Table Of Content‘The Bell System Technical Journal
Vol, XX tober, 704" Nog
‘The Reliability of Holding Time Measurements
‘By ROGER 1 WILKINSON
Te Ponts ro we SoLve
ONE te fn quai i rte engonerig he rae
lwation of aubaevibrs" cal. This figure ia scone titied by
the sverige number of cll exporced over a aSvon rate in am haat, abd
Ade by S00, zee the te Ton submited fn avecaze simulans
talle—or “the average” as it's commons calle. Tables and curves ste
‘widely avaiable whieh may then e cone fod fond the numberof pate
to be provided so that ao anre thea edested snl percentage of he alt
cated wil Sod all pate busy
The roe messurerent of cll lngths with stop watch occurs ce abe
oe bring the simplest mea fer obaing a sample o!holing times Te is
Edam used, however, due to the 2eauive simeess wih which ange
‘urmber of observation are accurmlaced coupled with the no inconsierable
expense of the small army of observers reed, each looking at one cal
A secon ect metal of taining hing tine enenrerens ft by
coving mecsnialy or electrically the length ofeach eal passing over
frowp of svitcken or Urns vlrig a era inteealof ime Warooe
Fran ine ere ale" ling thi ici Ben ued
‘oreo lees extensively ia he Bel System Tete dialvartage his
Tein fn requiring coneiderable time ana labor for summarising the reels.
roblems tthe perfect metennnee ofthe messing eqhipment have al)
ovrake pli ny api accanultion af ig ime a a
onder meer of valle relively igi exprse, the meted
fortch or plag counts has heen intraday, This cones fn scanning
Imerenialy, ela, hatageapialy ve Ly eye Ue gro tn a
oul terval aa revving each Cine te number foal Ty Sach
‘ats pve estimates immestely ofthe average la beng exis by
Snead ot thor We dmg ck has sph tg ee
7 noid SYSTENE FREHNICAL JOURNAL
reluvelystspleanalyis x caste of che reliability of sich an exile
fan's oblatwel. Elin editor tor ihe seme peed a record ie kao oa
fall ox parent eter ofthe mer of calls pacing over the group, St
te pomible asa to abten estimate othe sverage rll holding ie and the
relniy a auch an average
Direct mwinnesceat of Holling in a enitch counts sould nacurlly
tue mule ov groupe ving pois which are presi typi of those
overt which te sogineeing > ltimately crete. wally, although
Tot always, ih’ il oe che Insp ut buest owe nf che day duriog chr
Fo seas f te years Fx tdes to did iteligenty bow lag a pera
teed tobe stad fs say gin re some hnuwleegs ofthe persistence of
the same hing. sae universe is aecessey. This mht be obtained
Utena relay eal Hodge samples made n she Irs of interest
tery day for evesl weeks inthe any season, If spetines or “ack of
once} y ret aaezeat, txe problem wl be eomyaraively spied
Teme are peetent, hoveven wil be severe to Tnvestgste thir
natinefauch ae weber som one Hay oF the Week shows high holding
fine) ant apportion the main sanpling peoswlare ib s fashion to give
‘hese pecliartis wie proper weaning
Te wil be of iter rennin i this esptcovtain fied data at
tan taken by the peu teeter mele some sees ago om an ine
tbuak group 0 Newstk, New Jerwy. The kind af examivation mak
Tete wl sot to fate the proatne ich mr he fend wuiable fe
come degree for applistion ler groups whose raracterities are
relstivey lle knoe.
11 -Pwmunencany Sruow or Niwas: Dasa
1s lng Peon Kurt shat el subse el Bodog tines fllon
remarkably cesly she vtple exponent requence estiba ian
Hoa
ws
1
where}
Ue average holding ine? This wos found tobe subtansally
nae of he data colacted oi Eke toni: crane yeoup in Newack a6
own in ig. I for 7485 calle oberon] i 19 nts bsg soads fn the
Taige 150 Io) average siustenenes eal, The Gt of che ex>entia
fave having a aveenge equal to Use oseved average of 2.380 einates it
Seen to be site good. It miy be futher nosed that jp the exponential
Alsurbaton the standart deviation, o, equa the mean 8, In practice ©
3, Be urn an ta, ite hg oe ais
riick ei i hese
is usally fit be lightly Tage than #altbough nt marly ss We
tray use this inorttion to Yo! te Iomagencty ofthe Folin Lime ani
eve shuld al oars of theca le inuped indiscriminately
zs, .|t
oo [Brea Ber Bf obal shal bal nds hs
nie Tandon big. Zane shown thebleling time averge Jor: $8 hours
tigeroal at varnye tinee Pe fay aver 4 peroe af Satis. At es
rater citinet groups those bofre noon
1S rs bace wn be onsen
face deve apes i fai
fod thse ate wou, If
Heinng « hoaogencous group, cou these ling Lime avers aed in
te nfernon be seasonal cousidered 1 cong ron the samme waive?
