Usability perceptions and beliefs about smart thermostats by chi-square test, signal detection theory, and fuzzy detection theory in regions of Mexico

Abstract

It is well known that smart thermostats (STs) have become key devices in the implementation of smart homes; thus, they are considered as primary elements for the control of electrical energy consumption in households. Moreover, energy consumption is drastically affected when the end users select unsuitable STs or when they do not use the STs correctly. Furthermore, in future, Mexico will face serious electrical energy challenges that can be considerably resolved if the end users operate the STs in a correct manner. Hence, it is important to carry out an in-depth study and analysis on thermostats, by focusing on social aspects that influence the technological use and performance of the thermostats. This paper proposes the use of a signal detection theory (SDT), fuzzy detection theory (FDT), and chi-square (CS) test in order to understand the perceptions and beliefs of end users about the use of STs in Mexico. This paper extensively shows the perceptions and beliefs about the selected thermostats in Mexico. Besides, it presents an in-depth discussion on the cognitive perceptions and beliefs of end users. Moreover, it shows why the expectations of the end users about STs are not met. It also promotes the technological and social development of STs such that they are relatively more accepted in complex electrical grids such as smart grids.

Keywords

thermostats / perceptions / beliefs / signal detection theory (SDT) / fuzzy signal detection theory (FSDT) / chi-square (CS) test

Introduction

A smart thermostat (ST) is a novel electrical device that it is required for connecting smart homes (SHs) with smart grids (SGs). Typically, SHs are controlled using microcontrollers in an autonomous manner. Some of the micro-controllers in STs sense occupancy and sleep patterns [¹]; however, if the ST end users do not accept the ST, the ST is controlled in a semi-autonomous or manual manner, and thus, the operation of the ST is said to be limited. As it is well known that residential thermostats control a considerable portion of fuel and electrical energy (9%) [²], it is extremely important to save energy using STs. On the other hand, the economic inequality levels observed in the inhabitants of Mexico affect the use of electrical energy and generation of CO₂ [³]. Thus, the values of energy consumption change with regard to the specific population sectors (poor, medium, and rich sectors). Nevertheless, Mexico shows an increase in energy consumption every year across all the population sectors because the number of electrical devices per person also increases. Thus, the trend in energy consumption shows a dramatic increase [³]. Besides, thermostats, classified in Mexico as part of an air-conditioner system, are critical in several states of the country where the temperature reaches 100°F; thus, the STs are implemented to cool households. In fact, the number of end users adopting STs is increasing. Hence, the energy consumption in households highly depends on the correct selection and use of STs. Thus, it is critical to understand the perceptions and beliefs of end users about the key electrical devices that control the electrical energy in households. One such device is the ST, which has been transformed from a simple knot structure to an extremely complex electronic system such as a “nest,” which comprises sensors connected to the Internet and can be programmed autonomously [⁴]. In addition, the nest can track electrical energy consumption and can be programmed via a mobile app. Further, the nest has been developed using the concept of the Internet-of-things, which is one of the most advanced thermostats available on the market. It is also shown in Ref. [⁵] that the presence of occupants and their behavior affect the amount of energy consumed in buildings; therefore, STs can save energy when they decipher those conditions. However, some evaluations overestimate the amount of energy saved by STs; as a result, the end users are primarily attracted by saving energy and money by STs, but they do not adopt ST because their expectations about ST are not met. It is important to mention that the evolution of residential thermostats shows that several smart features are incorporated every year; however, sometimes, these new features are not used [²]. On the other hand, current studies show that programmable thermostats consume more energy than manual thermostats depending on how they are used by the end user [²]; therefore, the use of STs can increase the consumption of electrical energy. In addition, studies on how people ignore the correct use of thermostats owing to a lack of information about the operation of the thermostats and on how the selected thermostats are controlled manually have been conducted [⁶]. Moreover, it is crucial for the end user to make more informed decisions regarding the use of smart energy devices at home. When the end users do not have sufficient information about the smart devices that are used for saving energy, they are unlikely to non-optimize the functions of these smart devices, which in turn will lead to dissatisfaction with the product. In Mexico, there are several governmental websites that provide information about saving energy using thermostats when cooling or heating homes [⁷]; however, sometimes, the end user is not involved with the issues pertaining to energy consumption and saving, and they do not visit those websites. For instance, there are basic steps for saving energy such as resetting the thermostat when the end user is not at home. An ST can perform these tasks for the end user, and therefore, it appears to be the right choice of thermostat for controlling energy in households. The STs can automatically decrease the temperature by one or two degrees, without affecting the comfort level at specific hours of the day in order to save money. One of the main tradeoffs associated with the design of a thermostat is between the energy and monetary savings and comfort-loss for the end users [⁸,⁹]; therefore, one of the main aspects of designing a thermostat is ignoring the acceptance based on perceptions and beliefs of the end users. This paper proposes the understanding of the perceptions and beliefs about thermostats in Mexico using the signal detection theory (SDT), the fuzzy signal detection theory (FSDT), and chi-square (CS) test. It provides information for improving the acceptance level of thermostats and offers an excellent reference for increasing the acceptance level of STs. Furthermore, the results of this paper show how the SDT, FSDT, and CS are complementary methods that can construct a complete structure for understanding the perceptions and beliefs of end users in the energy sector. The CS test provides information about the relationship (dependence) among variables such as operation of thermostats and gender, and the SDT detects the manner in which the stimulus signals are perceived; therefore, a complete study about the ST end users can be conducted when both these techniques are implemented. If smart devices such as STs are relatively more accepted, the control of electrical energy will reduce energy consumption. Furthermore, the STs can communicate with smart meters; smart-metering systems are the next-generation power measurement systems that facilitate the provision of more information about the end user energy patterns to the electric grid. More importantly, with the integration of advanced computing and communication technologies at homes, the end user is able to make informed decisions about renewable energy resources and exploit distributed electrical grid intelligence [¹⁰]. Consequently, the acceptance of STs by the end user is crucial for the generation of favorable operation conditions for an SH and an SG. The unacceptability of a thermostat can adversely affect the growth of an SG. Moreover, a social study presented in Ref. [¹¹] shows that no statistical evidence for the thermostat settings between 1984 and 2007 is found. This scenario is unfavorable because it is imperative for an SG to improve energy consumption based on the knowledge of the end users consuming electrical energy; this condition limits the results of implementing complex systems such as an SH and an SG. Consequently, research papers that discuss the manner in which energy systems will be socially constructed and embedded exist [¹²,¹³]. As presented in Ref. [¹³], the consumer behavior is complex, which hardly follows the traditional economic theories of decision making. When choosing what products to buy or what services to use, consumers habitually believe that they are making smart decisions and behaving in ways that are highly rational and congruent with their values and intentions. However, daily life illustrates that this is often not the case. Electrical energy consumers regularly diverge from rational selections, in which one objectively weighs up the costs and benefits of all the alternatives before selecting the optimal course of action. This paper provides an excellent framework about the end users’ perceptions and beliefs of STs in Mexico. Generally, when the expectation is included in the analysis of products, only the performance of the product is considered; however, the performance of the company manufacturing the product must also be included [¹⁴]. For instance, consumer support, service, installation, and training must be integrated into the definition of expectation. Hence, small companies with a relatively weak customer support or training have a low credibility. This paper divides the end user scenario into three different categories, namely, usability, utility, and expectation; these categories completely describe the perceptions and beliefs of the end users. In this paper, it is important to observe that expectation is a variable with the lowest reliability of the ST end users in Mexico.

