Work Sampling Defined. Work Sampling. When is Work Sampling Appropriate? Historical Notes. Example: How Work Sampling Works.

Transcription

1 Chapter 16 Work Samplg Sectos: 1. How Work Samplg Works. Statstcal Bass of Work Samplg 3. Applcato Issues Work Samplg Work Samplg Defed Statstcal techque for determg the proportos of tme spet by subjects varous defed categores of actvty Large umber of observatos are made over a exteded perod of tme Statstcal fereces are draw about the proporto of tme spet by subjects varous defed categores of actvty Subjects = workers, maches Categores of actvty = settg up a mache, producg parts, dle, etc. For statstcal accuracy Observatos must be take at radom tmes Perod of the study must be represetatve of the types of actvtes performed by the subjects Hstorcal Notes Whe s Work Samplg Approprate? L. H. C. Tppett troduced the techque of work samplg (197): sap readg method sapshots to observe the actvty (uptme vs. dowtme) of the looms R. L. Morrow- troduced the techque US (1941): rato delay study Delays durg producto C. L. Brsley used the term work samplg (195) Suffcet tme should be avalable to perform the study Several weeks usually requred for a work samplg study Multple subjects Work samplg suted to studes volvg more tha oe subject Log cycle tmes for the jobs covered by the study Norepettve work cycles Jobs cosst of varous tasks rather tha a sgle repettve task Example: How Work Samplg Works A total of 500 observatos take at radom tmes durg a oe-week perod (40 hours) o 10 maches wth results show below. Category No. of observatos (1) Beg set up 75 () Rug producto 300 (3) Mache dle How may hours per week dd a average mache sped each category? Example: Soluto Proportos of tme determed as umber of observatos each category dvded by 500 Tme each category determed by multplyg proporto by total hours (40 hr) Category Proporto Hrs per category (1) Beg set up 75/500 = x 40 = 6 () Rug producto 300/500 = x 40 = 4 (3) Mache dle 15/500 = x 40 =

2 Work Samplg Applcatos Mache utlzato - how much tme s spet by maches varous categores of actvty Prevous example Worker utlzato - how workers sped ther tme Allowaces for tme stadards - assessmet of delay compoets PFD allowace factor Average ut tme - determg the average tme o each work ut Tme stadards - lmted statstcal accuracy whe stadards set by work samplg Statstcal Bass of Work Samplg Bomal dstrbuto, whch parameter p = true proporto of tme spet a gve category of actvty There are usually multple actvty categores, so we have p 1, p,.., p k,.., p K proportos for K dfferet actvty categores The bomal dstrbuto ca be approxmated by the ormal dstrbuto, where µ = p σ = p( 1 p) Alteratve Parameters The parameters µ ad σ ca be coverted back to proportos by dvdg by the umber of observatos p = σ = p µ p = p ( 1 p) Estmatg the Proporto p I a samplg study, we let pˆ = the proporto of the total umber of observatos devoted to a actvty category of terest The proporto pˆ s our estmate of the true value of the populato proporto p We would lke to have a good estmato of the true value, whch should be ubassed There should be o bas (e.g., f the huma subjects ca atcpate whe the work samplg observer were comg, they may be cled to adjust ther behavour respose). To elmate the bas by radomzg the observatos Should have low varace Ths ca be acheved by creasg the umber of observatos. Cofdece Itervals Our am s to estmate p wth a defed error rage at a cofdece level Cofdece Itervals Ths ca be rearraged to the followg Pr ( pˆ zα / ˆ σ p < p < pˆ + zα / ˆ σ p ) = 1 - α The geeral statemet of a cofdece terval for relatve to p ca be expressed as follows pˆ Pr pˆ p z < < + α / zα / ˆ σ p = 1 - α The probablty that the actual p les wth p-z*sgma ad p+z*sgma 007 Pearso s Educato, (1-alpha) Ic., Upper Saddle Rver, NJ. All rghts reserved.

