Lecture 8 on Work Measurement Techniques PDF

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This document provides lecture notes on work measurement techniques. It details different methods like time study, standard data, and time formulas for establishing time standards. The lecture covers calculations involved and how to analyze work content. Lastly, it touches on performance ratings of operators and identifying various work-related and personal differences in operators.

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Lecture 8 T!me Study · what are the work measurement techn!ques ? > T!me Study - > Standard data - >...

Lecture 8 T!me Study · what are the work measurement techn!ques ? > T!me Study - > Standard data - > T!me formulas - -Fundamental mot!on data -work Sampl!ng what Measurement ? · s work > - Object!ve data dr!ven , process for establ!sh!ng t me staddds what does work measurement uses ? > - plann!ng > - compar!ng alternat!ve work methods > determ!n!ng capac!ty - -just!fy purchase of new equ!pment > develop - pay system T!me Standards What s t!me standards ? · > - Appropr!ate and reasonable amount of t!me to perform a spec!f!c work task * Based on fa!r day's work : amount of work that ca be produced by a qual!f!ed employee when work!ng at a normal pace and effect!vely ut!l!z!ng h s t!me where work s not restr!cted by process l!m!tat!ons. Calculat!ng t!me stadods · T!me Standard = Work Content X Perfrat!ng X(1 + PFD) T!me · What s work content ? > - The amount of work conta!ned n a product or process , !n person-h!s or mach!ne h s what s total job t!me ? · i i i i i i i i i What · are t!me study procedural requ!rements ? > - standard!zed method n place > Prof!c!ent - operator > Preparat!on - > knowledgeable analyst - what the t!me study equ!pments? · are -Stopwatch -Cl!pboard -T!mestudy form -Calculator What the t!mestudy preparat!on dec!s!ons? · are > Stopwatch operat!on - - Snapback > cont nuous - -Def!ne elements > - Determ ne work cucles · How to measure work Content ? tobserve job d!v!de, !nto elements w th stat and stop po!nts Cons!der wh!le def!n!ng work elements > Cohes!ve groups of therbl!gs - - As f!ne as needed - Def!n!te stat and stop po!nts Stop for - element! s start for element ty - Repeated necessary -Separate mach ne and work elements -Separate constant advar able elements -Ass!gn labels and record n sequence on t!me study form i i i i i i i i i How ? many cucles to study 130 e2 1230- t · n = [] t- students 5- sample + stat!st!c staded dev k + tolarance * - sample mean Quest!on n =) poux 38 3. = 39 cucle to study Quest!on + = 2. 262 = Soydan 1. 2 sen ↑ = [222x 37 conduct!on T!me Study Enter descr!pt!on job Enter elements · keep track of t me from beg nn ng to end , > here ,!f cont nuous - W : Watch read!ng - OT : Observed element t me > NT : normal t!me - Rate the · operator - element by element , observat!on by observat on Tavg rat!ng for each element > for - whole perf. what the record!ng problems ? · are -Fore!gn element : unnecessary , non-product!ve - can be measured , mark n NT column -If too short t!me !nclude , n elemental t me , c rcle to des!gnate as w!ld - m!ssed element : Analust's error - des!gnate w th M n W column - Out of sequence element toperator var es order > lack of tra!n!ng - i i i i i i i i i i i i i conclud!ng a T!me Study Record f!n!sh!ng t!me · · Prov!de operator w th perf rat!ng Calculate OT (cont!nuous used · Complete Summary · - #of obs. Per element - !ncorporate Perf Rat!ng n Summary f not done obs. by obs. > - % Allowance - extra t me > three - categor!es Us!ng staded t me to Determ!ne Operator Eff!c!ency Eff!c!ency = 100 X staded has eoned Hrs on Clock Quest!on 36 33 x8 cycles. = 290 64 m n. Eff!c!ency * = 100 29p 64. = 121 1 %. 