The Accuracy of Snapshot Observations in Determining the Structure of Tree Harvester Operating Times

Abstract

Traditional time study methods are time-consuming and expensive and require experienced staff. Using a time sampling methodology based on video recordings might be a time-efficient and precise solution. This study scrutinized the accuracy and margin of error for various snapshot lengths and types (fixed and variable) when estimating the operating times of a tree harvester in clearcuts and thinnings of Scots pine stands. The study focused particularly on the impact of type, recognizing its potential to influence the accuracy of the estimates. The study examined interval lengths of 3–20 s (in 1 s increments), as well as 25, 30, and 35 s, in two types (fixed and variable length). While both the type and length of an interval affected the obtained levels of errors (particularly the mean absolute percentage error—MAPE), the random-length type usually resulted in a higher level compared to the fixed-length of the same length. The proportion of operating times did not differ from that obtained by a continuous time study for all lengths and types, for both thinnings and clearcuts. As fixed-length interval studies are much easier to conduct and result in lower error levels, it is recommended that the fixed-length intervals (up to 19 s in thinning and 17 in clearcuts) are used for this type of study.

1. Introduction

The modeling of utilization times of machines is instrumental for proper management and improvement in operational efficiency [1,2]. Conducting a time study is imperative for acquiring the necessary data to facilitate the development of a model. Techniques that involve traditional equipment (stopwatch and notepad or a handheld data logger) are time consuming and expensive and require some level of expertise or skill from the researcher [2,3,4,5,6,7].

Some of these issues are alleviated by using video recordings, which are easier to take and can be analyzed at a convenient time and proof-checked afterwards [3,4,6,8]. Moreover, when measuring brief elements of the work cycle, the utilization of video recordings is advantageous. This is due to the capability of slowing down the recording and employing time stamps from the video [9]. This may be a reason behind the common application of video analysis in the study of forest machinery. Nevertheless, the analysis of video recordings can be a time-consuming process, as sometimes the video must be replayed and examined in its entirety [3,10]. Recently, a structured and standardized approach was proposed for the semi-automatic synchronization of videos with machine-generated operational data. The objective of this approach is to facilitate the effective creation of datasets for machine learning applications [11]. While this approach shows great promise, it is still in the early stages of development.

One of the least time-intensive methods of work-time studies is work sampling, also referred to as activity sampling [1,2,6,12,13,14,15], frequency studies [9], or snapshot observations [16,17]. The earliest documented reference to this technique appears in 1935, when it was referred to as the “Snap Reading Method” by its inventor, L. H. C. Tippet [18,19]. At that time, it was employed in the textile industry. Subsequent refinement of this technique has led to its widespread utilization in medical practice [5,18,20] and various other economic sectors [21,22].

According to the International Labour Organization (ILO), work sampling is defined as a method of determining the frequency of occurrence of a specific activity by statistical sampling and random observations [2]. In other words, it can be used to estimate the proportions of total time devoted to the various activities that constitute a job or work situation [6]. This method entails the collection of a substantial number of instantaneous observations at predetermined intervals. The proportion of instances of a specific activity is indicative of the proportion of time spent engaged in that activity, with a certain margin of error [2,6]. The temporal separation (interval) between successive snapshots can be either constant or random [1,14,17]. The precision of the results depends on a sufficiently extensive number of observations and the duration of the data collection period [6]. It is evident that as the number of observations increases, the accuracy of the results approaches a state of near-completeness, akin to the scenario of continuous observation where the number approaches infinity. Conversely, the reliability of results derived from a limited number of observations is questionable [2]. It is therefore imperative to ascertain the minimum number of observations necessary to ensure the requisite level of accuracy prior to the commencement of the studies. Commonly used formulas to calculate the sample size take into account the confidence level (the most common is 95%) and a maximum margin of error of 5% [2,6]. Such formulas require the initial knowledge of the proportion of time spent on a particular activity. The determination of this proportion must first be performed through a pilot study, or it can be obtained from the existing literature on the subject [18,19]. According to researchers such as Laurow [23], Pszenny et al. [16], and Szewczyk [17], another viable option is the Steinhaus formula, given its capacity to account for the number of studied activities. It is evident that, irrespective of the formula employed, the numbers of observations obtained from these calculations should be regarded as minimum standards. In instances where economic viability permits, these values could be extended.

