TIMELINESS MEASUREMENT MODEL: A MATHEMATICAL APPROACH FOR MEASURING THE TIMELINESS OF HANDHELD APPLICATION USAGE

International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) Timeliness Measurement Model: A Mathematical Approach for Measuring the Timeliness of Handheld Application Usage Amalina Farhi Ahmad Fadzlah Department of Science Computer Faculty of Defense Science and Technology National Defense University of Malaysia Wilayah Persekutuan Kuala Lumpur, Malaysia amalina.farhi@upnm.edu.my ABSTRACT This study is aimed for developing a surveybased mathematical model specifically for measuring the timeliness of handheld applications usage. This study is designed to achieve five major objectives: identifying the elements for measuring timeliness, analyzing contributed factors of timeliness measures, developing a model for measuring timeliness, constructing formulas for measuring timeliness as well as prioritizing the overall timeliness of handheld application usage. As a result, a mathematical model namely Timeliness Measurement Model (TMM) is developed in which outlined thirteen timeliness measures in three different hierarchy levels of metrics, attributes and criterions. This model can be used for analyzing the timeliness of handheld application usage. KEYWORDS Design, tools, techniques, models, principles, handhelds interfaces, 1 INTRODUCTION Handheld computing device is set to support anyone, anywhere and anytime environment. Clearly, this device has been criticized as one of the most excessively hyped new technology of all time [1]. Maintained as a small size computing device, display and window dimensions are a very critical factor for handheld technology development [2], [3]. Constraining the screen size does have an effect on the performance of handheld computing devices and furthermore can significantly affect the timeliness of handheld application usage [4]. Several models were developed to overcome the problems however these models were not directly applicable to be implemented to measure the timeliness of handheld application usage specifically [5], [6]. One of the main gaps is that these models do not take into account the unique timeliness characteristics of handheld application usage. For examples, in [7], the researcher created a model that includes interactions and time that exist between the environment, participants and activities. In [8], [9] and [10], the researchers proposed a design model that considered the interaction between users, contexts, information presentations and data entry methods. Meanwhile, in [11], [12], [13] and [14], the models focused on the context of use, set requirements for the handheld application usage as the components of user, environment, tasks and interface. Although research on these previous studies provides a lot of useful 431 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) information in understanding components in evaluating the handheld application usage, there are however lack of effort being given to integrate the timeliness measures of handheld application usage and towards measuring the timeliness of handheld application usage mathematically [15], [16]. Measures that are not sensitive to the body of product exhibits can be interpreted as possesses an unrelated result in measuring the usage performance of handheld applications particularly and the timeliness of the handheld applications in specific [17]. In this regard, there is a strong reason to initiate a new research to develop a mathematical-based model specifically for measuring the timeliness of handheld application usage. Therefore, the main contribution of this study is the development of a model for measuring the timeliness of handheld application usage mathematically. Findings from this research not only reveal the interaction between handheld computing users and interface layout factors but will also provide a better understanding on the relationship of these factors. Furthermore, this model can be established as a concrete evaluation technique to be used during measuring the overall timeliness of handheld application usage. 