VariablesControlCharts:A MeasurementTooltoDetectProcessProblems

WithinHousingAndrew LunaUNIVERSITYOF LOUSIVILLE

INTRODUCTION

When housing administrators discovered that

female residents were unsatisfied with the equalityof hot water coming from the community showersin a high-rise residence hall, they relied on theconcepts of Total Quality Management (TQM) tohelp them identify both the causes of and possibleremedies for the problem. TQM is a method ofachieving quality using scientific and teamworkapproaches. By utilizing quantitativemeasurement, administrators believed they couldpinpoint the underlying causes of the hot waterproblem-something previous focus groups couldnot. After identifying the problem, they relied onvarious teamwork methods to discuss and

implement changes to improve the process of hotwater distribution.

Current literature concerning TQM in highereducation places heavy emphasis onnonempirical methods of achieving quality.Although teamwork, customer satisfaction, and

ownership are all important factors in TQM,authors who have written about these conceptshave failed to address the significance ofstatistical methods in quality control.

According to some (Luna, 1996; Teeter &Lozier, 1993), Statistical Process Control (SPC)is the one component separating TQM from otherimprovement methods. In fact, quality is definedin TQM as a measurable characteristic of a

product, process, or service [Montgomery, 1985).By using quantifiable measurement techniques,it is possible to synthesize and evaluate qualityin relationship to operational variables.Furthermore, one may examine the effects of thesevariables to any changes within a particularprocess under study.

Although examples of quantitative methodsof achieving quality are limited in the literature,

VOLUME 28, NUMBER 1 1999

some articlesdo exist. Grace and Templin(1994)used a simple form of statistical measurement tohelp them improve the quality of their studentservices departments. Macchia (1993) used SPCto measure the enhancement of student learning,and Koberna and Walter (1993) explained howa community college used many TQM tools toachieve quality. This study offers another exampleof how a traditional TQM tool can be used in

higher education, specifically in a residence hall.More often than not, higher education

professionals tend to use only the processdefinition tools available in TQM, and avoidimportant data generation and analysis tools.Koberna and Walter (1993) attribute this aversionto statistical methods to the newness of TQM in

the higher education community. By not utilizingStatistical Process Control tools, higher educationprofessionals may be creating barriers inachieving a better understanding of TQM in thefuture (Seymour & Collett, 1991). Before theyfully understood TQM, some professionals statedthat SPC tools may not be needed for achievingbetter quality in higher education [Vance &Schipani, 1993), and some have even criticizedTQM for its ambiguity and simplicity (Fisher,1993). Clearly, statistical tools can provide areliable solution for turning the enigmatic into theexact (Seymour & Collett, 1991).

This article focuses on one of the more

intricate statistical process control tools in TQM.The Control Chart is one of the most widely usedSPC tools in business and industry and probablyone of the least understood among those in highereducation.

THE CONTROL CHART

The underlying principle behind the Control Chartis that every process, no matter how well executedis imperfect. Because many variables areinvolved in all processes, deviations can occurin one or more of these variables, creating a lessthan perfect process. According to Tague (1995),the variables involved in a process can usuallybe placed into the four distinct categories ofpersonnel, machines, materials, and methods.

According to Shewhart (1986), variationsthat occur among these elements can producedeviations in central tendency which can lead tooutput variations in the process. Detectingchanges and controlling input variations fromeither of thesecategories requires a well-identifiedsystem for evaluating process output (Demming,1986).

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The Control Chart is a tool for determiningthe type of variation in a process. When aprocess is in control, it is subject only to a stablesystem of random causes. When a process isout of control, it is subject to an assignable causeor cause of variation (Montgomery, 1985).

Stated another way, TQM philosophyassumes all processes have internal and externalfactors effecting efficiency and reliability. Whenthese factors occur randomly, they are assumedto be caused by chance circumstances outsidethe control of the worker or the institution.

However, if these factors occur in a nonrandom

fashion, or if they exceed required specified limits,it is assumed that there is an underlying causewhich can be pinpointed and corrected. Theseunderlying causes are called "assignable"because they are identified as an assessablevariable which can be manipulated andcontrolled (Luna, 1996).