We fst nd the average bolding eime of the 18 forennon lunes to he
SS seconds. Since these hours aver! sin = 380 ral each, the
standard deviatia of the esas or shoal by theory, be eee
: a
i :
"he stator devas csorve i926 some 2% high, whi, ever,
sgrass wih the observation male be provioae paras On the
Tiypothass hae ivese of 1S ea hours hoe the perameses of
485 and » — 1.20, este thatthe ubssrvatis foreach of hese thnce
lock hocss could wey have womres The devitns of ter wwomnges
from 1188 axe 19,17 and 25 wero, respetively, and acorn thee
onthe conepanegstendel sn thee averages ane (= 22)
tan (= 22), ana tare (= 222) aut devia a ihn
ins the ancl eeu the asm ren ofthe Meg tc
‘The remsning2stecrstina tom non on ower age IL
Seconds afte il sony vec fn he tee oa
eee isu sin oe eg 1855 by me oe sey hee
assis snes she ston’ ein, stone indicating icant ifr:
nee hrimees te forenoon sl setzen hong tines. We conte hat
fetes ® aan. and nook. the holling net ate sat'sfactriy romeo
Nat that shnlem-atept ¢2 orale servations an afe-noon ho
wilh thea. Since he Feav est load her occured gener! inte moe
Mee sual conine ov dst migayremes oe switch coat 1 Hes hrs
Ine eerining the engicerizg told time
“TLiny ceeasonally bw wil to jvestgate the possity that restain
ddaysol th nees have, othe avenge anger holding sires than oer days
ifthe Newer +72 aan. data are ote by days of tae week a in Fig. 3
We see eh the averages for soca day Aceon coserably ux aon by
the Rey dot, cet Tse pnts che slit average ui thee For
ac day's hour taken asus eatimate of the standatd deviation of the
Fmoseecous universe fay nbc al fe houea se esac to hed
Then wit che weigher aithmet's eae uf the dliy useapes the bs
resinassavolable nr he aca of the iver caca day's average ened
hate eer it ool eeagosebly have ato from The 2x Hinge
rhies shook ichate ste 95% of the sy-averages are shen Fi 2
Thisscen that fo uf the six points alls ly alse thee its ndeat-
jag mvlerely sigoicent ieneace inthe Noting time conditions for
eign Saturday” Th sampling procedare te fli in such eases of,
mottled populations swt rigorously deizable. However, it or
thatthe amples shoal be dra fem the vsiousgecups of corti
tlewents hth polly go to eke op the unibsse ae oughly in se
prt to tac importa lobe agsigned to eaca each gro. Ti out
nimple bere ne sovlepesably at to aw samples 2 seat eoval x
rom the cali of eat week ey Go the wee,
inal there amy he ne quent tt a oy soy Ht eagle
tnd stabs Pliting of the some da foe she S-42 am, hours as in
1g 4A aed 48 yl el toile heels ‘The moran boul
sine averages for ech dof the week re plot el for several nek daring
he eurpecto: bury sezsor, Wide changes ir the led tough the passage
a
ig. t-Seapna end ie ing iver, 089 12 at ry, Neve
vcr ee mat by eye. Ta th case stated there appears no
onshterey of maven. cApplying the dentcl te: used in te pesious
rages far the dey-of Bowed eae, e Lad in Fig. AC that a the
Frat five werk peta uo movemen:s af saieanse took pace. Taweves,
Ve sith works nit allay! th Bits Beale an fatetval af bow
4 we, Sted = egioant crop suggesting the «proach of a ower
level of cic, "The tric engine would probably Gee to dehecule
Tong time obscretions tri he mae barbers ore to ive inlunve
‘ving determined sething at he chasacter oF the being ise
Lue if enys nity nour of the day, ih ays of the weak, sd seo
Shake year thetic sine ia bette pw ta ou a program
for sampling, He sll eexally want 2p eppertion Cae Uta eample be
