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The validity of predicted meanvote for air-conditioned offices

W.L. Tse and Albert T.P. SoDepartment of Building and Construction, City University of Hong Kong,

Kowloon Tong, Kowloon, Hong Kong Special Administrative Region, China

W.L. ChanDepartment of Electrical Engineering, The Hong Kong Polytechnic University,Hung Hom, Kowloon, Hong Kong Special Administrative Region, China, and

Ida K.Y. MakDepartment of Statistics, The Chinese University of Hong Kong, Shatin,

New Territories, Hong Kong Special Administrative Region, China

Abstract

Purpose To examine the role of predicted mean vote (PMV) in air-conditioned environments byconducting a thermal comfort study.

Design/methodology/approach A formal statistical approach was adopted for the credibility ofthe study. Thermal measurements and questionnaire filling were carried out in commercial offices tocollect the required data. Statistical analysis on the collected data and logical reasoning were thenemployed to derive the conclusions.

Findings Provide an evidence to support PMV to be an appropriate thermal comfort index inair-conditioned environments. Guarantee high productivity of occupants by using PMV inair-conditioning control.

Research limitations/implications Future research work should be carried out to investigateany significant relationship between improvement in PMV and the profits gained by occupants insidean air-conditioned space. With such relationship, it is possible to develop an intelligentair-conditioning control to yield the most cost-effective thermal environments for commercial offices.

Practical implications Air-conditioning engineers are highly recommended to employ PMV toassess the thermal comfort environment in air-conditioned offices.

Originality/value This paper highlights the importance aspect on choosing a thermal comfortindex for comfort assessment in air-conditioned offices. The index itself should not consider adaptiveactions. Otherwise, the productivity of occupants would be severely deteriorated. It is well known thatPMV is the thermal comfort index that can fulfill this requirement.

Keywords Office buildings, Statistical methods, Productivity rate, Temperature, Hong Kong

Paper type Research paper

IntroductionFanger (1972) conducted a series of experiments in America and Europe to obtain a setof human comfort data. By analyzing this data statistically and applying the theoriesof heat transfer inside a human body, he developed an index to measure the thermalsensation of a group of people. The index is called predicted mean vote (PMV). It is a

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The work described in this paper was fully supported by two grants from CityU (Project No.#7200004 and Project No. #7001535).

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Received September 2004Accepted June 2005

Facilities

Vol. 23 No. 13/14, 2005

pp. 558-569

q Emerald Group Publishing Limited

0263-2772

DOI 10.1108/02632770510627543
http://www.emeraldinsight.com/0263-2772.htmhttp://www.emeraldinsight.com/0263-2772.htm


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numerical figure with its range between 23 and 3. A negative PMV valuecorresponds to a cold human thermal sensation and a hot sensation is reflected by apositive PMV value. The most optimal thermal comfort level is resulted when a PMVvalue is equal to zero. Figure 1 shows the relationship between PMV and human

thermal sensation. Together with a PMV value, predicted percentage dissatisfaction(PPD) (Fanger, 1972) was proposed to estimate the overall percentage of thermaldissatisfaction inside an air-conditioned space. Mathematically, PMV depends on airtemperature, mean radiant temperature, relative air velocity, relative humidity, humanmetabolic rate and clothing insulation level. PPD is solely a mathematical function ofPMV.

PMV and PPD form the basis of the ISO Standard 7730 for human comfort (ISO,1995). It provides guidelines to determine the control settings of the existingair-conditioning system. However, there were several comments on PMV fromresearchers. Some reported that PMV could not yield good prediction for humanthermal comfort. In 2004, Feriadi and Wong (2004) found that PMV predicted warmerthermal perception as compared to what people in Indonesia actually felt in their