A further issue that must be addressed is the determination of the appropriate interval between snapshots for the analysis of a highly cyclical work process [12,17,24]. The harvester work serves as a good example. The accidental synchronization of snapshots with a specific cycle element may result in an over- or under-representation of the activity in question. To avoid that, snapshot observations should be taken in sufficiently short or random intervals. According to Szewczyk [17] the interval should be 2–3 times shorter than the average duration of the shortest activity in the work process. This duration must be established through a pilot study. A widely recommended alternative solution is the implementation of a variable interval [1,12,14,18,19].

The utilization of video recordings for work sampling enables the collection of a substantial number of observations within a limited time frame (recording time). The utilization of a customizable fast-forward button on a video player enables the instantaneous skipping of the video by a programmed interval. This approach is advantageous for researchers, as it reduces the time required for data analysis. However, it is important to note that this method is only applicable when the interval is fixed. In this study, relatively brief intervals ranging from 3 to 35 s were utilized, in both a fixed and random configuration. The primary focus of the study was on the influence of selected settings, specifically interval length and type, on error levels and changes in the resulting operating time structure, rather than on the structure itself. The structure was presented and discussed with the objective of serving as a reference for future studies.

The utilization of work sampling techniques offers numerous benefits for researchers. This method is both affordable and accessible, as it does not require specialized knowledge or equipment. Conducting prolonged studies is feasible, as it does not necessitate a significant degree of concentration. Additionally, the process of making snapshot observations is less onerous than that of conducting a classic time and motion study [18]. Furthermore, the interruption within the study only has minimal effect on the results [19]. Another resulting advantage is that one researcher is able to conduct the study for several workers at the same time [12]. It is also worth noting that the method facilitates a notable decline in what is referred to as the “Hawthorne Effect”, a phenomenon characterized by workers modifying their work behaviors when they are under observation [10,18]. The limitations of the work sampling method include its inability to assess the quality of work performed and its comparatively limited capacity to provide insight into work processes in comparison to conventional time studies [19]. Moreover, it must be noted that the snapshot method is not applicable in the context of evaluating cycle time in cyclical work processes. In the course of this study, an average cycle time was established from a continuous time study, solely for the purpose of ascertaining the potential synchronization of interval duration with cycle time.

Video recordings have been demonstrated to be an effective data source in the context of research into forestry technology [11,25,26,27]. Conversely, the employment of work sampling techniques for the estimation of the operation time structure of forestry machinery is comparatively rare [7,13,16,17,28]. Recent advancements in the field of data collection for time studies in forestry have focused on the utilization of automatic devices [29,30,31]. Additionally, numerous authors have emphasized the significance of utilizing data from on-board computers and fleet management systems [4,32,33,34,35]. The latest development is a framework for synchronizing video recordings and on-board computer data. This framework automatically annotates the resulting video stream, thereby generating a reliable data source for further analysis [11].

The objective of this study was to evaluate the applicability of the work sampling method to harvester work research. Specifically, the study sought to ascertain the accuracy of this method for assessing the operational time structure of a harvester working in typical late thinnings and clearcuts in coniferous forests. In particular, this study attempts to scrutinize the hypothesis that widely recommended variable intervals yield more precise results. It is especially important in the context of analyzing video recordings, where fixed intervals are more practical. The selection of the type and duration of the interval is often based on the researcher’s intuition. A considerable number of studies in the domain of forestry merely specify the chosen type and length of the interval, lacking a substantiation for this decision [7,16,17]. It is relatively uncommon for authors to assess the accuracy of operation time shares by testing various settings of intervals [13]. This study [13] incorporated considerably longer intervals (3, 5, 10, 12, 20, and 25 min, all of which were fixed-type) for the estimation of the time structure of a workday for a harvester operator, distinguishing the categories of main work time, complementary work time, maintenance time, repair time, and non-working time. For categories of such considerable length, intervals of 10–15 min have been demonstrated to yield precise results.

The present study sought to ascertain the precision of time studies by investigating the accuracy of measuring operations of a considerably shorter duration, spanning seconds rather than minutes. Additionally, the investigation focused on a comparison between fixed-length and random-length types. The inherent characteristics of harvester operations, namely their relatively brief duration and rapid succession, rendered video recordings a more suitable data collection method in comparison to field studies. The results of this study might serve as a case study and might support the decision for similar types of studies. A range of parameters were utilized in the execution of snapshot observations, encompassing an interval ranging from 3 to 35 s and a categorization of type as either fixed or random. The impact of the minimal number of observations and the corresponding minimum study duration on the reliability of the results was examined.