240 cucle t!me" 36 33 m ns. What are the other needs or tupes of stadods ? Temporary · standards > operator s learn!ng - Apply when - Spec!fy upper l!m!t · Set up stadods > - d!str!bute t!me across product!on t!me + treat separately Part!al · set up What are the adjustments to Measured T mes from T!me Study > - Perf rat!ng > learn!ng curves - t nd v dual d!ff > Allowance - + personal - fat!gue + delay i i i i i i i i i i i i Performace Rat!ng Normal T me = Perf rat!ng X Observed T!me Accounts for d!fferences between adw th n operators Cr!t!cal element of t me study Subject!ve Requ!res clear def of 'normal' operator what are the d!fferences between operators ? V ~ Work Related Personal - tra!n!ng -strength * - exper ence coord!nat!on - Sk ll -!ntell!gence > - v s on > apt!tude - > - att!tude What are the charachter!st!cs of a sound system? > - Accurate , cons stent > Easy to use - keyed > - to benchmarks When to use sound susten? study for > Dur!ng - t me > elemental rat!ng - - longer aycles , tasks -mach!ne t me rat!ng = 100 toverall rat!ng > - short cycle repet t ve tasks What are the rat!ng systems ? -West!nghouse - sk ll , effort cond t ons , , cons!stency * Sunthet!c - based on fundamental mot on t!mes + P = Expected t!me/observed t!me > - Speed rat!ng > - focus on work rate i i i i i i i i i i i i i i i i i > - Object!ve rat!ng -judge pace relat ve to bachmark task , then mod!fy for d!ff!culty West!nghouse System · Once each factor rated Sum the four values to g!ve allowance n% Or add to 1 to g!ve performance factor Best for whole job not !nd!v!dual elements · , Allowances The need for allowances : -Normal t me s st!ll deal zed , best case scenar o account!ng for > No nterrept ons problems breaks, etc - , , Allowance m!ght be appl ed to : - total cucle t me - personal needs delaus , workstat on clean up , m nor mach ne ma ntenance - mach ne t me only ~ tool ma ntenace, power var ence > - effor t me only -fat!gue , unavo dable delays i i i i i i i i i i i i i i i i i i i i i Determ ned through -product!on study -work sampl!ng What the types of fat!que ? · are - constant ~ personal-apl ed to total cucle t me -bas!c fat!que apl ed - to total cucle t me -Var!able -var!able fat!que -unavo!dable delays-superv!sor talk mach ne nterference,.. , -extra allowances · var able mater!al qual!ty clean and o l mach ne - to mach ne t me - shutdown ad tool ma!ntace-apply " pol!cy allowances -new employee l!ght duty , · What s the Personal Allowance(P) > Restroom and water break - > Affected by env!ronmental cond!t!ons (heat , cold) - + - 5% typ!cal What s fat!que allowances (F) : > Bas c - > - accounts for var!ab!l!ty n work pace - 4% s typ!cal for l!ght work > - Var!able > - less than opt!mal work cond!t!ons stress a worker phys!olog!cally Psycholog!cally , , or both ways > cond!t!ons - nclude : > heavy l!ft!ng - -h!gh (RA (AH/40-1) 100 * card ovascular demad = - h!gh mental demands h!gh v sual demands + cond t ons poor sensory Th!gh phys!call stress "monotonous or ted ous work i i i i i i i i i i i i i i i i i i i i i i i - Allowances for Unavo!dable Delays (D) Factors that !mpede (engel) operator effort : > !nterrupt!ons from superv sor, eng neer, etc - problems w th tolarances , spec!f!cat!ons ; mater als + -mach!ne !nterference Unavo!dable Delay Due to Mult!ple Mach ne Interference Mach ne !nterference t me = 1X mean serv ce t me % Allowance = mach ne !nterference t!me t me ( mach ne run + serv ceo Stand T!me/Prod Un!t ·.. = Imach!ne run t me + serv ce t me + mach ne !nterference t!me product!on un ts per run t me or Imach!ne = run t me + serv ce t!me) X(1 + allowance) product!on un ts per run t me Quest!on > - meanserv!ce un!ts per run t me EXI ↳ product!on N16 1 = 20 % mach!ne !nterference t!me = 20 % X10 m ns = 2 0m n. sand t!me/prod Un!t 150 2 32 4 m nlun t +. = 10 + =. 