To summarize, this paper proposes a complete study based on two complementary methods (CS test and SDT) for finding the usability perceptions and beliefs for STs. There are very few papers in the literature that evaluate the independence in variables and the relationship between the stimulus and the response of end users. However, the generated information from those methods allows achieving precise results regarding end users’ perceptions and beliefs as it is shown in this paper. Hence, those results can be used by designers of STs to reach the expectations of the end users, and governmental energy offices can motive consumers of thermostats for adopting STs. Besides, the fuzzy detection theory (FDT) has also been applied in this paper to increment the precision of the conventional signal detection method so the relationship between stimulus and response can include non-binary values [¹⁵]. Alternatively, some researchers have implemented surveys for detecting the perception of end users in technological devices, but surveys do not provide all the information about the stimulus and response in the manner that SDT does [¹⁶]. On the other hand, when surveys are implemented, usually, they need an additional statistical methodology to analyze the results. For example, principal component analysis (PCA) which is a statistical procedure that uses an orthogonal transformation is implemented with surveys, but PCA is not an optimal projection from a pattern classification perspective [¹⁷], so this statistical method could not be suitable for particular classification conditions. As a result, it is difficult to implement only one statistical methodology for analyzing the information regarding beliefs and perception from end users. Nevertheless, the SDT, the FSDT, and CS test can be a good alternative for evaluating perceptions and beliefs of end users. The problem for detecting usability perception and beliefs about STs is full of noise from the real environment. Moreover, the perceptual responses are biased with respect to a criterion which changes based on the preferences for particular outcomes in the end users. In addition, the ability to discriminate stimuli signals from noise signals is important for detecting problems. As a result, using the signal detect theory for this kind of problems is suitable.