Practical recommendations were derived from the analysis of the obtained errors, including the mean error (ME), the mean percentage error (MPE), the mean absolute error (MAE), and the mean absolute percentage error (MAPE). The latter was found to be the most meaningful. Tukey’s post hoc test for MAPE enabled the observations’ classification into homogeneous groups based on their resulting MAPE levels, distinguishing between those with lower and higher errors. Furthermore, the analysis of time structure fluctuations for various interval lengths and types provided additional evidence to support the hypothesis that the optimal setting for this particular instance was identified. It is imperative to acknowledge that these recommendations are to be regarded exclusively in the context of this specific type of work. They should be regarded solely as a reference point for future researchers when selecting snapshot study settings.

2. Materials and Methods

The video recordings collected during the eye-tracking study [36] were utilized as a foundation for experimental procedures. The audio-visual documentation was conducted utilizing a specialized pair of spectacles equipped with an integrated high-definition camera (Tobii Pro Glasses 2, Tobii AB, Stockholm, Sweden). The study comprised five recordings from thinning sites and five from clearfell sites. Thinning was carried out using a Ponsse Ergo harvester (Ponsse Plc, Vieremä, Finland), equipped with a H7 harvesting head, in the Oborniki Forest District in Central Poland in September 2019. The predominant species in the thinning plot was Scots pine. The clearfell site was situated in the Wymiarki Forest District in Western Poland, and the dominant species was also Scots pine. The clearcut operation was conducted in May 2019 using a Komatsu 931.4 XT harvester (Komatsu Forest AB, Umeå, Sweden) equipped with a C123 harvesting head. Both machines were of a relatively modern design and were in optimal working order. Both operators exhibited a high level of expertise, with over a decade of experience and no history of sight-related conditions. Both sites are representative of standard working conditions for Polish forestry, and the working technique was not modified in any way. The obtained efficiencies were consistent with the prevailing range observed in the context of Polish forestry conditions. The workflow within the study was not hindered or interrupted by any external factors.

The work-time structure of a harvester was divided into the following operations: positioning (from the initiation of the crane’s movement toward the tree until the commencement of the felling cut), cutting and felling (from the initiation of the felling cut until the crown made contact with the ground), processing (from the initiation of the crane movement with the fallen tree until the dropping of the top), driving (when changing the machine’s working positions), driving with the tree (when the machine moved backwards after the felling to the designated processing area, with the tree still kept in the harvesting head), and other miscellaneous tasks (e.g., removing small trees by pulling them out, tidying up the branches, etc.). The operations were defined to ensure that there were no gaps or overlap among them. The operations were executed sequentially, and it was not possible for two operations to occur simultaneously. In establishing the cycle time, the times for positioning, cutting, felling, and processing of a particular tree were aggregated.

The duration of the video recordings was approximately 25–30 min (150 min on clearcuts and approximately 133 min on thinnings). These videos were subsequently analyzed using Elan (Figure 1), an annotation software [37,38]. For each operation, a distinct layer was generated, and the span of the operation was annotated on the pertinent layer as an annotation, thereby providing the continuous time study results. These results were regarded as the standard against which the snapshot results were evaluated.

Figure 1. Elan 6.9 with video screen and layers visible.

The layers comprising snapshots were created subsequently. The snapshots were defined as brief (0.1 s) instances and were regarded as points, meaning that a single snapshot could overlap with only one operation. The snapshots (or more precisely, their initial moments) were separated by time intervals of varying lengths and types (fixed or random). The generation of variable interval lengths was accomplished through the utilization of the RANDBETWEEN function in MS Excel (version 2108), which ensured adherence to a normal distribution. Given that the function’s output is a vector of integers, the limits for the RANDBETWEEN function were determined by multiplying the desired average length by 50 for the lower limit and 150 for the upper limit. The resulting vector was subsequently divided by 100. To illustrate, a variable interval of 10 s indicates that the intervals varied from 5 to 15 s, with an average of 10 s. Obtained vectors of numbers were then added by the running sum method, resulting in a vector of time stamps for the snapshots of various interval lengths. This vector was than imported into Elan to create a layer with snapshots. This procedure was repeated for each film and each nominal interval length, resulting in a distinct vector of variable intervals for each film, while maintaining the same mean and distribution.

The results of the snapshot method (i.e., number of “hits”) were obtained by creating an additional layer in which the original continuous times of a specific operations were overlapping with a snapshot layer. This process yielded the number of “hits” for a particular operation and a specific setting of the snapshot. The resulting layers with snapshot “hits” as well as layers with annotations for continuous time study, complete with their respective times (with an accuracy to 1 millisecond [ms]) and identifiers, were subsequently exported to MS Excel for further processing.

