Question

The data below provides 71 samples of size 8, collected each hour, for a particular process.
a. Construct an X-bar chart for this process.
b. Does the process appear to be in control? Why or why not?

Hour Sample 1 Sample 2 Sample 3 Sample 4 Sample 5 Sample 6 Sample 7 Sample 8 1 98.2706038 98.82376357 101.8175074 100.1819029 102.9593775 101.1650034 95.25956892 98.97423155 2 100.7165664 101.8866288 98.56812516 98.77126304 101.8273173 98.20298422 101.6974716 99.63706154 3 98.99219967 101.984498 103.78587 97.94211132 100.9617896 102.5191448 97.33630733 101.6475776 4 103.24791 97.55057498 105.5941664 99.39358454 99.57921887 95.39694094 96.26236776 102.5666208 5 100.4029778 99.99953877 100.1253952 100.2100284 93.46717444 103.2010862 100.1246523 101.0385153 6 97.26686514 101.0598371 96.30829188 100.2401539 98.07447138 97.92167369 102.4082826 104.0686054 7 101.2242855 98.17465897 99.66764992 101.1059686 100.2891162 99.37136041 99.33442195 95.24574371 8 99.77303897 95.70567938 99.56149874 99.8988347 100.3117039 104.1330379 100.4444886 96.28673613 9 98.51186097 99.89239257 101.3761752 99.76018753 101.5631502 97.32040518 99.62124507 101.4165818 10 97.40903569 97.85004715 101.4200275 103.6547719 96.49856732 101.3962486 103.8804619 98.63671523 11 96.39459864 100.6757971 97.70221412 100.513671 100.5532008 102.7289451 99.08573642 105.709846 12 101.7456406 96.83618291 94.44251612 97.85219388 99.54752399 100.5065697 100.6628148 99.45919381 13 98.58297389 99.37053146 104.252266 101.7385807 96.27683972 97.96552855 102.3757957 99.04239482 14 106.8022265 102.2631527 100.8817948 99.15057321 98.48410765 101.0200418 105.0316759 98.64720696 15 100.7582166 103.742101 101.3377802 96.83202722 100.0421767 98.52132761 101.8445345 99.04535216 16 98.10538615 98.66564138 100.9444537 102.4100505 96.0830289 102.7917916 99.98628123 98.99988937 17 103.6664784 96.52341015 100.4978431 98.04449497 97.8276468 97.66326342 100.1405569 97.06758739 18 95.80096609 101.6905767 94.25367112 100.8360452 101.2347141 99.12823561 96.37774204 102.362566 19 104.6946292 98.31209069 101.0961888 103.2778116 102.0372018 99.48104265 103.9553887 99.89743513 20 96.40131591 101.3302551 95.84263605 97.12325069 96.16702611 99.7781199 99.36178571 102.9638062 21 104.8332557 101.8307775 102.5232992 101.1724849 97.85494184 99.9928349 99.60556627 101.9793987 22 101.5345348 99.93627189 103.2219646 100.0913857 97.8309604 101.4186234 101.8196353 100.4320505 23 102.492304 101.3525291 100.6560304 102.4467514 98.51498687 103.7650343 98.93916411 101.788599 24 101.8645518 102.3892203 101.9556306 98.28115632 101.8674515 102.3591568 98.55104523 97.54604529 25 97.38709719 96.5379453 101.7044044 99.72933943 100.828553 98.92170392 98.66198644 96.42026858 26 104.7386322 95.9637167 94.82859101 98.12525606 99.97113498 102.0262011 96.70268358 101.4762866 27 97.06819918 98.05796775 102.581173 101.7291403 101.9755883 101.8436642 101.9910356 98.52464452 28 103.1858633 101.875788 100.3557594 98.92471984 102.8585904 98.52860847 99.32713943 100.3410638 29 102.8074539 99.30524918 94.27103178 100.9363031 96.07426746 101.0718324 98.2731647 100.2667856 30 104.8592182 97.2180049 101.6675547 99.66650426 98.74929313 94.5155631 102.3439206 96.32073441 31 99.36157951 100.6845048 101.4020707 99.05658032 98.56996171 98.93306309 99.05895231 99.03324453 32 100.453053 108.1833451 100.4287802 100.0406513 101.1225455 99.60023636 101.4441209 102.0343384 33 96.20746234 104.1242036 104.3560713 96.35778147 96.75211857 102.9711076 105.3723434 104.3744915 34 100.9543646 95.77275807 99.46296257 100.1842564 95.99310829 100.439805 96.46211399 105.2955631 35 98.619124 97.44377174 99.70614652 97.57414837 98.4496318 105.0704723 99.88174377 95.71377611 36 101.0768453 96.96341976 95.47181328 103.1428992 99.51492788 98.97972365 101.7291115 98.1494432 37 100.8599869 101.3455167 102.3111811 96.92307443 102.856713 100.1749513 97.53712781 95.36834801 38 97.53464811 97.8973198 99.18325573 98.67257248 100.7652568 102.2141554 101.2532028 98.36649719 39 102.5722413 101.4977671 99.06005734 95.79318112 99.73084305 96.9672188 102.4798223 