Related work

The SDT has been used in many psychology areas to separate the ability of persons to differentiate between classes of motivational effects and response biases. Moreover, this theory is an adaptation of the statistical decision theory so that all algorithms developed on the statistical decision theory could be compared with the SDT. However, this comparison is not considered in this paper since there are several papers that show the SDT against the statistical decision methods. On the other hand, this paper proposes the use of the FSDT, which combines fuzzy logic and the conventional SDT to measure usability perceptions and beliefs about STs that have not been studied using a statistical method such as signal detection or fuzzy signal detection. Besides, the CS test has been incorporated in this paper since it is intended to test how likely it is that an observed distribution is due to chance. It measures how well the observed distribution of data fits with the distribution that is expected if the variables are independent. The SDT, the FDT, and CS allow multiple forms of qualitative and quantitative information to be used for determining the perceptions and beliefs about STs in regions of Mexico. In addition, several studies show the manner in which the thermostats are set and the behavior of end users in the households in order to reduce energy consumption. Besides, these studies also illustrate that the programming features in thermostats are either not used or they are overridden [¹⁸]. Typically, the updated versions of the STs exhibit complex functions for saving energy; however, the end users do not implement these functions because they do not completely accept the STs or they are unfamiliar with smart wearables such as smart watches that can be connected to the STs. For instance, ecobee3, an ST, can be connected to a smart watch [¹⁹]. Most of the studies focus on adding technological values to the ST, the results of which show that while the ST can reduce energy consumption [²⁰,²¹], it can only deal with technological issues. However, additional information about the perceptions and beliefs of the ST end users is required in order to increase the adoption level of the STs. Because the manufacturing sector is under pressure to realize new products [²²], sometimes, they deliver products relatively fast, in a more cost-effective manner; however, they do not completely consider the end users’ perceptions and beliefs about STs.

On the other hand, misconceptions about energy saving using thermostats are presented because end users do not use the thermostats as designed by the manufacturer. In addition, when households are occupied nearly all the time, energy saving is reduced because the ST cannot save sufficient energy, owing to which the benefits of the ST are underrated for the end user; this leads to dissatisfaction of the end user with the thermostat, and the degree of expectation is lowered. In addition, relatively more advanced systems such as Wi-Fi networks that can remotely control the thermostat for setting the set point of temperature for the entire day are not implemented correctly in several households. If a Wi-Fi network is implemented correctly, the thermostat can be remotely disconnected, and the consumption demand can be reduced [⁴]. However, if the ST end user does not accept to change the value of the set point of the ST using Wi-Fi networks, this wireless technology will not significantly increase the consumption of energy in households. Further, reducing the adoption level of STs affects the financial performance of companies; therefore, they must generate more information about the perceptions and beliefs of the ST end users.

In Ref. [²³], it is shown that there exists a difference in the thermal comfort and use of thermostats in Finland between men and women. However, the study conducted in Mexico does not show any such difference associated with the operation of the STs between men and women based on their perceptions and beliefs. Moreover, one of the main problems associated with the thermostat is that it needs to be programmed and used in a correct manner. The study presented in Ref. [²³] shows that men use thermostats more often than women; however, it does not clearly show whether men use the thermostat in a correct manner or whether the expectation about the thermostat is met.

On the other hand, the use of computer simulation can provide different thermostat strategies in order to save energy and improve electrical energy consumption in the cold climate [²⁴]. Nevertheless, these strategies will be able to save relatively more energy if the perceptions and beliefs about thermostats are included in the strategy because the fundamental end user perceptions are included in a complete manner.

Although STs are electrical-energy-saving devices used for controlling cooling or heating systems, they need to be accepted by the end users. Currently, these thermostats have not yet been completely accepted by the end users. Hence, this paper provides important information on the end users’ perceptions and beliefs about thermostats.

The experimental study was conducted in five states of Mexico in order to include the main ST consumers. Besides, this experimental study is focused on the population that adopts STs.

The respondent’s general information for this experimental study is summarized in Table 1. The respondents included young individuals (<38 years old) because the elderly (>38 years old) did not want to participate in this study (41 elderly individuals were contacted, but they did not answer the web based or email questionnaires).Thus, some personals interviews were conducted to get the general information about the behavior of elderly individuals. This information was used only for getting an idea about them but it was not part of the study in this paper.

Usually, in Mexico, the elderly are unfamiliar with the use of STs, whereas the youth quickly adopts such technological devices, thereby motivating the elderly to include such devices in their households. Therefore, owing to unfamiliarity, generally, the elderly do not program or use the ST on a daily basis. Typically, they seek help from young individuals to program the ST. Figure 1 shows the states of Mexico that participated in this study.