2 4100 1 25 % %. Allowance = =. (150 + 10) i i i i i i i i i i i i i i i i i i i i i i i i i i i i Other Allowances Attent on t me allowaces · > - mach ne run t me methods must match stadods - > conduct per!od!c aud!ts - - compl!ance > Operators - > superv!sor - -analyst Learn!ng Curve Pract!ce affects performance · Sk!lls mprove w th pract!ce Learn!ng curves quat!fy decrease n task performance t me , as funct!on of task repet t on Theory : as total quant!ty produced doubles t melun t decl!nes at , a constant rate (expressed as percentage) i i i i i i i i i i i i i i i i i i i i i i i i i What · are the Charachter!st!c Equat!on of Lean!ng Curve total un ts produced * eyx = kX or logYx = logk + Nlog X c t!meto produce N" = exponent V f!rst un t pred!cted tand lagle from log-log plot of data) = prodt meme un t · 2N = rate Quest!on 2 = 0. 82 enlog!o = log100. 82 +n = -0. 2863 Yx = kX - 0. 2863 45 = 94X 0 2863 45/au 10g10(45/94) -. = y + = - 0 286310g10X. X 1 1174. = log!o 1 1174. 10 - 13. 1 = X cycles Quest!on Determ!ne by calculat!ng the area under the lean!ng curve : * + [Yx )k[(X2 Ye)" = + - (X - Y2) 3/In + 1) > - Total t me ↓ ↓ ↓ ↓ exponent that represents the me tuher slope of the lean!ng curve 1 0 2863 + 1 2863 + gu((13 - 0 (1-0 2863). -. = + (2) - (1 - ). = 768m!ns product!on t me i i i i i i Quest!on 768 m!ns/13 cucles = 58 6 m nkucle. Quest!on 2" = 0 93. nlog!o 2 = 10g100. 93 + n = - 0 1047. Yx = 4X 1047 30X0. 20 = 0 1047 20/30 y. = log(20/30) = -0. 1047log!o X 1. 682 log!o X > X = 48 1 - =. Quest!on * k((Xc + yz)" 3/(n * [YX = - (x - yz) + 1) 1) 1-0 1047 +/ + -(101047. = 30 ((48 + (2) - (1 - = 1065 9 m ns. ( - 0 1047. + 1) Learn!ng Rem!ss!on · Perf decrement due to t me away from task Amount of rem ss on s a funct!on of locat!on on the learn!ng curve pr!or to !nterrupt!on (] #of cycles · Pred!ct!on of t me to produce f!rst un t after !nterrupt!on completethef!rst un t produced upa return from break 3x = 1 + t!me for f rst ↓ cycle # of cycles to reach send t!me i i i i i i i i i i Quest!on /(au-uz(-1)) 0.2863 -Bu s - !f no break occured 3 m!nsx = 33 5 m ns , 47 + 34 y = =.. Now 11 cucle !s the new f!rst cucle of new learn!ng curve 0 2863 4x (53 3)x -. =. Unavo!dable Delay : Mult!ple Mach!ne Interference Alternat!ve suggest!on when N6 · C = T! + T2 + T3 T tmach ne runt!me/cycle k = Tat s attent on percycle/mach!ne Ege s lost product!on t!me due to nterference C + Cucle t me Quest!on when N16 I=9 5. % mach ne !nterference t!me = 0 095X5. = 0. US Stand t!me/prod un t = (150 + 5 + 0. 48)/Jun!ts = 31. 1 un!t % Allowance = [0 48/(150 5)] x 100. + = 0 31 %. When N2, 6 50([ X-jumber of mach!nes/opat sen I = + ~ mach!nerunt!me MI = Interference & as % attent on t me i i i i i i i i i i i i Quest!on MRT = 150 1 = 502[(1 + 30-+ 10]" (1 + 30-!!)3 MAT = S I = 2510 % N = 55 ; X = MRT/MAT = 30 25 1x5 m ns. = 125 5 m ns. = mach!ne !nterference t!me Stadt!me/Produn!t (150 + 5 + = 125. 