99.95306137 40 99.13743349 99.28211638 95.1161705 100.363982 98.43017072 102.8944745 106.2915948 98.29997788 41 104.2666031 99.54083884 99.90148199 99.99488878 100.2584995 95.37964037 101.267824 101.4861889 42 102.7377043 95.22235215 100.7771603 96.61498832 98.8180775 98.72812379 98.5343944 97.65000837 43 105.353115 102.4029538 103.6311595 98.92174017 100.7062604 100.2540447 103.137895 102.4650586 44 97.90455832 101.7891934 101.7635709 100.8806995 99.2074673 101.6256524 102.6157196 100.9971793 45 101.1476844 102.9196757 98.94043407 100.5751682 99.42878267 102.8835816 99.46740801 102.718272 46 104.5045467 99.26291845 99.73354386 99.29556655 104.0631678 98.04755284 100.3140952 102.5256444 47 99.64085571 99.70559193 98.8232538 98.34415757 97.0835237 96.05699418 99.22825562 99.26170452 48 96.46623674 98.81790106 99.91357104 98.58322554 100.5280378 100.7109215 104.6070369 97.85396221 49 100.8657207 100.7770138 101.889217 99.8225421 98.59892488 99.59114279 101.8446459 100.6279773 50 101.8818265 104.0056626 100.3508485 104.0443672 98.6857676 99.46324297 98.93001329 104.461225 51 97.97619858 102.4055189 96.77656484 95.0922328 94.90316043 101.1444759 101.7137542 96.51593927 52 97.82241398 99.32468628 96.94652737 97.02025886 99.4890516 97.46608283 102.5428186 102.1027201 53 96.70366343 100.9481098 103.4955744 98.47828885 100.923478 100.1111931 100.2796099 102.9399032 54 101.0272156 100.9613813 97.92579672 99.82994165 98.98767401 101.3471881 99.64265028 102.2260821 55 98.26758647 101.1623982 99.4472615 99.6153919 95.84410589 100.3465516 106.0983734 100.4811268 56 95.1164097 99.16032737 100.2412657 98.18446991 101.5418866 97.85927472 98.24981407 95.03113152 57 100.7369839 101.9534205 105.636101 98.08757378 98.60521742 97.2203308 99.22599998 104.0419362 58 94.84039126 103.8270428 96.36710064 106.1870564 97.55289322 102.838836 97.33016926 96.64258099 59 103.7570767 96.5856266 97.3017027 102.0926308 102.6591282 103.1403063 104.1112758 96.84436051 60 96.70443779 105.8082799 100.5207127 99.25265956 105.1689897 98.77932734 98.57108568 97.31019189 61 102.8221237 101.82884 102.9848903 102.0587414 95.68600843 105.172471 101.5114534 95.9885082 62 100.3686663 101.2092026 101.5138226 98.17100602 100.7285695 100.0912466 104.1478307 103.779175 63 97.5752229 102.5880973 98.06316933 98.75004889 97.81445747 95.77741616 102.6108398 101.431112 64 98.09836418 99.60905667 98.49079469 100.0788319 101.3902363 102.4042617 99.45988925 99.32374174 65 100.770702 99.41703386 99.20331209 103.5468818 98.60531394 102.2735879 96.10456993 98.83456011 66 100.6227418 98.56945846 98.43058002 106.7361416 96.13946085 100.1428616 100.486599 93.70725843 67 99.61175491 100.3427371 95.88295455 102.9592614 101.8251651 98.87326266 101.0222377 100.1048189 68 97.4167486 97.21114442 102.1706076 99.39895119 104.4267052 104.4656092 95.23582581 95.98725913 69 101.5092913 99.79257631 99.74894095 100.4785584 98.08379534 103.5883693 101.6736364 106.0479859 70 95.64074217 102.9761829 101.3906682 101.35939 99.75904383 96.06209112 103.0656824 100.8101789 71 102.5140504 102.2188693 99.46776773 101.5514525 99.42745937 103.0893352 99.83755 99.66374352

Answer 1

Step 1: Insert the given data into excel  

Step 2: Compute X-bar ( i.e. an average of each subgroup) across all samples.

i.e. X-bar =x1 + x2 + x3 + x4 + x5 + x6 + x7 + x8 / 8

e.g.

Step 3: Compute X-dbar (i.e. average of all X-bar). This value will be the same across all samples.

X-dbar = x-bar1 + x-bar2 + x-bar3 + .... +  x-bar71 /71

Step 4: Compute the Standard deviation (SD) of X-bar

Step 5: Compute the Upper (UCL) and Lower (LCL) Control limit which is given by :

UCL=X-dbar+3SD

LCL=X-dbar-3SD

Step 6:Plot X-bar, X-dbar, UCL and LCL from the computed data.

i. Select the above mentioned computed columns.

ii. Select Line Chart from Insert Tab.

iii. Adjust the y-axis values basis LCL and UCL for better clarity of the chart. This can be done by right-clicking the chart and selecting the Format axis option.

Since all the Xbar points are within the control limit, it can be concluded that the process is in control.