On the other hand, normally, five respondents have been considered adequate for usability testing [²⁵–²⁷]. The results presented in Ref. [²⁶] show that at least 15 respondents are required to discover all the usability problems, and therefore, there is a risk of using only five participants [²⁸,²⁹]. In addition, if more respondents are added in the study, it could keep seeing the same usability problems again and again [²⁶]. However, when the number of respondents is increased to 20, the variance in the percentage of known usability problems could be reduced, and the levels of certainty could be increased [²⁸,³⁰]. Thus, 23 respondents have been selected this study to find the usability problems in the ST. The respondents have been selected from different states of Mexico in which cooling systems are required. Since Mexico is slowly adopting the ST, the number of respondents who have the ST is small. However, 23 respondents are sufficient enough to conduct a usability test as it has been presented in Ref. [²⁸]. Although this study does not show the data from elderly individuals, it has been presented in Ref. [³¹] that the usage of technological devices is not different from the motivational point of view of young people. On the other hand, the average age is 27 years in the population of Mexico [³²]. Thus, a group of young people with an average age equal to 23.8 years that is close to 27 years has been selected. However, a similar study could be conducted to get the information from elderly individuals.

The applied questionnaires were based on web and email to encourage technological methods since they are very attractive because of low cost and fast rate of response. Further, in Mexico, 63.8% of Wi-Fi network users are young individuals (<35 years old) [³³] and the average age of the Mexican population is 27 [³²]. Thus, the sample of respondents is representative of the population in question.

Several methods reported in the literature can be used for detecting the perceptions of users [³⁴,³⁵], so it is a complex task to select the correct method. Thus, the combination of signal detection, fuzzy signal detection, and CS test has features that are adequate for evaluating perceptions and beliefs of users. The main characteristics of each method are presented below to determine the advantages that can be achieved when they are applied.

The main features of the SDT are [³⁶] that the trade-off between hit rate and false alarm rate can be measured; the hit rate performance is a biased measurement; the decision of the end user can be detected under the presence of noise (internal/neural and external/physical); the sensitivity (discriminate a stimulus from noise) is independent of the criterion; the measure of discriminability is insensitive to criterion, and it can be computed from the hit rate and the false alarm rate; the observers are both sensors and decision makers; and to evaluate the occurrence of an event, the observers adopt a decision criterion.

The FSDT is an extension of SDT, so only the main features of fuzzy detection method are shown [³⁷], that is, events can belong to the set (signal) to a degree ranging from 0 to 1; and events can belong to the set (response) to a degree ranging from 0 to 1.

The main features of CS test are [³⁸,³⁹] that a cross classification table to examine the nature of the variables relationship is used; the results show the manner in which two variables are either related or are not linked to each other; the independence test examines whether the observed pattern between the variables in the table is strong enough to show that the two variables are dependent on each other or not; the independence test is concerned with the relationship between two variables; and the independence test is general and can be used with variables measured on any type of scale, nominal, ordinal, interval or ratio.

CS numerical method

The CS test is considered to be a nonparametric statistical method. Consequently, it can be implemented when data do not meet the assumptions required to run other analyses. Thus, the CS test is used to analyze the differences between the results of the current study and the expected results [³⁰,⁴⁰]. In this study, the CS test is performed to analyze the responses to the questions asked on the ST to determine the dependencies between variables.

Equation (1) is obtained using the CS test, which is used to analyze the differences between the results obtained and the results expected. In fact, this mathematical expression represents all the three tests belonging to the Karl-Pearson family of the CS test [⁴¹].

(1)x^{\mathrm{2}}={\displaystyle {\sum }_{i=\mathrm{1}}^n\frac{{(O_i-E_i)}^{\mathrm{2}}}{E_i}},

where O_i stands for the number observed in class i, E_i for the number expected in class i.

Finally, the level of significance (α) is equal to 0.05 in all the tests performed.

If Eq. (1) is applied to the evaluation of the respondents, the CS test will provide information about the ST end users. Below, a complete set of evaluations is presented based on the CS test (Tables 2, 3, and 4).

(1) The expected hypothesis (H₀) is described as follows:

H₀: There is no significant difference associated with the use of STs between men and women.

The significance level is equal to 0.05.

The CS statistic is 2.7184, and the p-value is 0.099195. This result is not significant at p<0.05. As a result, there is no significant difference associated with the use of STs between men and women.

(2) The expected hypothesis (H₀) is described as follows:

H₀: There is no significant difference associated with the operation of the ST between a house that is owned and one that is rented by an end user.

The significance level is equal to 0.05.