naturally ventilated houses. In his study, he clearly stated that people would performadaptive actions to compensate for the less comfortable thermal conditions. Theseactions included drinking, changing clothes, taking a bath, going around, etc. Insteadof using air-conditioning systems, Indonesian people preferred to operate fans andwindows to achieve higher wind speed for comfort. In the same year, Borong et al.(2004) reported that it was inadequate to apply PMV in Chinese vernacular dwellings.The buildings were also naturally ventilated at the time of conducting the study. Thesimilar failure of PMV in this kind of buildings was observed in the research work ofanother researcher, Ealiwa et al. (2001). He also reported that PMV performed properlyin buildings with air-conditioning systems in North Africa. He thus called formodifications on the PMV equation for comfort assessment in naturally ventilatedbuildings. Apart from this, there was another situation causing the failure of PMV.Chun et al. (2004) stated that PMV should not be used for human comfort prediction intransitional spaces. In his study, these spaces were characterized by dynamic, unstableand fluctuating thermal environments, in which people performed a variety ofactivities. He accounted all these variations in thermal environments and humanactivities for the PMV failure. Furthermore, two researchers severely criticized theperformance of PMV. Nicol (2004) compiled the results of previous field studies inthermal comfort. He summarized that people would find ways to make themcomfortable. One popular way was to turn on a fan to increase air velocity. This

Figure 1.A graphic comfort scale

for PMV

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matched with one of findings from Feriadi and Wong (2004). He also emphasized thatPMV performed poorly in tropical countries where hot climates are common. Anotherresearcher, Humphreys and Nicol (2002) stated that PMV differed markedly andsystematically from the actual mean vote, for naturally ventilated buildings and even

for air-conditioned spaces. Several origins of biases were discussed in his study. One ofthem was ambiguities in the assessment of metabolic rate and clothing insulation.

On the other hand, many researchers supported PMV. In 2002, Parsons (2002)observed that there were very small differences in the thermal comfort responses ofmale and female subjects for neutral and slightly warm conditions. Changes in thermalcomfort responses in neutral and slightly warm environments, due to acclimation toheat, were not significant. This obviously contradicted the findings of Nicol (2004),Feriadi and Wong (2004) who suggested that people would try to adapt to less comfortenvironments by performing some actions. Also, his work confirmed that there werefew group differences between thermal comfort requirements of people with andwithout physical disabilities. One year later, Chamra et al. (2003) reported that PMVperformed well in many of the cases in his study. The cases for proper PMV predictionfell within office environments having air-conditioning systems for comfort control.With activities up to 2.3 met, humidity at mid to high ranges and air velocity up to 0.25m/s, the prediction of PMV was confirmed to be valid. These situations were commonin air-conditioned environments. Recently, there have been many researchers stillemploying PMV in their research works for human comfort assessment. In 2003,Baskin and Vineyard (2003) employed PMV and PPD in thermal comfort assessment ofconventional and high-velocity distribution systems for cooling seasons. Thesesystems delivered high air speed to occupants to enhance cooling. The situations weresimilar to naturally ventilated buildings. Pan et al. (2004) proposed an energy-savingscheme by using a personalized partition-type fan-coil unit which increased air velocityup to 0.4 m/s. It was a similar situation as that found in Baskin and Vineyard (2003).

Once again, PMV was applied in this study to evaluate the performance of this scheme.In 2004, Kulkarni and Hong (2004) conducted a comfort survey in the situation of atransient pull down, which was similar to a transitional space (Chun et al., 2004). In hisstudy, a specific technique was developed to accurately measure PMV values to reflectthe thermal environment. Even in air-conditioning control, PMV has been treated as afavorite candidate to be employed in advanced control algorithms. More than ten yearsago, Simmonds (1993) replaced dry-bulb temperature with PMV in his rule-basedcontrol strategy. Every actuator was commanded so as to push PMV to a zero valuethat corresponded to the neutral comfort environment. Lower operating cost wasresulted. In 2004, Calvino et al. (2004) introduced a fuzzy adaptive controller for indoorcomfort control. Inside his complicated algorithms, PMV was employed as a controlindex. A set of optimal control actions was derived based on minimization of PMV. He

reported that an effective and fast control of the indoor microclimate conditions wasachieved. At last, Fanger and Toftum (2002) revised the PMV equation. In his newwork, he proposed an extension of the PMV model to account any discrepancies foundin naturally ventilated buildings. Expectancy factors were introduced. Improvementsin such buildings were observed.