The calculation of the time spent on each operation for the continuous time study was derived from the imported annotations. This calculation included the calculation of the mean time for each operation and an assessment of its distribution. The layers with “snapshot hits” provided the foundation for the calculation of the time spent on each operation. This calculation involved multiplying the number of “hits” by the nominal length of an interval (irrespective of the interval’s type, whether fixed or random.).

For establishing a minimum number of required observations, a general formula (Equation (1)) was used [6].

$$n={\displaystyle \frac{z^2\ast p\ast \left(1-p\right)}{d^2}}$$

(1)

where

• n—number of required observations;
• z—the value from the standard normal distribution for the given confidence level;
• p—estimated share of time (proportion) of a given operation;
• d—acceptable error of estimation.

The calculation of this number was performed for each activity, and a maximum number was selected as a necessary minimum for the assumed acceptable error and confidence.

In addition, the formula devised by Steinhaus and proposed by Laurow [23] was utilized, which takes into account the number of operations (activities) to be studied (Equation (2)).

$$n={\left({\displaystyle \frac{100\ast \sqrt{\frac{K-1}{K}}-E}{E}}\right)}^2$$

(2)

where

• n—number of required observations;
• K—the number of operations (activities);
• E—error of estimation (in percent).

The calculations were performed under the assumption of a confidence level of 95% and a corresponding z value of 1.96. The acceptable error of estimation was set at the 5% level. From the numbers established for each operation, a maximum value was selected to be the required number of snapshots to ensure assumed accuracy.

A reversion of Equation (1) was employed to establish an error margin for an observation (Equation (3)). The proportion of time spent on a given operation was retrieved from the continuous study results.

$$d=z\ast \sqrt{{\displaystyle \frac{p\ast \left(1-p\right)}{n}}}$$

(3)

where

• d—error margin.

The weighted average of the margin errors for each operation yielded the error margin for the entire method (i.e., the snapshot interval).

Initially, various measures of accuracy were checked: mean error (ME), mean absolute error (MAE), mean percentage error (MPE), and finally mean absolute percentage error (MAPE). The error is the extent to which the operation time obtained from snapshots differs from the continuous time study, which may be positive or negative and is expressed in seconds. The mean error (ME) is the weighted average across the operations, where operation time is the weight (see Equation (4)).

$$ME={\displaystyle \frac{\sum _{i=1}^K\left(E_i\ast t_i\right)}{\sum _{i=1}^K{t}_i}}$$

(4)

where

• K—the number of operations;
• $E_i$—error for a given operation;
• $t_i$—time of a given operation.

The mean percentage error (MPE) quantifies the relative value of these errors and is expressed as a percentage (Equation (5)).

$$MPE={\displaystyle \frac{\sum _{i=1}^K{E}_i\ast 100}{\sum _{i=1}^K{t}_i}}$$

(5)

A potential disadvantage of these measures is that the negative and positive errors may cancel each other out. This could create the illusion of a very accurate method, even if the values of the errors are substantial.

To address this challenge, an absolute value of error was employed to calculate mean absolute error (MAE—Equation (6)) and mean absolute percentage error (MAPE—Equation (7)).

$$MAE={\displaystyle \frac{\sum _{i=1}^K\left|E_i\ast t_i\right|}{\sum _{i=1}^K{t}_i}}$$

(6)

$$MAPE={\displaystyle \frac{\sum _{i=1}^K\left|E_i\right|\ast 100}{{\sum }_{i=1}^K{t}_i}}$$

(7)

These types of errors were calculated for every combination of interval length and type with one film as a unit of replication. A comparative analysis of the resulting errors was conducted using a two-way repeated-measures ANOVA with Tukey’s HSD post hoc test.

The primary outcome of a snapshot study is the percentage of time allocated to various work operations. The linearization of these proportions was achieved through the implementation of the Bliss conversion method. MANOVA with Wilk’s lambda coefficient was used to compare the time distributions of operations between the fixed and random types, with the proportions of operation times as the independent variables. These were analyzed separately for thinnings and clearcuts.

The method’s stability was examined for fixed intervals by offsetting the start point by one-third and two-thirds of the interval. In the case of the random type, two novel sets of random intervals were generated from the same distribution as the original (namely, a normal distribution with set limits, utilizing the Randbetween function in MS Excel). For each interval type, two new ELAN layers were created for analysis as distinct variants. The resulting error levels were compared using a one-way analysis of variance (ANOVA) with repeated measures.