5) /55 un ts = 5 1 m!nlun!t. 1 Allowace [125 5 /(150 +1) ] X 100 80 97% % =. =. MOST what are the alternat!ves to T me Study ? · - staded elemental data > Formula construct on - - predeterm!ned t me sustems -Work sampl ng · what s Predeterm!ned T!me Systems? - standard data systems for determ!n!ng stadad t mes for bas c elements of work > appl!cable to w de var!ety of manual tasks products and process - , -aka bas c mot on t mes , synthet!c t mes - some systems > Method T!me Measurement (MTM) - - Maynod Operat!on Sequence Techn!que (MOST) -Modular Arrangement of Predeterm!ned T me Systems (MODAPTS) i i i i i i i i i i i i i i i i ? · why we use predeterm!ned t me systems > Develop effect!ve method pr!or to product!on - > mprove current methods/explore alternat ves - -set t me standards > est mate product!on capac!ty - "select!ng effect!ve tools and equ!pment > produce accurate job descr!pt!ons for tra!n!ng - > n t me stadeds and - mproved cons!stency est mat ons > el m nate perf rat!ng - - update t!me staded after method changes How to predeterm!ned T!me Sustens ? · use > Select - job > Analyze elements ; record appropr!ate chart - work on > Record d!stances , parts and tool we!ghts other !nfo requ!red by system - , > system's for - Use table to determ ne NT each element -Sum elemental t mes , apply PFD allowances and result s ST est mate * most of the systems are propr!etary Systems d!ffer n > levels deta ls - on > Types of elements addressed - work > - Spec!al cond t ons -body part > - d!stance travelled -res!stance we!ght , - others -Appl!cat!on rules => Tables of t!mes for each element/cond!t!on What are the tupes of predeterm!ned T!me Systems - V ~ Average mot!on Add!t!ve - typ!cal work task performed > - Bas!c t!me + extraord!nary t me under tup!cal cond t ons requ!re -Work-Factor typ!cal amounts of t!me > MTM MOST , MODAPTS - , i i i i i i i i i i i i i i i i i i i i i i i Methods T!me Measurement (MTM) Performed m cromot ons on dr ll press operat!ons Found data to be appl!cable toall classes of work !nvolv!ng maual mot!ons" L!m!tat!ons e appl!cable when mot on t me s not !nfluenced by process Cons!derat!ons · > d!stance , tupes of reach , we!ght of objects moved prec!s!on , body posture - , and body part n mot on Vers ons · > - - 1 + most deta led cecler cal tasks -2- less deta led ; effort port!on of work cucle (m!n Mtwork!ng w!th m!croscope - > 3- st!ll less deta!l HC +health care - > -v - metal cutt!ng/mach!ne stop - ADAM : Computer system based on MTM t mes MOST What s MOST ? · > - A predeterm!ned t me system -Based Upon MTM-1 and MTM-2 - Less deta!led > Faster thanMTM-1 - What are the appl!cat!ons of Most ? > short cucle repet!t!ve tasks , to long , complex - tasks ; -off!ce work warehous!ng , , mater al handl!ng !ndustr!al , assembly,... What are three vers ons of MOST ? - ~ V Bas!c MOST Max!-Most M!n!-Most > - core of MOST system > - least deta!led - most deta!led - - > - for most !ndustr!al work operat!on occur less the 150 t!mes/wk operat!ons h!ghly > t!mes/wk - 2 repet!t!ve - operat!on recurs 150-1500 m ns > - up to 10m!ns -> 41. 6m n work s def!ned and descr!bed as the movement of objects (w = Fd) Spec!f!c stadod!ced sequences of · movement v. bas c mot on assessment Pr!mary un ts of work are fundamental act v t es ( collect!on of bas c mot ons). Cond!t!on affect durat!on of sequences T!me assessment based on 'aug sk lled operators' work!ng at on 'aug perf level' or' normal pace'.. · TMU[1 t!me measurement un!t TMU = 0. 00001h] i i i i i i i i i i i i i i i i i i i i i i i i i i i i i What are the Most Sequence Model ? -General move > - Controlled move > Tool use - - Manual Crane What s General more ? tunrestr cted movement of object through a r What are the subact!v!ty sequence of General Movement ? 