Both positive comments and negative comments of the performance of PMV onhuman comfort exist. Human, being the end user of an air-conditioning system inair-conditioned spaces, solely determines the performance of this system through

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his/her thermal sensation. Being active researchers in air-conditioning systems, it isnecessary to determine the role of PMV in air-conditioned spaces, particularlycommercial offices. Hence, we proposed this study for this purpose, in which sitesurveys, statistical analysis, logical reasoning and literature surveys were employed to

draw our conclusions.

MethodologyIn our study, Hong Kong was selected as the location for the site surveys. This decisionserved for two purposes. First, failure of PMV prediction often occurred in countrieswith hot climates as reported by Nicol (2004). Hong Kong, being situated insub-tropical regions, has its temperature up to 34oC in summer. This provided a goodchance to cross-check Nicols statement. Second, Chinese represent the predominantpopulation in Hong Kong and even in Asia. The derivation of PMV is based on theexperimental results from testing subjects in America and Europe (Fanger, 1972). NoAsians were involved in these experiments. Also, most of the research works with

conflicting results were undertaken in Asia (Feriadi and Wong, 2004; Borong et al.,2004; Chun et al., 2004). This study can also serve as a clue to any dependence of humancomfort on different kinds of race. Furthermore, Hong Kong has few naturallyventilated buildings. Our surveys focus on commercial offices with air-conditioningsystems. Each survey includes on-site measurement of thermal parameters andquestionnaire filling. The former task is used to determine the PMV. The latter onecollects the actual thermal sensation of occupants which gives out the actual mean vote(AMV) for comparison with PMV.

In order to enhance the credibility of our study, the surveys followed a formalstatistical approach. One-stage cluster sampling technique (Cochran, 1997), one of themost popular sampling techniques in statistics, was employed to extract testingsamples randomly for investigation. In this case, a cluster represents a commercial

office housing several Chinese occupants in an air-conditioned environment. All theseChinese occupants are treated as our sample items. It is very costly to carry outinvestigation on all these sample items which are numerous in amount. That is whyone-stage cluster sampling technique is adopted to preserve the credibility of the studyin resources-limited conditions.

Determination of the sample sizeOur investigation was carried out in office environments. We determined the samplesize (nD) for the survey subject applying an error criteria below 5 per cent. Based onstatistical principles, the sample size depends on the total population. In our case, thepopulation stands for the total number of commercial offices in Hong Kong, whichcannot be easily found. An alternative approach is to use the total number of listed

companies as the total population. This value is accessible from the stock market. Toemploy this approach, we have to confirm that there is no statistical difference betweenlisted companies and non-listed companies with respect to human comfort.

A pre-test was thus carried out on a listed company and a non-listed company.Their employees were asked to express their opinions on the comfort conditions oftheir offices. Independent-samples T test (Snedecor and Cochran, 1989) and Levenestest (Levene, 1960) were used to check for any difference in the mean value and thevariance of two populations respectively. Table I showed the test results obtained by

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SPSS. For the first test, the significant value was 0.285 while that of the second test was0.419. Both of them were bigger than 0.05, our specified accuracy, meaning that the

hypothesis of the two tests was accepted. Together with the fact that both populationsbelonged to normal distribution, this implied there was no statistical differencebetween the thermal preference of a listed company and that of a non-listed one. Thesample size of the study was determined based on the total population of listedcompanies. The sample size (nD) was estimated by Equation (1). The total population oflisted companies (N ) was found to be 943 at the time of performing the study. Thepopulation variance (s2), the error bound (B), the average cluster size ( M) were alreadyfound in the pre-test. The required sample size was then calculated to be 2.34 meaningthat three listed companies were invited for surveys.

nD Ns2

N

B2 M2

4 s2

1

The details of the site surveysEach site survey consists of two parts on-site measurement and questionnaire filling.Four thermal parameters are recorded by instruments. The recorded parameters aredry-bulb temperature (Trm ), wet-bulb temperature (Tw ), globe temperature (Tg ) andmean air velocity (v). The first three parameters are measured by Heat Stress Monitor

Office 1 Office 2 Office 3

Gender Male (%) 47.1 36.7 37.5Female (%) 52.9 63.3 62.5

Age group 20 or below (%) 0.00 4.10 12.521-30 (%) 58.8 59.2 75.031-40 (%) 35.3 28.6 12.541-50 (%) 5.90 4.10 0.0050 or above (%) 0.00 4.10 0.00