2 RESEARCH METHODS This study is designed to achieve five major objectives: identifying the elements for measuring timeliness, analyzing contributed factors of timeliness measures, developing a model for measuring timeliness, constructing formulas for measuring timeliness as well as prioritizing the overall timeliness of handheld application usage. A total number of two hundred nineteen respondents among handheld applications users was analyzed to the purpose of this study. For the number of two hundred nineteen samples, the response rate was approximately about seventy-seven percent. This percentage was considered as satisfactory in which the responses exceeded the research minimum acceptable level of fifty percent plus one. Identifying the elements for measuring timeliness In order to identify the elements for measuring the timeliness of handheld application usage, a questionnaire survey namely ‘Investigating the Timeliness Measures for Measuring the Handheld Application Usage’ was developed. The purpose of conducting this survey is to elicit the responses from the target respondents to detect which measures need to be included in and which measures need to be excluded from being the timeliness measures of handheld application usages. A pilot study was also conducted to confirm the validity and reliability as well as to obtain the understandings towards the construct of the questionnaires. Analyzing contributed timeliness measures factors of Data collected from the final questionnaire was entered on the Statistical Package for the Social Sciences (SPSS) for the analysis process as well as to classify the timeliness measures into the hierarchical structure of metrics, attributes and criterions. This brings together two parts of evaluation tests: Pearson’s Chi-square test and the Spearman’s Rho test. Pearson’s Chi432 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) Square test was conducted to measure the amount of association between two different timeliness measures in two different hierarchy levels and the Spearman’s Rho test was conducted to comprehend the relationship strength between two different timeliness measures in two different hierarchy levels. Developing a model for measuring timeliness In order to develop a model, four stages were involved. This brings together four parts of ranking, mapping, coding and weighting the timeliness measures. The construction of ranking as well as mapping, coding and weighting, thus results a hierarchical model for measuring the timeliness of handheld application usages, namely Timeliness Measurement Model (TMM). Constructing formula for measuring timeliness As to construct formulas, three stages were involved. This brings together the formula for measuring the metrics and attributes as well as the timeliness of handheld application usage. The combination of ranking as well as mapping, coding and weighting, thus results a mathematical-based model for measuring the timeliness of handheld application usages. Prioritizing the overall timeliness result In measuring the timeliness of handheld application usage, analysis can be done by converting the values into words or sentences that can be interpreted accurately and comprehensively. This brings together the timeliness levels, thresholds as well as overall the overall analysis. 3 TIMELINESS MEASUREMENT FRAMEWORK In order to develop a hierarchical model for measuring the timeliness of handheld application usage, a conceptual framework, namely Timeliness Measurement Framework was introduced (Refer to Figure. 1). This framework brings together different timeliness measures in different timeliness hierarchy levels as detailed below. Each level represents interaction with other level and impacts one another to measure the timeliness of the desired product. This can be explained as either none, one or more metrics could represent a single attribute. The combination of these metrics could be represented as the components that contributed to only one attribute. And finally, these attributes are used to support in the calculation of the criterion that can be concluded as directly affected the timeliness of a product. This is the case at every level in which could be represented as an M-1 relationship. For example, metric M1 … Mn are the input to attribute A1 and criterion C1 is an output for the attribute A1. Consider if the value of metric M1, M2, … , Mn-1 or Mn increases so as the value of attribute A1 and criterion C1. Again, if the value of metric M1, M2, … , Mn-1 or Mn decreases so as the value of attribute A1 and criterion C1. 433 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) M1 … A1 Mn … C1 M1 … An Mn Metric Relationship between Metric and Attribute Attribute Criterion Relationship between Attribute and Criterion Figure 1. Timeliness Measurement Framework. Each level represents interaction with other level and impacts one another to measure the timeliness of the desired product. This can be explained as either none, one or more metrics could represent a single attribute. The combination of these metrics could be represented as the components that contributed to only one attribute. And finally, these attributes are used to support in the calculation of the criterion that can be concluded as directly affected the timeliness of a product. This is the case at every level in which could be represented as an M-1 relationship. For example, metric M1 … Mn are the input to attribute A1 and criterion C1 is an output for the attribute A1. Consider if the value of metric M1, M2, … , Mn-1 or Mn increases so as the value of attribute A1 and criterion C1. Again, if the value of metric M1, M2, … , Mn-1 or Mn decreases so as the value of attribute A1 and criterion C1. 