3 Number of Observatos Requred Ivreasg the umber of obseratos creaases the accuracy (?) ad the precso (?) of our estmate. But observatos are costly. So here comes the queato: How may observatos are requred to acheve a gve cofdece terval about the estmate of p? We eed to decde two parameters: 1. Cofdece level 1 - α Ths allows us to fd the correspodg value of z α/ Number of Observatos Requred Gve z α/ ad c, the umber of observatos requred to acheve the specfed cofdece level s gve by the followg ( z ) pˆ ( pˆ ) / 1 = α c. The half-wdth c of the cofdece terval, defed as the desred acceptable devato from p Thus, we have p ± c Example: Determg the umber of observatos Prevous example. Determe how may observatos wll be requred to estmate the proporto of tme used to setup the 10 maches the automatc lathe secto. The cofdece terval must be wth ±0.03 of the true proporto, whch the forema tally estmates to be pˆ =.0. A 95% cofdece level wll be used. Use of Work Samplg to Measure Average Task ad Stadard Tmes Work samplg ca be used to determe average task tmes ad stadard tmes. However, the stadard tmes obtaed by work samplg are ot approprate for wage cetve plas. Soluto: z α/ =1.96. c=.03 =1.96 (0.)(0.8)/0.03 = observatos are requred ( z ) pˆ ( pˆ ) / 1 = α c So use work samplg to measure the stadard tmes oly whe other work measuremet techques become mpractcal e.g., very log cycle tmes, orepettve tasks Determg Average Task Tmes Example: Determg average task tmes Average task tme for a gve work category s determed by computg the total tme assocated wth the category ad the dvdg by the total cout of work uts produced by that category p( TT) T c = Q where T c = average task tme, p = proporto of observatos assocated wth category, TT = total tme, Q = total quatty assocated wth category Cosder the example slde 5. A total of 167 uts were completed by the 10 maches ad that a total of 3 setups were accomplshed durg the 5-day perod. Determe (a) the average task tme per work ut durg producto (b) the average setup tme. Remember that proporto of observatos assocated wth category rug producto was foud as 0.6. For beg set up t was Soluto: TT=40 hr (10 maches)=400 hr (a) T producto =0.60(400)/157=9.16 m (b) T setup =0.15(400)/3=.609 hr p( TT) T c = Q 3

4 Determg Stadard Tmes Whe the purpose of the work samplg study s to set tme stadards, the aalyst must rate the performace of the worker durg each observato Frst determe ormal tme for actvty p T = ( TT)( PR ) Q where T = ormal tme for work ut assocated wth actvty PR = average value of the performace ratgs for all observatos category, The determe stadard tme T std = T (1 + A pfd ) p( TT) T c = Q Defg the Actvty Categores Some gudeles: Must be defed to be cosstet wth objectves of study Must be mmedately recogzable by observer If output measures are cluded, the actvty categores must correlate wth those measures If more tha oe output measure, the a actvty category must be defed for each Helpful to lmt the umber of categores to te or fewer Work Samplg Observato Form Schedulg Observatos Preparg a schedule of radomzed observatos Improve the statstcal accuracy Reduce bas Samplg stratfcato: Total umber of observatos s dvded to a specfed umber of tme perods so that there are a equal umber of samples take each perod Observato tmes perod are radomzed k k s Reduces the varace ( Var( x) = s vs. = W 1 ) s :sample std. dev. perod, W : proporto of samplg perod ad s <s for all ) Example: Geerato of radom observato tmes For the mache utlzato example, geerate the schedule of 10 observato tmes for the frst day. The shft hours are 8:00 a.m. to oo, the 1:00 p.m. to 5:00 p.m. Soluto: Geerate a set of three dgt umbers betwee 1 ad 999 (usg a pseudo radom umber geerators). Coverso of umbers to clock tmes Numbers wth frst dgts=8,9,1,,3 ad 4 are read drectly as the clock hour Numbers wth frst dgts=0 ad 6 are read as clock hours 10 ad 11, respectvely Numbers wth frst dgts=5 ad 7 are dscarded Numbers wth secod dgts 6 through 9 are dscarded 4

5 Advatages of Work Samplg Ca be used to measure actvtes that are mpractcal to measure by drect observato Multple subjects ca be cluded Requres less tme ad lower cost tha cotuous drect observato Trag requremets less tha DTS or PMTS Less tresome ad tedous o observer tha cotuous observato Fewer aberratos tha short-ru observatos Beg a subject work samplg s less demadg tha beg watched cotuously for a log tme Dsadvatages ad Lmtatos Not as accurate for settg tme stadards as other work measuremet techques Work samplg provdes less detaled formato about work elemets tha DTS or PMTS Not proper to set stadards for cetve pay systems Usually ot practcal to study a sgle subject Sce work samplg deals wth multple subjects, dvdual dffereces wll be mssed Workers may be suspcous because they do ot uderstad the statstcal bass of work samplg Behavor of subjects may be flueced by the act of observg them 5