The CS statistic is 0.8776, and the p-value is 0.348861. This result is not significant at p<0.05. Therefore, there is no significant difference associated with the operation of the ST between a house that is owned and one that is rented by an end user.

(3) The expected hypothesis (H₀) is described as follows:

nH₀: There is no significant difference associated with the environmental impact created by CO₂ between men and women.

The significance level is equal to 0.05.

The CS statistic is 2.7184, and the p-value is 0.099195. This result is not significant at p<0.05. As a result, there is no significant difference associated with the environmental impact created by CO₂ between men and women.

SDT

Since developed by Refs. [⁴²–⁴⁴], the SDT has been used in different areas in order to understand the responses to different input signal conditions. The SDT is a theoretical approach to distinguish between the signal (stimulus) with noise and noise (distracters) alone in which the response is classified into binary categories [⁴⁵]. This concept is based on normal distributions of both signals. Although the SDT does not require the presence of a noisy environment or signal, it assumes that each response is strictly classified into one of the two categories (1/0). The possible responses depending on the input signal are defined in terms of the SDT matrix representation, in which the possible responses are classified into the following four categories: ① correct rejection (the signal is absent, and the response is detected correctly), ② miss (the signal is present, and the response is not detected correctly), ③ hit (the signal is present, and the response is detected correctly), and ④ false alarm (the signal is absent, and the response is not classified correctly). The criterion line delimits the boundaries in which each zone is divided, and the sensitivity index d and the likelihood ratio b are used to describe the detection of the stimulus signals [⁴⁶]. The sensitivity index (d) is the standard distance between the normal distribution curve approximating the signal and the one approximating the noise distribution; hence, it is defined as the horizontal distance in terms of the standard deviation between these curves. The hit rate (HR) of the observer on a normal distribution minus the false alarm rate (FAR) on a normal distribution is defined as the distance between noise and the signal plus noise. Further, d is the distance between the means of the probability distributions associated with the signal and the noise, which is calculated by the z-score associated with the HR and the FAR [⁴⁷,⁴⁸]. This distance represents the observer sensibility, and it can be represented by the receiver operating characteristic curves (ROCs), which illustrate the relationship between these components. The ROC curve shows the tradeoff between the observer’s sensory performance and the observer’s decision biases.

The HR and FAR are calculated using Eqs. (2) and (3), in which the HR is the proportion of signal 1 to which the observer responded 1 and the FAR is the proportion of signal 0 to which the observer responded 1. Further, the HR can be defined in terms of the number of hits S(H) divided by the total number of possible signals.

(2)\mathrm{HR}=P("\mathrm{1}"|\mathrm{1}),

(3)\mathrm{FAR}=P("\mathrm{0}"|\mathrm{1}).

Thus, the sensitivity index (d) is calculated by Eq. (4) as

(4)\delta =Z\left(\mathrm{HR}\right)-Z\left(\mathrm{FAR}\right).

The likelihood ratio (LR) is derived using Eq. (5) as

\beta ={\mathrm{e}}^{\ln \beta }={\mathrm{e}}^{\ln (\delta \cdot c)},

(5)\beta ={\mathrm{e}}^{(Z{\left(\mathrm{FAR}\right)}^{\mathrm{2}}-Z{\left(\mathrm{HR}\right)}^{\mathrm{2}})/\mathrm{2}},

where C=-{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\left[Z\right(\mathrm{HR})+Z(\mathrm{FAR}\left)\right].

The LR value can be compared with an optimized value based on the ratio of the probability of noise to the probability of receiving a viable signal ({\beta }_{\mathrm{opt}}=P\left(N\right)/P\left(S\right)). When , the LR value is said to be conservative, and when \beta >{\beta }_{\mathrm{opt}}, the LR value is said to be liberal. Typically, the desired value is approximately equal to the optimization criterion {\beta }_{\mathrm{opt}}. The criterion location (C) is a measure of the response bias. If C is evaluated relative to the point at which the two distributions intersect, C=-{\displaystyle \frac{\mathrm{1}}{\mathrm{2}}}\left[Z\right(\mathrm{HR})+Z(\mathrm{FAR}\left)\right] can be used to determine its value.

FSDT

The FSDT allows to have degree values in the range of [1,0] that can be used in signal and response [⁴⁹]. These values accurately describe the perception of an academic researcher. For the complete description of each step of the FSDT algorithm, refer to Ref. [⁵⁰].

The basic steps of the FDT algorithm are described below:

(1) The mapping functions are defined on the basis of the data and requirements of the analysis. Further, the mapping functions for the signal and the response describe the states in terms of the membership values in the range of [0,1].