3.1 Timeliness Hierarchy Timeliness hierarchy is classified into three hierarchical levels of metrics, attributes and criterions. Metrics is described as the lowest hierarchy level. The main objective of the metrics is to identify measurable data for the purpose of measuring the timeliness of handheld application usages. The middle hierarchy level is described as attributes, whereas the highest is described as criterion (i.e. the Timeliness). This timeliness hierarchy which brings together three different timeliness levels of metrics, attributes and criterions is as detailed below (Refer to Table 1). 434 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) Table 1. Timeliness Hierarchy Hierarchy Description Metric Attribute The lowest hierarchy level; A collection of measurable data expressed in units The middle hierarchy level; A collection of metrics which belongs to a class of measures The highest hierarchy level; A collection of attributes for measuring the timeliness of handheld application usages Criterion 3.2 Timeliness Measures A total number of ten metrics and three attributes were identified having associated towards measuring the timeliness of handheld application usage. The definition of each timeliness measure as well as the classification of these timeliness measures according to its corresponding hierarchy levels is as depicted below (Refer to Table 2). 4 ANALYSES OF TIMELINESS MEASURES 4.1 Association Test Association test reported the importance of the association of metrics and attributes as well as the importance of the association between attributes and criterion towards measuring the timeliness of handheld application usage. The association test reported that metrics of Time of Actions Presented (M = 4.35, SD = .824), Time of Data Obtained (M = 4.48, SD = .680), Time of Objects Pointed (M = 4.19, SD = .846) and Time of Responses Retrieved (M = 4.36, SD = .718) are contributed towards attribute Interaction Mode with p < .001. Results also found that metrics Time of Items Remembered (M = 4.25, SD = .896), Time of Knowledge Acquired (M = 4.42, SD = .618) and Time of Understanding Perceived (M = 4.42, SD = .734) are contributed towards attribute Learning Interval with p < .001. Meanwhile, metrics Time in Pausing Tasks (M = 3.90, SD = 1.060), Time to End Tasks (M = 4.00, SD = 1.062) and Time to Start Tasks (M = 4.15, SD = .948) were also found contributed towards attribute Until Event with p < .001. Finally, result of the association test also stated that the attributes of Interaction Mode (M = 4.39, SD = .729), Learning Interval (M = 4.23, SD = .758) and Until Event (M = 4.21, SD = .889) were found contributed towards Timeliness as the criterion also with p < .001. The summarization of each association result is as depicted below (Refer to Table 3). 4.2 Relationship Test Relationship test reported the strength of the correlation between metrics and attributes as well as the strength of the correlation between attributes and criterion towards measuring the timeliness of handheld application usage. The coefficient value revealed that there was a moderate, positive linear relationship between metric Time of Action Presented (R = .439), Time of Data Obtained (R = .469), Time of Objects Pointed (R = .400) and Time of 435 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) Responses Retrieved (R = .495) towards attribute Interaction Mode with p < .001. Results also found that the coefficient value of metrics Time of Items Remembered (R = .464), Time of Knowledge Acquired (R = .415) and Time of Understanding Perceived (R = .371) are moderate and positive linear relationship with p < .001. The relationship test also revealed that there was a moderate, positive linear relationship between metrics Time in Pausing Tasks (R = .419), Time to Start Tasks (R = .420) and Time to End Tasks (R = .439) with p < .001. Finally, result of the relationship test also indicated the correlation strength between attributes Interaction Mode (R = .436), Learning Interval (R = .406) and Until Event (R = .465) as moderate and having