Qualification Primary school (%) 0.00 4.10 0.00School certificate (%) 23.5 42.9 62.5High school/vocational certificate (%) 29.4 10.2 0.00Degree (%) 47.1 36.7 37.5Master (%) 0.00 6.10 0.00PhD or above (%) 0.00 0.00 0.00

Position Manager or above (%) 11.8 10.6 0.00Senior staff (%) 23.5 8.50 0.00

Staff or below (%) 64.7 80.9 100Temperature Maximum 19.7oC 22.8o

C 24.9o

CMinimum 18.5oC 21.6oC 24.5oC

Relative humidity Maximum (%) 68.3 78.7 51.0Minimum (%) 61.9 58.4 49.6

Mean air velocity Maximum 0.265m/s 0.373m/s 0.487m/sMinimum 0.245m/s 0.337m/s 0.387m/s

Mean radiant temperature Maximum 20.6oC 23.1oC 25.8oCMinimum 19.5oC 22.5oC 25.7oC

Table I.The backgroundinformation of testingsubjects and themeasured thermalenvironments in thestudy

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HSM100 with the error of 0.1 per cent. The last one is measured by Kata Thermometerwhich is a typical instrument for air speed measurement in a comfort survey. Fromdry-bulb temperature and wet-bulb temperature, relative humidity is obtained. Meanradiant temperature (Tmrt) is found from Trm, Tg and v by using Equation (2).

T4mrt T4g 0:247 109ffiffiffiv

pTg2 Trm 2

To assess the comfort level in commercial offices, the four recorded thermal parameterswere measured at three different levels from the ground 0.1m, 0.6m and 1.1m. Theiraverage values were then used to calculate the PMV value. Apart from them, two extraparameters specific to each testing subject were required. They are the type of clothingand the activity performed at the time of measurement. As suggested by Humphreysand Nicol (2002), questions for retrieving these two data were specially designed in thequestionnaire, which are mentioned later. A spreadsheet was developed to automatethe calculation of PMV by solving Equation (3) iteratively. In this equation, met is themetabolic rate of an occupant, h is the mechanical efficiency, Pa is the vapor pressure

in ambient air, Trm is the dry-bulb temperature, fcl is the ratio of the surface area of theclothed body to the surface area of the nude body, Tcl is the temperature of the outersurface area of a clothed body, Tmrt is the mean radiant temperature and hcl is theconvective heat transfer coefficient.

PMV 0:352e20:042met 0:032 {met12 h2 0:35432 0:061met12 h2pa2 0:42met12 h2 502 0:0023met442pa2 0:0014met342 Trm2 3:4 1028fclTcl 2734 2 Tmrt 27342fclhclTcl2Trm}

3

In parallel with the site measurement, occupants are requested to complete aquestionnaire. Each questionnaire has a total of 25 questions and consists of five parts:

(1) personal particulars;

(2) personal comfort;

(3) work area satisfaction;

(4) job satisfaction; and

(5) health status.

The first part is used to identify the background of each testing subject. It should benoted that body height and body mass were included in the questionnaire. As reflectedfrom the formula of the PMV, body heat loss affects thermal sensation. Nicol (2004)even stated that people will attempt to use changes in posture to alter convective andevaporative heat loss. Excessive body mass obviously obstructs heat loss. It is worth to

investigate whether there is any correlation between body mass and PMV. Body heightand body mass are thus included in this part for later analysis. The second part is themost important for our analysis. Actual thermal sensation, the type of activities andthe information of clothing are included in this part. Both present activities and theactivities few minutes before are requested. In case of big difference between these twoactivities, the arithmetic mean of two activities is used in the calculation of PMV. Forclothing, we ask the testing subject for any jacket worn. It is a common practice forpeople in Hong Kong to wear jacket in an office if they feel slightly cool. In such an

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event, extra value will be added to the clothing insulation of a typical summer clothingto cater for the jacket. In this way, a more accurate estimation of the activity level andclothing insulation is achieved, which was much concerned by Humphreys and Nicol(2002). For the next two parts, Likert scale is employed to investigate their levels of

satisfaction on their working environments and their jobs. For the last part, theinformation of health status is collected. As for body mass, health status is expected toaffect body heat loss to the surroundings. Any correlation between this factor andthermal sensation will be found out.