The statistical procedures were executed using the Statistica software (version 13.3, TIBCO Software Inc.), with an assumed alpha level of 0.05. Figure 2, Figure 3 and Figure 4 were created in R Studio (version 2023.6.0.421) using the ggplot2 package (R version 4.2.1) [39,40].

Figure 2. Values of researched types of errors for various interval lengths and variants (F_th—fixed-type for thinnings, F_cc—fixed-type for clearcuts, R_th—random-type for thinnings, R_cc—random-type for clearcuts).

Figure 3. Proportion of work time spent on various operations for thinnings, for different interval lengths and types (0 indicates continuous time study results).

Figure 4. Proportion of work time spent on various operations for clearcuts, for different interval lengths and types (0 indicates continuous time study results).

3. Results

The video recordings utilized in the study consisted of ten films, each spanning approximately thirty minutes—five from thinnings and five from clearcuts. The total duration of these recordings was 133 min and 20 s, and 145 min and 59 s, respectively. The range of snapshot intervals was from 3 to 20 s inclusive, with additional intervals of 25, 30, and 35 s.

The continuous time study yielded insights into the working times for each operation performed by harvesters in thinnings and clearcuts. Each instance of an operation was identified and measured (Table 1).

Table 1. Results of continuous time study of harvesters’ work in thinnings and clearcuts.

Cutting Type	Operation	Average Operation Time (SD) [s]	n	Proportion of Time [%]
thinning	positioning	5.54 (2.47)	130	9.04
	felling	7.30 (3.19)	133	12.13
	processing	23.78 (7.18)	133	39.53
	driving	21.26 (15.47)	117	31.11
	driving with tree	6.57 (3.47)	44	3.64
	other	15.69 (15.36)	23	4.55
clearcut	positioning	6.34 (5.51)	166	12.08
	felling	6.58 (6.01)	169	12.70
	processing	25.57 (11.13)	197	57.53
	driving	5.80 (3.76)	65	4.39
	driving with tree	7.25 (3.43)	25	2.07
	other	11.63 (21.31)	84	11.23

The average cycle time was determined for both clearcuts and thinnings separately. The average cycle time was 56.384 s for thinnings (SD = 18.9) and 44.937 s for clearcuts (SD = 16.06).

The minimum number of observations necessary to achieve the required accuracy was determined separately for each operation using (Equation (1)), and then the largest was selected. The result of this calculation was the number of observations that provided 95% certainty that the error made in calculating the operation time would not exceed 5%. It was established that a minimum of 368 snapshots were required for thinning operations, while 376 snapshots were necessary for clearcut operations. In the present study, the minimum required number was achieved by all snapshot intervals up to 20 s in duration in both thinning and clearcutting scenarios. Conversely, all intervals between 25 and 35 s fell below the requisite benchmark.

The minimum number of observations calculated using the Steinhaus formula (Equation (2)) was 298, and this was met by all snapshot intervals up to 25 s, regardless of the cutting type.

The number of obtained snapshots was found to be predominantly higher for fixed intervals when compared to variable intervals of equivalent mean length (Table 2, columns 2, 5, 8, and 11). The discrepancy in the number of snapshots obtained ranged from 3.25% to 5% for thinnings and from −1.16% to 5.14% for clearcuts. As previously indicated, for intervals measuring less than 20 s, the numbers were adequate for precise observations.

Table 2. Obtained number of snapshots (n), calculated theoretical margin of error (d), and obtained mean absolute percentage error (MAPE) for various interval lengths and types (fixed and random) for thinnings and clearcuts.