positive linear relationship with p < .001. The summarization of each relationship result is as depicted below (Refer to Table 4). Table 2. Timeliness Measures and Descriptions Hierarchy Criterion Attribute Measures and Descriptions Timeliness Capability in acting at a fitting or advantageous time or performing exactly at the time appointed Interaction Mode Capability in completing interaction tasks at an opportune time Learning Interval Capability in completing learning tasks at an opportune time Until Event Capability in performing given tasks at an opportune time Time of Actions Presented Capability to present actions at an opportune time Time of Items Remembered Capability to remember items at an opportune time Time in Pausing Tasks Capability to pause tasks at an opportune time Time of Data Obtained Capability to represent data at an opportune time Time of Knowledge Acquired Capability to acquire knowledge at an opportune time Time to End Tasks Capability to end tasks at an opportune time Time of Objects Pointed Capability to point objects at an opportune time Time of Understanding Perceived Capability to perceive understandings at an opportune time Time to Start Tasks Capability to start tasks at an opportune time Metric Time of Responses Retrieved Capability to retrieve responses at an opportune time 436 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) Table 3. Result of Association Test Timeliness Measures Mean Metric  Attribute Time of Action Presented  Interaction Mode Time of Data Obtained  Interaction Mode Time of Objects Pointed  Interaction Mode Time of Responses Retrieved  Interaction Mode Time of Items Remembered  Learning Interval Time of Knowledge Acquired  Learning Interval Time of Understandings Perceived  Learning Interval Time in Pausing Tasks  Until Event Time to End Tasks  Until Event Time to Start Tasks  Until Event 4.35 4.48 4.19 4.36 4.25 4.42 4.42 3.90 4.00 4.15 Attribute  Criterion Interaction Mode  Timeliness 4.39 Learning Interval  Timeliness 4.23 Until Event  Timeliness 4.21 Legend of the table: Grayed entries denote that the association of metrics and attributes listed has no significant association in measuring the usability of handheld applications. Table 4. Result of Relationship Test Timeliness Measures Metric  Attribute Time of Action Presented  Interaction Mode Time of Data Obtained  Interaction Mode Time of Objects Pointed  Interaction Mode Time of Responses Retrieved  Interaction Mode Time of Items Remembered  Learning Interval Time of Knowledge Acquired  Learning Interval Time of Understandings Perceived  Learning Interval Time in Pausing Tasks  Until Event Time to End Tasks  Until Event Time to Start Tasks  Until Event S-Rho .439 .469 .400 .495 .464 .415 .371 .419 .439 .420 Attribute  Criterion Interaction Mode  Timeliness .436 Learning Interval  Timeliness .406 Until Event  Timeliness .465 Legend of the table: Correlation is significant at the 0.001 level (2-tailed) and range in the value of +1 to -1 5 TIMELINESS MEASUREMENT MODEL In order to develop a model for measuring the timeliness of handheld application usage, four elements were involved. This brings together the ranking of each timeliness measure as well as mapping, coding and weighting of the relationship or association of 437 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) timeliness metric towards its corresponding attribute and between each timeliness attribute Timeliness as the criterion. towards Table 5. Rank of Timeliness Measures Timeliness Measures Rank Metric  Attribute Time of Data Obtained  Interaction Mode Time of Knowledge Acquired  Learning Interval Time of Understandings Perceived  Learning Interval Time of Responses Retrieved  Interaction Mode Time of Action Presented  Interaction Mode Time of Items Remembered  Learning Interval Time of Objects Pointed  Interaction Mode Time to Start Tasks  Until Event Time to End Tasks  Until Event Time in Pausing Tasks  Until Event 1 2 3 4 5 6 7 8 9 10 Attribute  Criterion Interaction Mode  Timeliness Learning Interval  Timeliness Until Event  Timeliness 5.1 Ranking Each of the timeliness metrics and the timeliness attributes were ranked according to the highest priority to the lowest priority based on the value of importance of these measures towards measuring the timeliness of handheld applications usage (Refer to Table 5). 5.2 Mapping Each of the timeliness metrics were mapped towards its corresponding attributes. These attributes then were mapped towards Timeliness as its corresponding criterion. The purpose of 1 2 3 mapping is to create a graphical relationship of each measure towards measuring the timeliness of handheld application usage (Refer to Figure 2). 