Results and analysis of the surveysThree listed companies were invited for the site surveys in summer. A total of 73occupants working in commercial office environments served as testing subjects in thestudy. They were requested to complete questionnaire so as to assess their thermalsensations as well as other relevant information stated before. At the same time,thermal parameters were recorded down for the calculation of PMV. The general

background of testing subjects and the measured thermal environment were shown inTable I. About 60 per centof subjects were female. More than 80 per centwas in agegroups of 21-30 and 31-40. About 40 per cent have attained first degree or above andless than 3 per cent have only studied in primary schools. Most of them were generalstaff and few were in senior positions. The physical layout of one of the offices wasshown in Figure 2.

Predicted mean vote and actual mean voteAs each testing subject is allowed to specify his/her own activity level and clothingin the questionnaire, a total of 73 PMV values were calculated for the whole sampleas well as their actual mean vote (AMV) values. A set of AMV and PMV wasobtained in the site surveys. Statistical calculation was then carried out. Table II

listed out the final results. The AMV value was found to be 0.018 very close to 0.This indicated that the average thermal sensation of the testing subjects was inneutrally thermal comfort condition. On the other hand, PMV was calculated to be20.114 which was still close to 0.

In order to check whether PMV matches with AMV scientifically, further statisticalanalysis was required. First, the difference between AMV and PMV (i.e.diff AMV2 PMV) generated another set of 73 data named as diff. This data setwas used to produce normal quantile-quantile (Q-Q) plot to explore the nature of thedistribution of diff. Figure 3 showed the Q-Q plot. It was observed that most of the datafell along the straight line in this figure. This indicated that diff followed normaldistribution and so did AMV and PMV. With this finding, we carried outPaired-Samples T test (Snedecor and Cochran, 1989) to investigate the significance of

the difference between the mean of AMV and that of PMV. In this test, a hypothesiswas set up in which the mean difference was assigned to zero. The test statistics wasfound to be 0.767 which fell within the 95 per cent confidence interval. The nullhypothesis could not be rejected. From the statistical point of view, there was nosignificant difference between AMV and PMV. It implied that PMV could predict thethermal sensation of a group of Chinese in Hong Kong office environments with 95 percent confidence interval. In addition, it was observed that the air velocity in Office 3was high as compared to others. The measured PMV in this office was close to the

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reported AMV. This finding also confirms that PMV is still valid in an environmentwhere high air velocity is present.

Relationship between body mass and human thermal sensation

In this part, body mass index (BMI) is employed to represent the degree of body massof each testing subject. It is defined in Equation (4).

BMI WH2

4

where W is the weight of the subject in kilogram and H is the height in meter. Theywere obtained from the questionnaire. In this way, another set of 73 BMI data was

Figure 2.The layout of one of the

offices invited for comfortsurvey

Mean Standard deviation Standard mean error

Actual mean vote (AMV) 0.018 1.297 0.152Predicted mean vote (PMV) 20.114 0.685 0.080

Table II.The final results of AMV

and PMV

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generated. Pearson coefficient of correlation was employed to measure any correlationbetween BMI and AMV based on a correlation coefficient. In this case, a relativelysmall correlation coefficient was found, which was equal to 0.111. Same as before, ahypothesis was set up, which corresponded to null relationship between BMI andPMV. The test statistics was found and was converted to the significant value of 0.387.As the significant value was bigger than the error bound of 0.05 (i.e. 5 per cent), the null

hypothesis could not be rejected. This implied that there was no significantrelationship between body mass and human thermal sensation.

