Moving Average Charts

Moving Average Charts - MOVING AVERAGE CHARTS Advantages In...

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Unformatted text preview: MOVING AVERAGE CHARTS Advantages: - In situations where data are collected slowly over a period of time, or where data are expensive to collect, moving average charts are beneficial. - - Moving average charts can help bring trends to light more rapidly than is possible with conventional charts. - Moving average charts use the central limit theorem to make data approximately normal. Disadvantages: oAdjacent points on the moving average chart are not independent. Therefore, runs tests are not valid. -There is a tendency to forget that individual observations have more variability than do the averages. SPC-OQD WWW—m SlaLlSliCEtl Process Control © 1991 Eastman Chemzcal Company 21 1 Control Chart for AIM/i EXMPLE AMA & MR CHARTS - Calculation Worksheet n = Number of Measurements in Moving Average = 2 MR = 1 Current Measurement — Previous Measurement I ‘ =_1mmmmas__ =*__7__‘i.7__ = - R Total number MRS 20 3ng f =__'[01aLoLMeasuremenis“_ = 9C; 85 Total number of Measurements 2 ( _ . UCL MR = 3.267 X R ' LCLMR =7- '0 = 3.267 x 5.3385 = 3.02 UCLAMA= X +3 LCLAMA‘-A=- Y — 39E ﬁ Vﬁ t’ﬁ 5.5.3 v—T‘ UCLAMA = 9285 '+ 3( 2.50 1' LCLAMA = 9285 - 3% LCLAMA = 9255 - 3( 2.50 V ) UCLAMA =‘2‘28S + 3 UCLAMA = 57285 + 7.5 ' LCLAMA = \$285 — 7.5 UCLAMA = [07 3.5 LCLAMA i 92. 35 SPC-HQ Statistical Process Control © 1991 Eastman Chemical Company 213 22 23 17 18 19 20 21 .— — = = # a = _..""""""... m = a = = a = 15 16 l .- - - - — -—n— — a _ — — m _ — — _ a u — _ u = m ﬂ _ = = _ w = h. — _ _ m w _ H — — _ — -— “ ﬂ — _ — _ _ _ * “I — _ — — — _ — — — m — E: E: a mummnmnunmmumunnnmmmmn Illllllllllllllllllll IIIIIIIIIIIIII1||||||||l||l|l1||||Illlllllllllllllllll nnnuuummnnummmn |||||||||IlllllllllllllllllllIllllllllllllllllllllllll IllllllllllllllllllllllllllIIIIIIII lllllll|||IlllHlllllllllllliigllllllllllllllllllllllll llIllllllllllllllllllllllliiﬂillll illlllllllllllllllllllllllllllsllllllllllllllllllllllll mummmmmumumm llllllllllIIIIIIIIIIIIIIII!!II.a' llllllllIIlIlllllllllllIIh:!llllllllllllllllIlllllllll muummmmnnunmum '2 lllllllllllllllIIIIIIIIIIIIIIIlllllllllngu “"3! 1" nmnumnmmmum"1mImmammmm IllllllllllllllllllllllllllEll: mmmmmmnmuummum"mummm ||I||l||l|l|||i§lllllll!!!!!lllll I||l||||l|IlllllllllllllllllllIllzalllllllllﬂlllllllll IIIIIIIIlllIlIIIlIIIIIlIIIImlllll III a IllllIIIIIIIIIIIIIIIIIIIIIIIIIl|i§ll|||l||||lJIIIIIIIII llllllllllllllllllllfﬁiillIlllllll III ~ ll||||||||IlllllllllllllllllllIla lllll|||llll|l|||l||hl!!llIllllﬂl IIIE u» IIIIIIIIIIIIIIIillllllllliilllIllllIIIIIIIIIIJIIIIIIIII IIIIIIIIIIIIIIIIIIIIIIIEEEEillllﬂl III w ummmmlunmunmmmnmun«mum Illllllllllllllllllllllllll1mm! Ill ~ lllllllllllllllllllllllllliﬁllllllIIIIIIIIIIJIIIIIIIII |||||llllllllllllllllllllllllllli'sl vIlIIIIl||||||||1ll||||||Ill|||lllllllllllllll1||||||ll| lllllllllllllllIllllllllllI 1 MA EMA/1&5 — § ||l|||||||||||IIllI|III|I||||l|l||||||||||||||||||I|ll| lllllllllllllllllllllllllllllllllll "" llllllllllﬂllllllll IIIIIIIIIIIIIIIIIIII! lllllllllll Illllllll|||||l||||l|||l.!l|||||l 4!! 1| "I ||||llllllllllllllllllllllllllltalllllllllllllllllllll ||l||||llllllllllllllllllllIlllllzi "‘ ~ “""lllllllllllll |lll|l|||||l|||l||||||||ll||||fluilllllllllllllllllllll ||||||||ll|||||..::!!!