5.3 Coding Each of the associations between timeliness metrics and its corresponding attribute were represented using the following timeliness measure codes. Code MmAaCc were used to represent the association between each timeliness metric towards its specific attribute (Refer to Table 6). 438 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) Time of Data Obtained Time of Knowledge Acquired Interaction Mode Time of Understandings Perceived Time of Responses Retrieved Time of Action Presented Learning Interval Timeliness Time of Items Remembered Time of Objects Pointed Time to Start Tasks Until Event Time to End Tasks Time in Pausing Tasks Figure 2. Map of Timeliness Measures. This figure illustrates the mappings of each metrics towards its corresponding attributes as well as the mappings of each attributes towards measuring the timeliness of handheld application usage. The sequence of these timeliness measures are according to the highest rank to the lowest rank. Symbolized as Mm, M represents the timeliness metric while m represents mth sequence number of timeliness metric such as 1, 2, …, m. Subsequently, symbolized as Aa, A represents the timeliness attribute while a represents ath sequence number of timeliness attribute such as 1, 2, …, a. Similarly, symbolized as Cc, C represents the Timeliness as the criterion while c represents the c-th sequence number of criterion; in this case c is equal to sequence numbered 1. For example, the forth timeliness metric, symbolized as M4, that contributes towards the first timeliness attribute, symbolized as A1, in which further identified as influencing the Timeliness as the criterion, symbolized as C1, can be coded as M4A1C1. This code can be further sentenced as metric Time of Object Pointed is contributed towards attribute Interaction Mode that further contributed towards measuring the timeliness of handheld application usage. 5.4 Weighting Each of the associations between metrics and its corresponding attributes as well as the associations between attributes and the Timeliness as its criterion were weighted and coded using specific values and representations (Refer to Table 7). ω represents the symbol of weights, meanwhile symbolized as ATTm, m 439 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) represents the m-th timeliness metric that contributed towards attribute ATT while symbolized as CRTa, a represents the a-th timeliness attribute that contributed towards criterion CRT. The construction of ranking the timeliness measures as well as mapping, coding and weighting the relationship or association between the metrics towards its corresponding attribute and between the attributes towards measuring the timeliness of handheld applications, thus resulting the model for measuring the timeliness of handheld applications, namely Timeliness Measurement Model (TMM) (Refer to Figure 3). Table 6. Timeliness Measure Codes Code Mm•Aa •Cc M1•A1•C1 M2•A1•C1 M3•A1•C1 M4•A1•C1 M1•A2•C1 M2•A2•C1 M3•A2•C1 M1•A3•C1 M2•A3•C1 M3•A3•C1 Timeliness Measures Metric  Attribute  Criterion Time of Data Obtained  Interaction Mode  Timeliness Time of Responses Retrieved  Interaction Mode  Timeliness Time of Action Presented  Interaction Mode  Timeliness Time of Objects Pointed  Interaction Mode  Timeliness Time of Knowledge Acquired  Learning Interval  Timeliness Time of Understandings Perceived  Learning Interval  Timeliness Time of Items Remembered  Learning Interval  Timeliness Time to Start Tasks  Until Event  Timeliness Time to End Tasks  Until Event  Timeliness Time in Pausing Tasks  Until Event  Timeliness Table 7. Timeliness Weight Codes Code ωATTm ωIM1 ωIM2 ωIM3 ωIM4 ωLI1 ωLI2 ωLI3 ωUE1 ωUE2 ωUE3 ωCRTa ωTML1 ωTML2 ωTML3 Timeliness Measures Metric  Attribute Time of Data Obtained  Interaction Mode Time of Responses Retrieved  Interaction Mode Time of Action Presented  Interaction Mode Time of Objects Pointed  Interaction Mode Time of Knowledge Acquired  Learning Interval Time of Understandings Perceived  Learning Interval Time of Items Remembered  Learning Interval Time to Start Tasks  Until Event Time to End Tasks  Until Event Time in Pausing Tasks  Until Event Attribute  Criterion Interaction Mode  Timeliness Learning Interval  Timeliness Until Event  Timeliness Weight .469 .415 .371 .495 .439 .464 .400 .420 .439 .419 .436 .406 .465 440 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) Time of Responses Retrieved (M2•A1•C1) Time of Action Presented (M3•A1•C1) Time of Objects Pointed (M4•A1•C1) Time of Knowledge Acquired (M1•A2•C1) Time of Understandings Perceived (M2•A2•C1) Time of