Relationship between health status and human thermal sensationIn this part of questionnaire, ten symptoms and five dichotomous questions wereposted to the testing subjects. The 100 per cent stacked bar chart of ten symptomssummarized their feedbacks as shown in Figure 4. The first six symptoms rarelyoccurred in the past week while sleepiness and fatigue occurred frequently. Thisobservation could be explained by the fact that over-time works were quite frequent inHong Kong under a relatively poor economic environment. Fishers Exact Test forR C Tables (Freeman and Halton, 1951) executed by SASw was used to test whether

there was any association between these symptoms and AMV. Test results were listedout in Table III. It was found that all significant values were greater than 0.05. Thehypothesis could not be rejected. It indicated that there was no significant associationbetween health status and human thermal sensation.

The role of PMV in an air-conditioned systemThe sensation experienced by a building occupant solely determines the effectivenessof the air-conditioning system. Usually, the thermal sensation of a large group of

Figure 3.The normal Q-Q plot ofdiff

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people follows a normal distribution. This fact is supported by this study, as the AMVof 73 testing subjects followed such a distribution. This suggests that most of thepeople inside an air-conditioned space have thermal sensation votes more or less equalto the PMV value. In this way, PMV contributes a lot to an air-conditioning system byproviding an accurate indication of comfort level of occupants. Air-conditioning

engineers can employ PMV to achieve optimal air-conditioning design for newbuildings. They can also adjust the settings of existing air-conditioning systems for abetter thermal environment that corresponds to the larger proportion of occupants inneutrally thermal conditions.

Now, let us consider a situation where there is a change in external factorsworsening an indoor thermal environment. For example, heavy rain in a hot summercauses a sudden drop in ambient air temperature. In this situation, many occupants feeltoo cold. The simple solution is to have some automatic adjustments to restore the

Health status Significant values

Headache Thermal environment acceptability 0.6263Dizziness Thermal environment acceptability 0.4103Sleepiness Thermal environment acceptability 0.5739Eye irritation Thermal environment acceptability 0.6365

Trouble focusing eyes Thermal environment acceptability 0.2215Nose irritation Thermal environment acceptability 0.3438Sore or irritating throat Thermal environment acceptability 0.2049Skin dryness, rash or itch Thermal environment acceptability 0.8528Fatigue Thermal environment acceptability 0.8301Difficulty concentrating Thermal environment acceptability 0.0694

Table III.The result of Fishers

exact test for R C table

Figure 4.The bar chart showing the

health status of testingsubjects in the study

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environment back to the comfortable level for most people. One might argue thatpeople can adjust the settings manually or even perform some actions to restore theirsensations back to comfort levels. We totally agree with this argument from a comfortpoint of view. In fact, some researchers realized that such adaptive actions occur in

some tropical countries where air-conditioning systems are limited (Feriadi and Wong,2004; Borong et al., 2004; Ealiwa et al., 2001; Nicol, 2004; Humphreys and Nicol, 2002).However, for occupants in commercial offices, their efficiencies greatly affect the profitof their companies. Occupants may not be allowed to perform such adaptive actionswhen they are working in offices. Thus, air-conditioning systems should automaticallyadjust the environment to the comfort level indicated by some sorts of comfort index.This comfort index should not include the effect of adaptive actions in its derivation.Obviously, PMV is one of the best candidates to serve as this index as supported by thefindings of surveys conducted in this study. The four environmental factors affectingPMV, namely air temperature, air velocity, relative humidity and radiant temperature,are considered as instantaneous values instead of mean values in some comfort indices.In this situation, PMV can indicate a more instant thermal sensation of a group ofoccupants for the system to act on. This explained why there are research worksutilizing PMV in air-conditioning control (Simmonds, 1993; Calvino et al., 2004) forbetter control performances. With the increasing usage of human comfort-basedair-conditioning control, PMV would be the best candidate to be employed in suchcontrol algorithms to enhance the comfort level as well as the productivity level.

ConclusionsBased on the statistical results, two findings were established. The first one was thatPMV accorded with the distribution of the thermal sensation vote of a group ofoccupants in air-conditioned environments. PMV accurately represented the averagethermal sensation of occupants. Also, it was not affected by other human factors such

as body mass and health status. The findings suggested that PMV is a good comfortindex in the area of human thermal comfort. By employing logical reasoning andrevising the previous research works, we came to a conclusion that PMV can serve asignificant role in air-conditioning systems. Therefore, advanced human comfort-basedcontrol should employ PMV in its control algorithms to improve the thermal comfortlevel and the productivity level of occupants in a building.