teen the tours of ss nlc show sgniount difeseaces amang trem
Sie roi pooprtcn co the relive ras ng wt chose levels
"The les epee infra aa the tafe Tow curators the more
importans it wil he to sped she abeerations over © verity of hous,
fy or wecks
TEA Syrnsracroay Sante oF Dusgeriy Migsteyn Horne Tawes
The etandord deviation # of ivi ell eng oer, we can
‘estimate the sandler ofthe sverngr of measurements a
©
Since wll lly be several hurdnl we ex abt a good gue for «
by caleletng the standard deviation, Sof the 1 observations. 8S ples]
bre for exert ene hos Tl het fat Brom the average Wing
tine f wie may be subsite for w Hf great accuracy isnot eeuee
Thetis sapling ie repeeataively ce froma wn ese noe sly
Ihomogeneous, te eter hy fet ¢ tony be theater hat ofthe
Mandasd éovation found in the aap singe in wo sed Puesor Sampling
It stele but norhomogetacks univer ve suadayd eto of the eerie
ay bo somenat reduced fom SV
‘We may now mike: the sstemen that i ge the probity tat
thetrucaveragholdingtine dst die ms thas obsered by more than
zc 1 second, where Pao ee yo inthe table below.
or example if we hove mesnated she indvidoal lege 0 0 calls which
show an average of 130. seconds, wane ten 9% sue tha: the tree
Ftng time necro: Ue sap univer Fs lovely wich the sage
16033
yon
1503 2816
tot fs Intaaen 1574 end 1642 seconds, (The bees singe estima, of
owrse, i the observe! aversor of 1803 esconds;) Oe eouversy, if one
‘Hou desice to determine He tue average Ping te within 8 seconds
wvtha suregy of = he nay taco agprosimate value af the standard
evita for the evermgr holding time) based ox pase experienre
sate = (ef,
to sbtais the number uf cll o be musi Tht — 180 seconds here,
noma
The sare information is satan fa Tig. $ whit yes tbe po cot
ron #102, in seiner vedaverege not exer wil probabil?
TA thsi based on Ue asonplion shat ach of Ue cal lengths 5
aceurae enough messared sta te appre eros ateduced for
thossouee,Obsiosl then: in point n expen meh cEOr in ear
{ally “weveationing” a sample we ae t be representative of she vagatee
ofthe universe if enh he calla 9 chown ero py accurately meas
trol, This monte nuit as fate as mewsring very accurately the
Ihling timer a cubes of eal’ chosen during seme tort tie pein
Unhien right Lax out be ely we pia! oferta ef hn meta
Dedode niceties les Fo ese ivot meceuresent ces tll
probably he ele sasicacory H eae als menses ith a anion
ror of woven onectent nf JPV/e. Tn our exe 900 calls tis
‘youl be ATT seconds, thet ie reanement of each cal to the nearest
second
WoMosowe Tins mY Somes: Causes Micros
Wewh ei’s holding ine east sneak mde acuracy it
ie tmumatiete'y ear that addons calls must ne alnerved “h onder
fonupersat three, This tae sition sn ce seed of site events
fe isin eet a sean for noting eeguarntervas whether particue
Ter eal docs oro not exit. Thue nome f tbe eal ere at all ely
Ineasureé forthe ladidual lente. tbe eos wil ko hve bn Be
Tinidesed sino at the ginning of the period some switch exmts are
evitably inluced ox a aazier of wall fom the seceding hour al st
She enn! Fe peri some of oh eas ry stacd op che peg runt meter
‘ellen leyond the por with else pet of ses proper cuss.
Sewrreu cheve ave inthis etl tae dstinet rem of Balding te
(ror wine tags we sal proceed to investigate in tara:
bh Erma tthe wm of he servation pero
1h Mire athe end of the siervation period:
Rens the bognning snd eed af sc cl