The Control Chart is a graph representingthe variability of a process variable with respectto time (see Figure 1). The horizontal axis on thegraph represents rational subgroups over aperiod of time. Each point on the horizontal axiscoincides with observations made on a subgroup

Upp<r Control LinU (3 Sigma)---------------------3 Standard Deviations Above Mean

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Lower Control Limit (3 Sigma)---------------------3 Standard Deviations Below Mean

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Figure 1. Example of a Control Chart

drawn from the process at a particular point intime. Stated another way, a subgroup is a pointin time when a series of measurements are

gathered during a particular time within theprocess. The subgroup then becomes the meanof each of the observations within that time

period.The center line is drawn horizontally across

the chart to represent an average value. Thisvalue can be obtained from the subgroup data,or it can be in the form of a specification meanevolving from longer-term historical data. For ameans chart, the center line is derived from the

sample observation averages within each

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subgroup. For a range chart, the center line isthe average range of samples within eachobservation. Lines above and below the center

line represent the upper control limits (UCL) andthe lower control limits (LCL) of the averagerespectively. The upper and lower control limitsare based on three standard deviations above

and below the mean (referred to as "3 sigma" inTQM terminology). The control chart mayindicate an out-of-control condition either when

a point falls beyond the control limits, or whenthe plotted points exhibit some nonrandom patternof behavior. Ishikawa (1990) defined nonrandomcauses of variation as follows:

1. Runs - when several points line upconsecutively on one side of the central line.2. Trends - when there is a continued direction

of a series of points.3. Periodicity - when the points show the samepattern of change over equal intervals.4. Hugging of the control line - when the pointson the control chart fall close to the central lineor to the control limit line.

If there is no reason to suspect an out-of-control condition, changes should be made tothe system and further measurements conducted.If the change positively effects the process, thedata in the control chart will move toward a

controlled state. If the change brings a negativeeffect, the control chart will indicate that the

process is more out of control than before thechange.

Many control charts are available for thestudy of a process. The major factor indetermining which chart to use is the type of datagenerated from the study. Again, the mostfundamental concept ofTQM is the ability to countor measure a particular characteristic. However,counting and measuring are two differentfunctions in statistics and should be treated

differently in TQM. The process of countinginvolves a finite scale and scores generated arebased on the binomial distribution. The tool for

this type of data is the Attributes Control Chart.The process of measuring involves an infinite scaleand scores generated are based on the normaldistribution. The tool for this type of data is theVariables Control Chart. To understand fully howdistributions and Control Charts are related and

used, refer to Montgomery (1985).

METHOD

The purpose of this study was to determine if thecurrent process of supplying hot water to a high-

JOURNAL OF COLLEGE AND UNIVERSITY STUDENT HOUSING

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rise residence hall for women at a Southeastern

Doctoral I granting institution was in control. Aftera series of focus groups among the residents inthat hall, it was determined that they were mostlyconcerned about the consistency and availabilityof hot water in the building.

One resident assistant (RA) from the fourth,ninth, and twelfth floors was involved with the

study. These floors were predetermined so thatthe building was separated into lower, middle,and upper areas. Each RA measured thetemperature of hot water (in Fahrenheit) comingfrom a common area bathroom faucet on their

floor. This was done during the morning, noon,and evening at specified times during the dayfor 14 days. Therefo(e, each RA recorded 42observations for a total of 126 observations.Because the data measurement was based on a

continuous scale, the x (pronounced x-bar) RControl Chart was used which shows changes inthe mean of the process (x) and changes of thedispersion of observations (x and R).

If the subgroup observations tended to hugaround the mean, it was inferred that multiplefactors were mixed into a subgroup and that theprocess of supplying hot water was not consistentthroughout the building. Therefore, the sameindividual temperature observations werestratified by floor and each floor was re-examined. If each floor were treated individually,

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subgroups then contained observations from eachof the three time periods per day for 14observations per floor. Stated another way, fora given floor, each subgroup represented theaverage of a particular day's three temperaturereadings.

RESULTS

The results of the initial test indicated a problemwith hugging of the mean within the central lineof the x or means chart (see Figure 2). Thisshowed that the majority of observations fellwithin a close proximity of the mean, indicatingthat more than one factor was being measured.Observations within the R or Range Chart,however, indicated an out-of-control state because

of a possible run problem for the first sixobservations, a possible trend problem, forobservations 19 through 27, and twoobservations, 26 and 32, which exceeded the

lower and upper control limits respectively. TheR chart in this example exhibits an out-of-controlstate because observations either exceeded the

control limits of 3 sigma or groups fell into patternsof nonrandom behavior.