1) reach 2) ga!n manual control 3) move object Get(1 , 2).... Put (3 u) ,... Return (5) 4) place obj S)return (mostly hor!zontal > - D!Act!on D!stance + B: Body mot on (mostly vert!cal - G : Ga n control + p : placement + # : !ndex value of the parameter Parameter Index!ng - character!ze the move · > 1) what moved ? - s be!ng 2) If tool , what k nd ? Is t used ? > - > - 3) How s !tem moved ? If tem s not tool that s used , and travel s unrestr cted , then General Move sequence s appropr ate -4) what does operator do to get object ? to determ!ne ndex values for ABG -!) What does operator do to put object ? to determ!ne ndex values for ABP -6) Does operator return or clear hands ? · And for method analus!s , be!n w th + 7) Is th s to do the ? act!v!ty necessary job i i i i i i i i i i i i i i i i i i i i Quest!on l!ghtwe!ght port freely , no obstruct on > - general move S gets w!th reach A no body mot on Bo l!ght object GI Total TMu = (1 +0+ 1 + 1) + 6 + 1 + 16)x10 put 10 steps away Ald bend down to pallet B6 = 410 put no throw, PI no adjust Total seconds = 410/27. 8 = 14 75. Al6 yes 10 steps , D! Bo G! Ald Bo Pr A16 put return get i i Quest!on what does operator get ? small object How does operator moxe? general move & what does operator do to get ? walks 8 steps Al6 goes through doorway B16 p!cks up small object G1 what does operator do to put ? Total TMU = (16 + 16 + 1 + 1 + 6 + 1 + 0) x10 = 410 puts wh t n reach Al Bend down to floor B6 Total seconds = 14 75. adjust P put no throw , Returns ? No Ald Beo G! A! Bo Pe Do put return get Quest!on = G3 Do e(1 1)xb] A! Bo AlBoP 3 + (1 + 160 TMUS + + 10 = return get Quest!on A! Bo Gy Al Bo Pr Do put return get [1 + 3+ (1 + 1)x6]x 3x10 = 480TMUS i i · what s controlled move ? - Object movement path s def!ned or restr!cted · What are the subact!v!ty sequence of Controlled path 1) reach 2) ga!n movement 3) move object 4) allow t me to process to occur sall!gn object follow!ng controlled move or at conclus on of process 6) return A B G M X I A get all!gn or return actuate A : Act on d!stance (mostly hor!zontal) B: Body mot on G : Ga n Control M : Move controlled X : Process t!me I : Al!gnment · When controlled move occurs ? 1) Object s restra!ned by attachment to another object 2) Controlled dur!ng move bu contact w th surface 3) Moved along controlled path to accompl sh act!v!ty Parameter Index!ng character!ze the move · > 1) what moved ? - s be!ng 2) If tool , what k nd ? Is t used ? > - > - 3) How s !tem moved ? If tem s not tool that s used , and travel s restr cted , then Controlled Move sequence s appropr ate -4) what does operator do to get object ? to determ!ne ndex values for ABG + 5) What does operator do to move or actuate object ? to determ!ne ndex values for MX1 (Move !mpl!es Mand I nvolved :actuate nvolves Mand X !nvolved ( -6) Does operator return or clear hands ? · And for method analus!s , be!n w th + 7) Is th s to do the ? act!v!ty necessary job i i i i i i i i i i i i i i i i i i i i i i i i i i i Quest!on what s be!ng moved ? several ports How s tem moved ? Controlled movement & What does operator do to get ? reachs several ports Al Bo no body mot on Collect several Gy What do to all!gn or actuate ? (1 + 0 + 3+ 3 +o + o+ o X10 = 70 TMU sweep!ng mot!on Ma No process t!me Xo 10 Return ? No Do i i i i Quest!on vazgeçmek > sum - of two stages & What does operator do to get ? reachs several ports Al Bo no body mot on l!ght object G What do to all!gn or actuate ? (2 6) X0 + = SO THUS Two stages MG No process t!me Xo 10 Return ? No Do Quest!on 3 reach A none Bo Heavy object Gy TMu = (1 + 3 + 3)x10 = 70 pushes Mz(12) no process t!me Xo Io Ag....... i Quest!on What s moved ? Pedal How moved ? Bu foot + controlled move What do to get ? & w!th!n reach Al none Bo l!ght object G How move ? Total TMU = (1 + 1 + 1 + 10) X0 < 12 I , stage M1 = 130 actuate for 3 5s X10. Total t me = 4 68 sec. none 10 Returns ? NO Ap D! Bo G! M. X!o lo Do get move or actuate return * Tool use + for use w th had tools had as tools , , or bra n as tools Maual Crane & for use w th manual crones i i i i i Work Sampl!ng · what are the methods for establ!sh!ng t