Items Remembered (M3•A2•C1) Time to Start Tasks (M1•A3•C1) Time to End Tasks (M2•A3•C1) Time in Pausing Tasks (M3•A3•C1) ωIM1=.469 ωIM2=.415 ωIM3=.371 INTERACTION MODE ωTML1=.436 ωIM4=.495 ωLI1=.439 ωLI2=.464 LEARNING INTERVAL ωTML2=.406 ωLI3=.400 TIMELINESS Time of Data Obtained (M1•A1•C1) ωUE1=.420 ωUE2=.439 UNTIL EVENT ωTML3=.465 ωUE3=.419 Figure 3. Timeliness Measurement Model (TMM). This figure illustrates the timeliness measures codes and weights sequenced according to its rank and association map 6 FORMULAS CONSTRUCTION As to construct formulas and further to measure the timeliness of the handheld application usage, four stages were involved. This brings together the formula for measuring the metrics, formula for measuring the attributes as well as formula to measure the overall timeliness of handheld application usage. 441 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) 6.1 Measuring Timeliness Metrics Score for each timeliness metric can be calculated generally as the proportion of the difference between the expected time Timeliness Metric (M1…m•A1…a•C1) = 1– Δ of expected and actual time of activities occurred T of expected time of activities occurred Detail representations for measuring each of the timeliness metrics Time of Data Obtained (M1A1C1), Time of Response Retrieved (M2A1C1), Time Time of Data Obtained (M1•A1•C1) = 1– Time of Responses Retrieved (M2•A1•C1) = 1– Time of Actions Presented (M3•A1•C1) = 1– Time of Objects Pointed (M4•A1•C1) = 1– = 1– (1) of Action Presented (M3A1C1) and Time of Object Pointed (M4A1C1) that contribute towards timeliness attribute Interaction Mode thus can be referred as Δ of expected and actual time of data obtained T of expected time of data obtained Δ of expected and actual time of responses retrieved T of expected time of responses retrieved Δ of expected and actual time of actions presented T of expected time of actions presented Δ of expected and actual time of objects pointed T of expected time of objects pointed Detail representations for measuring each of the timeliness metrics Time of Knowledge Acquired (M1A2C1), Time of Understanding Perceived (M2A2C1) and Time of Item Remembered Time of Knowledge Acquired (M1•A2•C1) of activities occurred and the actual time of activities occurred out of the total expected time of activities occurred minus one. Hence can be represented as (1.1) (1.2) (1.3) (1.4) (M3A2C1) that contribute towards timeliness attribute Learning Interval thus can be referred as Δ of expected and actual time of knowledge acquired T of expected time of knowledge acquired (1.5) 442 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) Time of Understandings Perceived (M2•A2•C1) = Time of Items Remembered (M3•A2•C1) = Δ of expected and actual time of understandings perceived 1– (1.6) T of expected time of understandings perceived 1– Δ of expected and actual time of items remembered T of expected time of items remembered (1.7) Task (M3A3C1) that contribute towards timeliness attribute Until Event thus can be referred as Detail representations for measuring each of the timeliness metrics Time to Start Task (M1A3C1), Time to End Task (M2A3C1) and Time in Pausing Time to Start Tasks (M1•A3•C1) = 1– Δ of expected and actual time to start tasks T of expected time to start tasks (1.8) Time to End Tasks (M2•A3•C1) = 1– Δ of expected and actual time to end tasks T of expected time to end tasks (1.9) Time in Pausing Tasks (M3•A3•C1) = 1– Δ of expected and actual time in pausing tasks T of expected time in pausing tasks weights of timeliness attributes and the value of timeliness metrics out of the total of accumulated weights for each timeliness attribute. Hence can be represented as 6.2 Measuring Timeliness Attributes Scores for each timeliness attribute can be calculated generally as the proportion of the accumulated products of the m = max(m) Timeliness Attribute (ATT) ∑ = (1.10) ωATTm (Mm•Aa•Cc) m=1 m = max(m) ∑ (2a) ωATTm m=1 which can be further expanded as 443 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) Timeliness Attribute = (ATT) ωATT1 (M1•Aa•Cc) ωATT1 + ωATT2 + … + ωATTmax(m)–1 + ωATTmax(m) + ωATT2 (M2•Aa•Cc) ωATT1 + ωATT2 + … + ωATTmax(m)–1 + ωATTmax(m) + (2b) … ωATTmax(m)–1 (Mmax(m)–1•Aa•Cc) ωATT1 + ωATT2 + … + ωATTmax(m)–1 + ωATTmax(m) + ωATTmax(m) (Mmax(m)•Aa•Cc) ωATT1 + ωATT2 + … + ωATTmax(m)–1 + ωATTmax(m) Detail representations for measuring timeliness attribute Interaction Mode m=4 ∑ Interaction Mode (IM) = (IM) that contribute towards criterion Timeliness can be referred as ωIMm (Mm•A1•C1) m=1 m=4 ∑ (2.1a) ωIMm m=1 hence can be further expanded as Interaction Mode (IM) = ωIM1 (M1•A1•C1) ωIM1 + ωIM2 + ωIM3 + ωIM4 + ωIM2 (M2•A1•C1) ωIM1 + ωIM2 + ωIM3 + ωIM4 + ωIM3 (M3•A1•C1) ωIM1 + ωIM2 + ωIM3 + ωIM4 + (2.1b) ωIM4 (M4•A1•C1) ωIM1 + ωIM2 + ωIM3 + ωIM4 which involved the total of the product of weight and value of timeliness metrics Time of Data Obtained (ωIM1 x M1A1C1), Time of Response Retrieved (ωIM2 x M2A1C1), Time of Action Presented (ωIM3 x M3A1C1) and Time of Object Pointed (ωIM4 x M4A1C1). Detail representations for measuring timeliness attribute Learning Interval (LI) that contribute towards criterion Timeliness can be referred as 444 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) m=3 ∑ Learning Interval (LI) = ωLIm (Mm•A2•C1) m=1 m=3 ∑ (2.2a) ωLIm m=1 hence can be further expanded as Learning Interval (LI) = ωLI1 (M1•A2•C1) ωLI1 + ωLI2 + ωLI3 + ωLI2 (M2•A2•C1) ωLI1 + ωLI2 + ωLI3 + (2.2b) ωLI3 (M3•A2•C1) ωLI1 + ωLI2 + ωLI3 which involved the total of the product of weight and value of timeliness metrics Time of Knowledge Acquired (ωLI1 x M1A2C1), Time of Understanding Perceived (ωLI2 x M2A2C1) and Time of Item Remembered (ωLI3 x M3A2C1). Detail representations for measuring timeliness attribute Until Event (UE) that contribute towards criterion Timeliness can be referred as m=3 ∑ Until Event (UE) = ωUEm (Mm•A3•C1) m=1 m=3 ∑ (2.3a) ωUEm m=1 hence can be further expanded as Until Event (UE) = ωUE1 (M1•A3•C1) ωUE1 + ωUE2 + ωUE3 + ωUE2 (M2•A3•C1) ωUE1 + ωUE2 + ωUE3 + (2.3b) ωUE3 (M3•A3•C1) ωUE1 + ωUE2 + ωUE3 which involved the total of the product of weight and value of timeliness metrics Time to Start Task (ωUE1 x M1A3C1), Time to End Task (ωUE2 x M2A3C1) and Time in Pausing Task (ωUE3 x M3A3C1). 445 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) 6.3 Measuring Timeliness Criterion Scores for overall timeliness can be calculated generally as the proportion of the accumulated products of the weights a = max(a) Timeliness Criterion = (CRT) ∑ of timeliness criterion and the value of timeliness attributes out of the total accumulated weights of timeliness criterion. Hence can be represented as ωCRTa (M1…m•Aa•Cc) a=1 (3a) a = max(a) ωCRTa ∑ a=1 which can be further expanded as Timeliness Criterion = (CRT) ωCRT1 (M1…m•A1•C1) ωCRT1 + ωCRT2 + … + ωCRTmax(m)–1 + ωCRTmax(m) + ωCRT2 (M1…m•A2•C1) ωCRT1 + ωCRT2 + … + ωCRTmax(m)–1 + ωCRTmax(m) + (3b) … ωCRTmax(m)–1 (M1…m•Amax(m)–1•C1) ωCRT1 + ωCRT2 + … + ωCRTmax(m)–1 + ωCRTmax(m) + ωCRTmax(m) (M1…m•A max(m)•C1) ωCRT1 + ωCRT2 + … + ωCRTmax(m)–1 + ωCRTmax(m) Detail representation for measuring of the criterion Timeliness (TML) that contribute towards measuring the overall a=3 Timeliness (TML) ∑ = timeliness of handheld application usage can be referred as ωTMLa (M1…m•Aa•C1) a=1 a=3 ∑ (3.1a) ωTMLa a=1 hence can be further expanded as 446 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) Timeliness (TML) = ωTML1 (M1…m•A1•C1) ωTML1 + ωTML2 + ωTML3 + ωTML2 (M1…m•A2•C1) ωTML1 + ωTML2 + ωTML3 + (3.1b) ωTML3 (M1…m•A3•C1) ωTML1 + ωTML2 + ωTML3 which involved the total of the product of weight and value of timeliness attributes Interaction Mode (ωTML1 x IM), Learning Interval (ωTML2 x LI) and Until Event (ωTML3 x UE). and comprehensively. This brings together the levels, thresholds as well as overall analysis for evaluating the timeliness of handheld application usage. 7 PRIORITIZING TIMELINESS 7.1 Analyzing Timeliness Level Prioritizing the timeliness of handheld application usage can be done by converting the values into words or sentences with which evaluators from various backgrounds and understanding can interpret the information accurately Timeliness level was categorized into five distinct classifications in which determined by the score of each timeliness measure (Refer to Table 8). Table 8. Prioritizing Timeliness Levels Level Score (TMLscore) Description 1 0.000 ≤ TMLscore < 0.200 2 0.200 ≤ TMLscore < 0.400 3 0.400 ≤ TMLscore < 0.600 4 0.600 ≤ TMLscore < 0.700 5 0.800 ≤ TMLscore ≤ 1.000 Most badly absence or shortage of a desirable usage quality that attains timeliness level of unable to perform comprehensively Lack of a desirable usage quality that attains timeliness level of the least excellent Average of a desirable usage quality that can be tolerable to consider good enough Complete the specific requirements of a desirable usage quality that achieves timeliness level of almost in a state of being practical Fulfill all the requirements of a desirable usage quality that achieves timeliness level of very high distinction of proficiency 7.2 Analyzing Timeliness Threshold Prioritizing the usage satisfaction thresholds is possibly important to relate the feeling of contentment towards handheld applications usage. Timeliness threshold was categorized into three distinct classifications in which determined by the score of each timeliness measure (Refer to Table 9). 