The results of the initial test also indicated

that because of the high variance of observationsin the R or Range Chart, water temperaturevariance problems may exist between the three

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floors. This assumption was later supported byindependent floor tests. One of the major keysin reading this chart was looking at observations26 and 32 in the range chart. Observation 26indicated that no variance existed within this

subgroup while observation 32 exceeded a rangeof more than 40 degrees. Because the results ofthis test indicated high variance among subgroupswithin the Rchart and hugging of the mean withinthe x chart, the test was rerun after separatingthe floors and redesigning the subgroup to containobservations from each of the three time periodsfor each day.

The observations for the fourth floor (seeFigure 3) indicated that the Range Chart was incontrol because observations did not fall outside

of the 3 sigma control limits and because nopatterns existed among groups of observations.The means chart, however, was out of control.

Observations 5 through 10 on the means chartindicated a possible trend problem andobservation 10 exceeded the upper control limits.Although most of the observations from the meanschart tended to hug the center line, the rangechart indicated that the variance was within

acceptable limits. It was clear to see that thefourth floor experienced higher watertemperatures than the other two floors and that,in some cases, these higher temperatures farexceeded the 125 degree mean. Additionally,observations 3 and 10 on the means chart

indicated that the higher temperatures occurredon Wednesdays and, according to the RangeChart, little temperature variation occurred amongthe three time periods in these days.

The observations for the ninth floor (seeFigure 3) also indicated that the Range Chartwasin a controlled state. However, the means chart

for the ninth floor indicated a possible periodicityproblem. This type of problem is harder to detectthan other out-of-control states and is usuallybased upon experience and a greaterunderstanding of the process (Ishikawa, 1990).The periodicity problem was apparent after every3rd observation and continued over equalintervals during the entire length of timemeasured. According to the means chart, watertemperature for both weeks increased onThursday through Saturday and decreased onMonday through Wednesday.

Although the observations for the twelfth floorindicated that the Range Chart was in a controlledstate, the means chart for this floor showed anout-of-control state more severe that the other two

floors (see Figure 3). Observations 3 through 7

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and 10 through 14 indicated possible runproblems and observations 5 through 10exceeded the lower control limits. Additionally,these observations indicated periodicity problemsstarting after the 5th subgroup. By looking atthis chart, it was apparent that water temperatureswere significantly lower for this floor duringThursdays and Fridays and that, on average, thewater temperatures were lower than on the othertwo floors. Furthermore, observations 5 and 10on the means chart also indicated wide variation

within the subgroups. Specifically, the controlchart indicated that a wide variation existed

between the observations within these subgroups.After observing the raw water temperature data,it was determined that the water temperaturesfor the afternoon and evening hours weresignificantly lower than during the morning hours.

Each of the three floors indicated that the

Range Chart was in a controlled state. Thisshowed that the source of variation in the water

temperature on any floor during the morning,noon, and evening hours was not attributed topatterns of change on that floor. The x or meanschart for each floor, however, indicated an out-of-control state because observations exceeded

the control limits or formed patterns of behaviorover a day-to-day period.

DISCUSSION

This study demonstrated the use of the VariablesControl Chart for detecting problems with aresidence hall hot water supply. Through thisstudy, a better understanding of the hot watersupply was achieved and recommendations forthe improvement of the system were made.

The Variables Control Chart indicated three

problems: (a) high variation of water temperaturesfrom floor to floor, (b) much higher watertemperatures on the 4th floor than on the 12thfloor, and (c) lower temperatures or higherdemands for hot water during the afternoon andevening hours on Wednesdays, Thursdays, andFridays.