me standards ? - Est mate - Records > - work Measurement techn!ques what are the work measurement techn ques ? · - T!me study - Standard data -T!me formulas - Predeterm!ned t me sustems "work sampl!ng What s work ? sampl!ng · -I s one way to determ ne t!me stadods for longer cucle tasks or low rep tasks. Jalso used : to determ!ne appropr!ate allowance percentage for + use n t me study - n safety assessment -to assess equ pment ut!l!zat!on What ? the work sompl!ng advantages · are - does not requ!re cont nuous obs -less total analyst t me -one analyst can observe mult ple operators what s the l m tat ons of work ? sompl ng · -results are only as good as collect on methodology - may not be pract!cal !f task s < 15 % of total t me What are the charachter!st!cs of a good work sompl ng studu ? > Suff!c!ent of samples - number -Samples collected dur!ng representat ve per!od -Random sampl!ng Theory · Bas!s s b nom al d!str!but!on > poss!ble events (0 1) - only two , + p(x 0) = = P , P(X = 1) = 1 - p -assume n > 30 +p s proport!on of somple possess!ng a charachter st c of nterest - mea = p -Stand err(p) = (pp/n)" i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i i How samples (observat!ons) needed ? · many are n= f(des!red accuracy , proport on of t me of task element) n z p(1 p) = - = 2p(1 - p) Aa2 (Arp)2 It s score from normal d str. Ant s absolute accuracy Art s relat ve accuracy Conf!dence Interval for · : p cl = p [2 - 42[p(1 -p)/n]" Da ↓ ↓ rel!ab!l!ty stadd est mator coeff c ent · CI puts nterval around est mate , s nce cannot expect p = P In repeated sampl!ng from populat!on 100(1-1) percent of all els w ll cata!nP · , Quest!on - - %90 20 05 = 1 645.. /s 20 25 = 1 96.. %99 20. 005 = 2 576. 22 (p( -p)) n Cux0.6) = = = (Arp)2 > 406 - samples should be collected Quest!on 3 C = p = 21 an [Pl -p!/ f the sample aug = 60 % then you can say w th 90 % conf!dence that , n the long run , de t me 0 4 42 % between " 04 36 adly w th 40 % be!ng the most l!kely est mate, f th!ngs stay the some [oux0.1062. -- 1 645 1. 645[0. 4x0. 6/406] = 36. 0 Fl i i i i i i i i i i i i i i i i i i i i i i i Quest!on ( = p = 21 - x(p(l - p)/n]" pIDa Aa = IAa = Arp = [1. bur [0. 33 (0. 67)/406]" =1 0 0384. Arp = 11 64 % wh ch does not meet relat ve (% 10). accuracy goal ↳ 1. Quest!on n = 2 -(p(1 p)) = - (1. 96)2(0 25 x0 75).. = 288 12. Aa2 10 0532. > - 289 must be collected Representat!ve Sample ? s the goal of sampl!ng study · what a work elt s to collect data that accurately reflect true cond!t!ons · Cons!der the effects of the follow!ng when des!gn!ng a study : e strat!f!cat!on -Separate dota by Strata for more !nfoldous sh!fts ) ,... -!nfluence ~ do not let obs. !nfluence what you are observ!ng -Per!od!c!ty > - can occur n work - should not occur n sampl!ng i i i i i i Data Analys!s Use 2x2 table and Ch!-spr d!str!but!on : X =n.. (Inuna-N!znal-0. n.. ) n. nz n 1 n 2... Quest!on 2 X (Innzz-manz!l-0 n ) n..... = 1452/1122 * 640-90 * God-o 5 *52)"=. 5 72. 722 * 730 S * 1240 * N.2 R. IR 2.. 212 · What are the Work Sampl!ng Data Collect!on Methods ? > - Ind!rect D rect v - n person · d!ar!es random rem nders · · v!deo · event counter i i i i i Use to Establ!sh Labor Stadods total obs of ↑ element NT! n!TR Performace rat!ng factor = > NP total operator t me n study V normal elemental t!me ( Total prod for obs. Fal. to per!od obs. n study OT! = n!T NP ↓ observed elemental t me NT! = OT!R ST! = NT! (1 + Allowance) ↳Stadedelemental t!me Quest!on 107 235 2400 ⑳ toplae OT! = (n!T)/Np ST! = NT! (1 + Allowace = (107x2400 = 0 9629x(1 09) 0 9927.. =. 235x1100 = 1. 0496 NT! = 0 T!R = 97 0 9927. x 0. = 0. 9629 i i i i

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