF OF

WORKERS INVOLVED CATEGORIES DAYS OBSERVED OBSERVATIONS OBSERVATION ROUNDS

I 5

# 4

# 3

# 2

# 1

-ADJUSTED FOE EATING -ADDITIONAL DAYS NEEDED FOR DESIRED ACCURACY

-ADJUSTED FO[~ R A T I N G -ADDITIONAL DAYS N E E D E D FOR DESIhED ACCURACY

-ADJUSTED FOR RATING -ADDITIONAL DAYS NEEDED FOR DESIRED ACCURACY

-~DJUSTED FOR RATING -ADDITIONAL DAYS N E E D E D FOR DESINED ACCURACY

-ADJUSTED FOR R A T I N G -ADDITIONAL DAYS NEEDED FOR D E S I R E D A C C U R A C Y

CATEGORIES

NO. ~0. IO. ~0. IO.

0,07968

0.C9770 0.0

~

U.07464

END

~

~OYK

0,05009

0.14729

: COR&~LATED

0,11572

0,08751

~LTI{OD

0,0718~ 0,0 ('~****)

0.20038

CLEW

0.0~770 u.O

O. 071o'4 0,0 i 0.9)

0.17720 0.0 (6.2)

0,62105 0,49842

(*****)

0,03161 0.u19~4

P

WORK

0.17720 0.0 { 1. 7)

0,58471

0,01950

CORRELATED P-B

{ 12.1)

0,65108

0,04223

REPORT

O,b2165 0,49842 ( 5.8)

(~****)

0,031ol 0,01954

ASSUMPTION P R÷A

Pi\EFE~SED

0,05617

0.15403

0.59221

0.02099

~!NOMIAL P-A

9 5 5. 0.00 138.00

FINAL

O. 1,~07~

0 •09359

0,Z0711

0.65869

O. 0 4 3 7 2

CR~W P÷ B

O. 2)

0.07184 0,0 ( 12. I)

0,09770 0,0 ( O. 4)

0,07698

0.11720 0.0 ( 6. 8)

0,62165 O, 49d42 [ 12,7)

(

P+C

0,11842

0,10881

0.20795

0,65932

0,05195

EFFECTS

0,03161 0,01954

DAY P

0.034~7

O. 1 4 ~ 4 U

0,58398

0,011-.'7

RANDOM P-C

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{

B

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