(2) In the case of mapping, the signal and the response are analyzed to calculate the membership values for hit (H), miss (M), false alarm (FA), and correct rejection (CR). These values are obtained using implication functions. In Eq. (6), the fuzzy set membership for the four possible outcomes is defined as follows.

(6)\begin{array}{l}H=\min (s,r),\hfill \\ M=(s-r,\mathrm{0}),\hfill \\ \mathrm{FA}=\max (r-s,\mathrm{0}),\hfill \\ \mathrm{CR}=\min (\mathrm{1}-s,\mathrm{1}-r).\hfill \end{array}

(3) After n observations, the HR, FAR, MR, and CRR are calculated using Eq. (7).

(7)\begin{array}{l}\mathrm{HR}={\displaystyle \frac{{\displaystyle {\sum }_i^n}{H}_i}{{\displaystyle {\sum }_i^n}{S}_i}},\hfill \\ \mathrm{FAR}={\displaystyle \frac{{\displaystyle {\sum }_i^n}\mathrm{F}{\mathrm{A}}_i}{{\displaystyle {\sum }_i^n}\mathrm{1}-s_i}},\hfill \\ \mathrm{MR}={\displaystyle \frac{{\displaystyle {\sum }_i^n}{M}_i}{{\displaystyle {\sum }_i^n}{S}_i}},\hfill \\ \mathrm{CRR}={\displaystyle \frac{{\displaystyle {\sum }_i^n}\mathrm{C}{\mathrm{R}}_i}{{\displaystyle {\sum }_i^n}\mathrm{1}-s_i}}.\hfill \end{array}

(4) The fuzzy sensitivity (d) and likelihood ratio, also known as the criterion (b) values, are calculated using the signal and false alarm fuzzy values. As a matter of fact, in the case of the SDT, the sensibility and criterion fuzzy values have the same meaning. In Eqs. (8) and (9), the sensibility and criterion are determined using the fuzzy value.

(8)\delta =Z\left(\mathrm{HR}\right)-Z\left(\mathrm{FAR}\right),

(9)\beta =Y\left(\mathrm{HR}\right)/Y\left(\mathrm{FAR}\right).

The ordinates of the normal distribution of the HR and FAR are represented by Y (HR) and Y (FAR), respectively. These values are determined using Eq. (10).

Y\left(\mathrm{HR}\right)={\displaystyle \frac{\mathrm{1}}{\sqrt{\mathrm{2}\mathrm{\pi }}}}\exp (-{\displaystyle \frac{Z{\left(\mathrm{HR}\right)}^{\mathrm{2}}}{\mathrm{2}}}),

(10)Y\left(\mathrm{FAR}\right)={\displaystyle \frac{\mathrm{1}}{\sqrt{\mathrm{2}\mathrm{\pi }}}}\exp (-{\displaystyle \frac{Z{\left(\mathrm{FAR}\right)}^{\mathrm{2}}}{\mathrm{2}}}).

End user perception and beliefs based on SDT and FDT

Although the ST end user needs to adjust his patterns of electrical consumption in order to achieve an efficient electric household operation, it is rather difficult for most end users to accept simple demand management for institutional reasons [¹,⁵¹]. Moreover, while the ST can automatically adjust the patterns of electrical consumption to save energy, the ST end user does not use such advanced functions on the ST. The end users were questioned about different conditions that transmit different stimuli to observe the responses. Moreover, some conditions were focused on individual responses that affect the complete electrical grid or community consumption. For designing some of the principal conditions, an in-depth survey that provides the characteristics of utility, usability, and expectation was conducted to extract the main information [⁶,⁷,¹⁵]; it should be noted that some relevant published information was included in the survey [¹²,⁵²]. The main paradigm is to define the perceptions and beliefs of the end users about STs in order to increase their acceptance level. This study also attempts to promote a decrease in energy consumption in households with STs. The end users’ responses are classified into values ranging from 1 to 7, and the threshold is set to 4 (confident criterion) [⁵³]; in that regard, Fig. 2 shows the scale that is used by the ST end users in the surveys.

Table 5 summarizes the survey conducted to understand the utility of STs and the stimulus signal. As shown Table 5, this survey focuses on the manner in which the ST is designed to perform, particularly when it is operated by the end user. Tables 6 and 7 present the results of the SDT, and Table 8 shows the results of the FSDT when a specific stimulus is applied. As summarized in Tables 8 and 9, the end user can detect the stimulus signal, and therefore, he/she can select an ST that is best suited to his/her requirements, without being perturbed by the functions that do not meet the desired performance requirements. On the other hand, the end users are open to trying new functions that are incorporated in the ST on the basis of the value of (B); however, they do not adopt these functions if these functions are not considered essential by them. The FSDT suggests (Tables 7 and 9) that end users clearly detect the functions that are beneficial to them in their everyday routine; however, liberal end users are incapable of accurately making an informed decision and detecting suitable functions that meet their requirements. Hence, such users attempt to use new functions of the ST by selecting random functions and analyzing their usefulness.