447 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) Table 9. Prioritizing Timeliness Thresholds Thresholds Score (TMLscore) Description Low 0.000 ≤ TMLscore < 0.333 Medium 0.333 ≤ TMLscore < 0.667 High 0.667 ≤ TMLscore < 1.000 Below an acceptable usage satisfaction that derives timeliness threshold in a state of being frustrate Ordinary extent of an acceptable usage satisfaction that derives timeliness threshold in a state of being moderate Above an acceptable usage satisfaction that derives timeliness threshold in a state of being content 7.3 Analyzing Overall Timeliness Determined by two different timeliness elements of usage quality and usage satisfaction, a matrix was developed to map between the timeliness level and the timeliness threshold. The timeliness matrix that mapped the highest timeliness level and timeliness threshold should always have the strongest priority. In turn, the timeliness matrix that indicates the lowest timeliness level and timeliness threshold should always have the weakest priority (Refer to Table 10). Table 10. Timeliness Matrix Timeliness Threshold Low Medium High Level 1 Weak Weak Weak Level 2 Weak Weak Moderate The matrix defined by the relationship between timeliness level and timeliness threshold, thus can be categorized into Timeliness Level Level 3 Weak Moderate Moderate Level 4 Moderate Moderate Strong Level 5 Moderate Strong Strong three distinct classifications of overall timeliness analysis (Refer to Table 11). Table 11. Overall Timeliness Analyses Timeliness Description Weak Critical condition which needs greater effort for reconstruction process that indicates timeliness rating in a state of crucial decision making towards enhancing usage quality as well as increasing usage satisfaction Medial condition which needs less effort for reconstruction process that indicates timeliness rating in a state of uncertain decision making towards enhancing usage quality as well as increasing usage satisfaction Stable condition which needs no effort for reconstruction process that indicates timeliness rating in a state of firmly established that not involve further decision making towards enhancing usage quality as well as increasing usage satisfaction Moderate Strong 448 International Journal on New Computer Architectures and Their Applications (IJNCAA) 2(3): 431-450 The Society of Digital Information and Wireless Communications, 2012 (ISSN: 2220-9085) 8 CONCLUSIONS Although there have been interesting advances by previous models, however, these existing models suffer from various shortcomings. Several of these models focused on the generic effects of timeliness characteristics while others concentrating on developing metrics that are defined and mapped according to different viewpoints. Less attention was given to integrate the mathematicalbased calculation towards measuring the timeliness of handheld application usage. Hence, this study was conducted to develop a comprehensive mathematical model for measuring the timeliness of handheld application usage. This study is designed to achieve five major objectives: identifying the elements for measuring timeliness, analyzing contributed factors of timeliness measures, developing a model for measuring timeliness, constructing formulas for measuring timeliness as well as prioritizing the overall timeliness of handheld application usage. The construction of ranking, mapping, coding and weighting measures, results a hierarchical model for measuring the timeliness of handheld application usage. As to construct formulas, formula for measuring the metrics, attributes as well as the overall timeliness of the handheld application usage were involved. Finally, prioritizing was done by converting the timeliness values into words or sentences with which can be interpreted accurately and comprehensively. For the future, it is recommended to evaluate cases between the timeliness model and the actual handheld environments. With extensive application experiences, timeliness measures of handheld application might change. Additional new criteria could be included in the future work. Therefore, the model developed need to be refined practically through many applications in the real work environment. 9 REFERENCES 1. Dvorak, J.: “Conceptual Entropy and Its Effect on Class Hierarchies,” J. IEEE Computer, vol. 27, no. 6, pp. 59-63, 1994. 2. Chae, M. and Kim, J.: “Do Size and Structure Matter to Mobile Users? 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