_ . . III'" III|""' "‘-' IlllllllllIllllllllllllllllllululll|||||||||l||||||||l Illlllllllllllsmlllllllllllllllll ‘ ' '°= llllllllllllllllllllllllllllF" - I. .1“ III e ||||||||l|lII||1|||llllllllliiilllll||l|l||||l||l|l|||| ||l||||ll|||||lll|l|Illllliiii’a III a |||||IlllllllllJIllllliiilllllllllllllll|||||l||||l|||l l|||||||lll|||l||l||||||l||Iliillll :1 H I! 107. 35 10 «- UCL CONTROL CHART FOR N I c < . E < Measurement X SPC-HB Statistical Process Control © 1991 Eastman Chemical Company 212 9 / SEecial TQE'cs Concerning Control Charts for Measurements Moving Range Chart. When a Moving Range value falls outside the range control limits, it is an indication of a sudden change in the series of Individual Values. This identifica- tion of discontinuities in the original time series is the major contribution of any Moving Range Chart. I 9.4 Control Charts for Moving Averages Some authors suggest using Moving Average Charts with Periodically Collected Data. These are essentially ordinary Average and Range Charts constructed using a m0ving subgroup of size two or larger. " EXAMPLE 9.4: Moving Average and Moving Range Charts: The weights of the first 45 sequential batches run during one week are shown below. (The time order sequence for these values is given by reading the values row by row.) These values will be used to obtain a Moving Average Chart. 905 930 865 895 905 885 890 930 915 910 920 915 925 860 905 925 925 905 915 930 890 940 860 875 985 970 940 975 1000 1035 1020 985 960 945 965 940 960 920 980 950 955 970 970 1035 1040 The only unique aspect of the construction of a Moving Average and Moving Range Chart is the construction of the moving subgroups. The first 14 values are arranged into moving subgroups of size n = 2 below—each value is written down twice on a diagonal so that it occurs in exactly two successive subgroups—then averages and ranges are computed for each "subgroup." 905 930 865 895 905 885 .890 930 915 910 920 915 925 860 \- \A N N ‘1 \a \a \L N \A N N \A N 905 930 865 895 905 885 890 930 915 910 920 915 925 860 905 930 865 '395 905 885 390 930 915 910 920 915 925 860 905], 9301 8651 3951 9051 885i ssoJ, 9301 915], 910], 9201 9151 9251 860 m2 " 917.5 897.5 880.0 900.0 895.0 887.5 910.0 922.5 912.5 915.0 917.5 920.0 892.5 mR 25 65 30 10 20 5 40 15 5 10 5 10 65 With a Grand Moving Average of 936.08, and an Average Moving Range of 27.84, the limits for the Moving Average and Moving Range Chart are constructed just like those for an ordinary Average and Range Chart with subgroup size n = 2: (See Exercise 3.3 for the computations for these data.) For an n-period Moving Average each value would be written down n times on a diag— onal. When n values are stacked up they form a moving subgroup of size n. Then the average and range are computed for each subgroup and these values are plotted on a chart with the usual limts for subgroups of size n. 219 Before a Moving problem will have to persist for at least 1: time peri— hart is still available to detect sudden changes in the as the size of the moving subgroup increases. ...
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This note was uploaded on 02/20/2012 for the course STAT 513 taught by Professor Na during the Spring '11 term at Purdue.

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Moving Average Charts - MOVING AVERAGE CHARTS Advantages In...

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