Table 10 shows the usability of STs. From Table 10, it can be observed that this survey focuses on sending the stimulus regarding the perception of the end users when the ST is effective and easy to use. The end user will recommend the ST if it is effective and user-friendly; thus, the information about the ST can be transmitted to new consumers, which, in turn, will increase its acceptance level. Tables 11 and 13 show that the end users can detect the stimulation signal and recognize when the ST is user friendly and efficient; however, the liberal end users cannot accurately detect signals (Tables 12 and 14), owing to which they try new STs to determine an ST that meets their requirements of being user friendly and effective. Thus, the functions that are associated with improving the efficiency of STs will be accepted by the end users. Table 14 illustrates that the end users detect the stimulus in a correct manner.

Table 15 shows the end user’s expectation about the ST when specific stimuli are applied. The results (Tables 16 and 18) show that the end user does not accurately detect the stimulus signal, owing to which their expectation about the ST is unclear. It is possible that the end users expect more functions that decrease the complexity of operation of the device and increase technical support; however, it is clear that the end users are unclear about the expectations of an ST, owing to which they are unable to detect noise from the stimulus signal (Tables 16 and 19). Moreover, because the end users are not confident of using the ST, it is imperative for the designers to come up with a new idea for reducing the complexity associated with the operation of the ST.

On the one hand, many successful programs for saving energy in Mexico have been conducted to motivate the end users to replace the electrical devices in their households [⁵⁴]; however, those programs could have a bigger impact in several sector of the population if those are always implemented based on the best technology available in the energy market for achieving the end user expectations. On the other hand, several end users do not attend programs about environmental impact because they are unable to grasp the motive of such programs, which, in turn, sets unclear expectations in their minds. Therefore, a program with a stronger motive is required, such as that promoting both monetary benefits over a relatively short period of time and effective financial assistance for low-income inhabitants. In depth, the results presented in this paper suggest that expectation is one of the main problems that influence the acceptance level of the STs. Moreover, the ST end users are unable to accurately understand the functions and advantages of the STs, owing to which their expectation from the STs is highly skewed. In addition, the expectation results show that the end users need to receive accurate and complete information about the STs in order to understand the relationship between kilowatts-hour and CO₂ so that they are eventually motivated to install STs in their homes. However, if the end users are unclear about this relationship, they will not understand the environmental impact of incorrectly operating STs. From the results presented in Tables 16 and 17, it is found that expectation is the classification that confuses the ST end users; therefore, the ST designers need to provide accurate information about the STs for improving their acceptance level in Mexico.

Discussion

This paper enables an in-depth understanding of the perceptions and beliefs of end users about STs. If the electrical designers and electric companies do not understand the perceptions and beliefs of the end users about the STs, the STs will continue to remain unaccepted by the end users for a relatively long period of time, which, in turn, will adversely affect their foray into the electrical market; in other words, the end users who have understood the functions and reached their expectations of the STs will readily accept the STs as compared to those who have unclear expectations of the STs. As a result, the entire smart electrical grid can be directly affected because either the STs are not being used in a correct manner or the STs are not adopted. Therefore, it can be concluded that the electrical consumption system is not working well to save electrical energy.

On the other hand, although the STs can be simple and effective, they have not yet been accepted by the end users, and different studies have failed to provide the perceptions and beliefs of the end users about the STs. This paper includes the SDT and the CS test to achieve a greater understanding of the end user. Further, this paper considers the utility, usability, and expectations of the STs as the main factors that affect the end users’ perceptions and beliefs.

The results of the CS tests show that there are no differences associated with the use of STs between men and women; therefore, it can be concluded that men and women possess the same operation skills. Moreover, the end user operates the ST in either an owned house or a rented one. Further, there are no differences associated with the environmental impact created by CO₂ between men and women. These results indicate that it is not necessary for the designers to generate special functions for men or women. In other words, they do not need to customize the STs as per the requirements of men or women because both of them use the STs in the same manner. In addition, if a previous ST is deployed in a rented household, the existing end user uses the ST in the same manner as the previous end user. The selection of the ST by the landlord does not change the manner in which the ST is operated by the end user. Thus, the ST does not motivate the end users to improve the manner in which they would operate them. Moreover, there are no differences associated with the knowledge of the environmental impact created by CO₂ between men and women. Both of them require accurate and complete information about the environmental impact created by CO₂; moreover, the information provided by the ST designers is not good enough for the end users because it does not motivate them to reduce the generation of CO₂ through the efficient use of the ST.