The first recommendation concerned the first

two problems. High variation of watertemperatures from floor to floor and highertemperatures on lower floors indicated potentialwater flow problems. Increasing the overall watertemperature piped into the building will increasethe temperature for the higher floors, however itwill not address the variation problems betweenfloors and will lead to even hotter water on thelower floors. Remedies for these variation

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VOLUME28, NUMBER1 1999 53

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problems could include, but are not limited to,better pipe insulation, repairing or replacinginternal pumping systems, adding booster systemswhich would reheat water on the higher floors,and redesigning of the hot water supply system,

The quality team charged with the initialinvestigation of the hot water supply processrecommended that Physical Plant staff exploreremedies for improving the process. Theseremedies would be classified according to costand perceived effectiveness and be introducedinto the system one at a time. By including costas a factor in the order of remedy, lower costchanges would be introduced to the system first.Thus, if the system entered into a controlled state,it would do so at the lowest possible cost.

There was a chance that the third problemof day and time might be controlled by finding asolution to the first two problems, but it wasrecommended that the same team investigateadjusting the delivery of hot water to the buildingto increase the temperature when the system ismainly in use, such as Thursdays and Fridays.likewise, the delivery of hot water could bedecreased when demand is less, such asWednesdays.

The third recommendation concerned future

monitoring. For TQM to remain effective, aprocess must undergo continuous measurementto determine if changes increase quality or if thesystem falls back into an out-of-control state. Forthis reason, it was recommended that the water

temperature be continually measured for twoweeks for both fall and spring semesters.

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CONCLUSION

Statistical Process Control is an importantapplication to Total Quality Management. To fullyutilize the concepts of TQM, one must define,synthesize, and evaluate quality. The VariablesControl Chart is one of many tools for achievingthese goals. Because it is used with variablesthat are measured, this tool can be used for anycontinuous repeating variable such as money,time, scores on a surveyor evaluation, weights,distance, or volume.

For example, housing personnel could usethis chart to measure utilities' output within thehalls in conjunction with energy saving changesto the buildings. It also could be used to tracksurvey responses of residents each week over aperiod of time, or to track the completion rate forwork orders This chart also has been used to

track the difference between predicted and actual

54

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values in forecast models to locate patterns which,if detected and changed, could improve the abilityof the model to make more accurate predictions.

Although the Variables Control Chart mayseem complicated and foreboding at first, withpractice it can be a relatively simple tool to use.Many software companies offer packages thatmake entering data and interpreting ControlCharts effortless. As seen in this study, the ControlChart is a powerful tool in measuring the qualityof a process and assessing the effects of changesto it. Because the Variables Control Chart works

with continuous data, it can be used to evaluate

any process for which this type of data can becollected.

REFERENCES

Demming, W. E. (1996). Out of the crisis.Cambridge: Center for Advanced Engineer-ing Study, Mil

Fisher,J (1993). TQM: A warning for highereducation. Educational Record,74(2), 15-19.

Ishikawa, K. (1990). Guide to quality control.Tokyo: Asian Productivity Organization.

Grace, R. E., & Templin, 1 J (1994). QSS:Quality Student Services. NASPAJournal,32(1), 74-80.

Koberna, S., & Walter, P. (1993). Using totalquality managementtools to improve orga-nizational wellness. In G. G. lozier & D.JTeeter (Eds.), Pursuit of quality in highereducation: Case studies in total quality man-agement. San Francisco: Jossey-Bass.

luna, A. l. (1996). Workorder nonconformityand the TQM process. Journal of Collegeand University Student Housing, 25(2), 31-37.

Macchia,P.[1993}.Totalquality educationandinstructional systems development. Educa-tional Technology, 32{7}; 17-21.

Montgomery, D. (1985). Introduction to statisti-cal quality control.New York: Wiley.

Seymour, D., & Collett C. (1991). Totalqualitymanagement in higher education: A criticalassessment. Methuen, MA: GoaI/QPc.

Shewhart,W. A. (1986). Statistical method fromthe viewpointof qualitycontrol. New York:Dover.

Tague, N. R. (1995). The Quality Toolbox.Milwaukee: ASQC.

Teeter,D. J, & lozier, G. G. (Eds.). (1993).Total quality management in higher educa-tion: Case studies in total quality manage-ment. San Francisco: Jossey-Bass.

JOURNAL OF COLLEGE AND UNIVERSITY STUDENT HOUSING

Vance,C. L.,&Schipani, P. D. (1993). TQRE-total quality residential experience. Jour-nal of College and University Student Hous-ing, 23(2), 3-7.

For additional information, contact Andrew Luna,

Research Analyst, University of Louisville, Louis-ville, KY40292.

VOLUME 28, NUMBER 1 1999 55

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