References

Baskin, E. and Vineyard, E.A. (2003), Thermal comfort assessment of conventional andhigh-velocity distribution systems for cooling season, ASHRAE Transaction, Vol. 109,Part 1, pp. 513-9.

Borong, L., Gang, T., Peng, W., Ling, S., Yingxin, Z. and Guangkui, Z. (2004), Study on thethermal performance of the Chinese traditional vernacular dwellings in Summer, Energyand Buildings, Vol. 36 No. 1, pp. 73-9.

Calvino, F., Gennusa, M.L., Rizzo, G. and Scaccianoce, G. (2004), The control of indoor thermalcomfort conditions: introducing a fuzzy adaptive controller, Energy and Buildings, Vol. 36No. 2, pp. 97-102.

Chamra, L.M., Steele, W.G. and Huynh, K. (2003), The uncertainty associated with thermalcomfort, ASHRAE Transaction, Vol. 109, Part 2, pp. 356-65.

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Chun, C., Kwok, A. and Tamura, A. (2004), Thermal comfort in transitional spaces basicconcepts: literature review and trial measurement, Building and Environment, Vol. 39No. 10, pp. 1187-92.

Cochran, W.G. (1997), Sampling Techniques, John Wiley & Sons, New York, NY.

Ealiwa, M.A., Taki, A.H., Howarth, A.T. and Seden, M.R. (2001), An investigation into thermalcomfort in the summer season of Ghadames, Libya, Building and Environment, Vol. 36No. 2, pp. 231-7.

Fanger, P.O. (1972), Thermal Comfort Analysis and Applications in Environment Engineering,McGraw-Hill, New York, NY.

Fanger, P.O. and Toftum, J. (2002), Extension of the PMV model to non-air-conditionedbuildings in warm climates, Energy and Buildings, Vol. 34 No. 6, pp. 533-6.

Feriadi, H. and Wong, N.H. (2004), Thermal comfort for naturally ventilated houses inIndonesia, Energy and Buildings, Vol. 36 No. 7, pp. 614-26.

Freeman, G.H. and Halton, J.H. (1951), Note on an exact treatment of contingency, goodness of fitand other problems of significance, Biometrika, Vol. 38, pp. 141-9.

Humphreys, M.A. and Nicol, J.F. (2002), The validity of ISO-PMV for predicting comfort votes inevery-day thermal environments, Energy and Buildings, Vol. 34 No. 6, pp. 667-84.

ISO (1995), ISO 7730: Moderate Thermal Environments Determination of the PMV and PPDIndices and Specifications for Thermal Comfort, 2nd ed., International Organization forStandardization, Geneva.

Kulkarni, M.R. and Hong, F. (2004), An experimental technique for thermal comfort comparisonin a transient pull down, Building and Environment, Vol. 39 No. 2, pp. 189-93.

Levene, H. (1960) in Olkin, I. (Ed.), Contributions to Probability and Statistics: Essays in Honor ofHarold Hotelling, Stanford University Press, Stanford, CA, pp. 278-92.

Nicol, F. (2004), Adaptive thermal comfort standards in the hot-humid tropics, Energy andBuilding, Vol. 36 No. 7, pp. 628-37.

Pan, C.S., Chiang, H.C., Yen, M.C. and Wang, C.C. (2004), Thermal comfort and energy saving of

a personalized PFCU air-conditioning system, Energy and Buildings, Vol. 37 No. 5,pp. 443-9.

Parsons, K.C. (2002), The effects of gender, acclimation state, the opportunity to adjust clothingand physical disability on requirements for thermal comfort, Energy and Buildings,Vol. 34 No. 6, pp. 593-9.

Simmonds, P. (1993), Thermal comfort and optimal energy use, ASHRAE Transaction, Vol. 99,Part 1, pp. 1037-48.Snedecor, G.W. and Cochran, W.G. (1989), Statistical Methods, IowaState University Press, Ames, IA.

Further reading

ISO (1998), ISO 7726: Ergonomics of the Thermal Environment Instruments for Measuring

Physical Quantities, International Organization for Standardization, Geneva.

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The Validity (1)