Since SDT and FDT show the strength of the signal according to the noise presented (d), this paper gives the strength of the signal when the end user is evaluated in three different categories: utility, usability, and expectation. Besides, the SDT and FDT reflect the strategy of responses of the end user (B).

In terms of the utility of the ST, this paper shows that the end user accurately detects the stimulus signal and that the number of hits is higher than the number of false alarms. As a result, the end user considers the operation of the ST to be easy and efficient, and he/she is able to remember the instructions for using it. On the other hand, the strength of the signal is high (d) and the strategy of responses of the end user (B) shows that the end users say “yes” easily rather than “no”; hence, they try the operation of the ST. Moreover, it is important to remark that the end users are open to trying the new functions incorporated in the ST. The stimulus signal and noise signal are well separated for the end user. The utility of the ST is well understood by the end users, and the user provides excellent responses to the stimulus. Consequently, when new functions are incorporated in the ST, the end user believes that the installation and operation processes are likely to be relatively easy and the number of errors will be low.

In terms of the usability of the ST, the end user has a higher strength in the signal than signals sending from the study of utility. This strength in the signal makes it possible to send stimulus in this category, and the end user can detect the stimulus in a correct way, and the number of false alarms is low. In addition, the strategy of the response of the participants shows that they can easily give an affirmative answer when a stimulus signal is transmitted. The end user is liberal in terms of the evaluation of the usability of the ST; therefore, it is believed that the ST is more likely to be useful in the daily life than not.

The expectation of the end user presents a different perspective because the end user has a lower HR and a higher FAR. The end user cannot accurately detect the stimulus signal when the expectation is evaluated. Thus, the end user increases the number of false alarms. This is an important factor that should be considered because there are several electric companies that focus only on the utility and usability of STs, and not on giving out stronger messages in favor of STs that would enable the end users to have a realistic and positive expectation in their minds. The strength of the signal is lower (d) and the strategy of the response of end user is higher so the end user can be motivated to say “yes” if they find the correct stimulus. The end users do not have sufficient information about decreasing the generation of CO₂ through the efficient operation of the ST. Perhaps this information regarding the environmental impact created by the production of CO₂ should be provided in an unconventional manner.

Moreover, the end user is not confident about using the ST, and he/she is unaware of all the different brands and types of STs available on the market. As a result, the end user is unaware of the amount of energy required by the ST when operated in households.

The utility and usability of the ST are well understood by the end users; however, the expectation is not defined in a precise manner by the information provided by the electric companies, which causes confusion in the minds of the end users. Most importantly, if the electric companies do not understand the expectations of the ST end users, they will not be able to change their perceptions and beliefs about the ST. For example, it is imperative for the designers to provide information about saving energy and reducing the environmental impact caused by the incorrect operation of the ST in more than one way. Given that the end users have different expectations, it is important to understand the segment of the market that is using STs in order to adapt the ST to the expectation of the end users. Moreover, electric companies need to create functions in favor of providing realistic expectations of the STs, which will motivate the end users to accept and adopt STs in their households. Besides, it is necessary for the electric companies to link the expectations of the end users with the usability and utility factors of the STs in order to improve the perceptions and beliefs of the end users. Because the expectations are not based on a particular sector of end users, the ST must be able to adapt to several market sectors. The ST will have a higher acceptance level if it is able to provide a realistic and positive expectation for the end users.

Conclusions

The results of this paper show that there is no significant difference associated with the operation of the ST between men and women, and the ST is operated in the same manner, irrespective of whether it is installed in an owned household or a rented one. It is critical for the ST designers to take the end users’ expectations into consideration because the end users have not been motivated enough to adopt STs in their households. Thus, the end users confuse the stimulus signal with noise, owing to which the expectation of the end users confirms that the ST is not operated correctly by the end users. Besides, the end users expect a more effective service from the ST companies and are not confident of using the ST. On the other hand, the end users currently are not using the ST for saving energy because they have not been motivated enough to do so by the lack of information provided by the ST designers and the government. Therefore, it is critical to motivate the end users to reduce the generation of CO₂ through the proper operation of the ST; in this regard, the end users need to be given precise information regarding the environmental impact caused by the incorrect use of the ST so that they are cautious about operating the STs in a proper manner. On the other hand, the end user prefers a non-complex thermostat with minimum functions, claiming that such a thermostat is essential for living comfortably. Thus, the end user requires an ST that includes a minimum number of functions and one that operates efficiently; it is also critical that the expectations set by the ST designers are met.

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