Interval [s]	Thinning						Clearcut
	Fixed			Random			Fixed			Random
	n	d [%]	MAPE [%]	n	d [%]	MAPE [%]	n	d [%]	MAPE [%]	n	d [%]	MAPE [%]
1	2	3	4	5	6	7	8	9	10	11	12	13
3	2847	1.54	1.64	2740	1.57	3.18	2816	1.53	1.58	2709	1.56	2.51
4	2135	1.78	1.99	2052	1.81	3.44	2082	1.78	2.13	1998	1.81	3.42
5	1707	1.99	2.73	1639	2.03	4.29	1724	1.95	2.57	1654	1.99	3.60
6	1421	2.18	3.31	1371	2.22	4.52	1441	2.13	3.78	1385	2.18	4.07
7	1218	2.35	3.93	1172	2.40	5.59	1240	2.30	4.00	1189	2.35	3.53
8	1068	2.51	4.42	1022	2.57	5.96	1069	2.48	3.67	1014	2.54	6.09
9	949	2.67	4.14	911	2.72	7.10	948	2.63	4.97	903	2.70	6.07
10	852	2.81	5.88	817	2.87	7.57	822	2.83	5.33	788	2.89	6.69
11	776	2.95	5.74	744	3.01	8.86	759	2.94	6.40	725	3.01	7.63
12	709	3.08	8.39	683	3.14	8.83	738	2.98	6.41	710	3.04	7.75
13	655	3.21	7.07	629	3.28	8.70	665	3.14	8.56	639	3.21	9.88
14	608	3.33	7.50	586	3.39	7.19	578	3.37	8.11	556	3.44	7.94
15	567	3.45	10.55	546	3.52	9.08	582	3.36	7.58	562	3.42	11.41
16	533	3.56	4.90	508	3.64	10.71	532	3.51	10.34	514	3.57	9.52
17	501	3.67	7.85	480	3.75	8.83	514	3.57	8.37	499	3.63	12.57
18	471	3.78	9.00	454	3.86	13.52	463	3.77	9.67	448	3.83	13.48
19	448	3.88	9.47	430	3.96	9.55	471	3.73	10.32	455	3.80	11.23
20	423	3.99	13.63	406	4.08	9.05	420	3.95	10.32	407	4.02	11.19
25	338	4.47	11.21	327	4.54	13.80	345	4.36	14.02	349	4.34	10.59
30	280	4.91	18.68	266	5.04	18.41	286	4.79	17.34	279	4.85	15.28
35	236	5.35	18.34	225	5.48	20.55	243	5.20	17.70	235	5.29	19.01

Note: errors exceeding the assumed 5% threshold are in bold; observations with a number smaller than the calculated minimum are in italics.

Since the number of snapshots obtained was generally higher than the calculated required minimum, the margin of error obtained using Equation (3) was, in most cases, rather small. The margin only exceeded the allowed 5% threshold for the longest intervals (see Table 2, columns 3, 6, 9, and 12).

The mean error (ME) levels obtained (see Equation (4)) exhibited oscillations around 0 for each cutting type and interval type (see Figure 2). A significant discrepancy was observed in the levels of ME produced by the two interval types. Specifically, the random-type interval yielded a substantially higher level of ME compared to the fixed interval type of equivalent length. Additionally, the value of ME for random type demonstrated a high degree of volatility, exhibiting a rapid change in response to a minimal increase in interval length. This phenomenon was particularly evident in the clearcut scenario, as illustrated in Figure 2a. Statistical tests showed no influence of interval length on the value of ME—for each type of interval and cutting type.

The mean percentage error was also very erratic for random intervals and also did not show any interaction between interval length and the MPE value (Figure 2b). For the fixed-type interval, the trend seemed much more stabilized with some sharp dips in the 20 s length for thinnings. The value of MPE for fixed type exhibited a gradual decline, reaching its minimum at 35 s intervals, with a minimum of −1.56% for thinnings and −1.29% for clearcuts. Conversely, random type demonstrated the most significant positive values, reaching 1.97% for 16 s intervals for thinnings and 17 s for clear cuts, and negative values for 20 s intervals for thinnings (−2.96%) and 30 s intervals for clearcuts (−2.83%).

This analysis demonstrated that random-type intervals returned values of both types of error (ME and MPE) that were significantly more unstable and reached higher values and extremes compared to fixed-type intervals.

The mean absolute error (MAE) is a statistical metric that utilizes the absolute value of the discrepancies, thereby ensuring that positive and negative values are not canceled out (Equation (6)). Consequently, it is logical that the resultant values are significantly greater than the mean error (ME) and are not subject to rapid fluctuations from positive to negative values. In our case the values of mean absolute error demonstrated a gradual incline with increasing values of interval length (Figure 2c). In most cases, the MAE from random-type intervals exceeded that of fixed intervals (except for 15, 20, and 30 s for thinnings and 7, 14, and 30 s for clearcuttings), albeit not to the same extent as in the case of ME and MPE. The results of the repeated-measures analysis of variance (ANOVA) demonstrated that the length of the interval had a significant impact on the value of the mean absolute error (MAE) for both types of intervals and both cutting types. The post hoc Tukey test enabled the identification of some homogeneous groups. These groups aggregate cases where the values of the MAPE are not significantly different. For fixed-type intervals on thinnings, there was a slight overlap between the groups. The first group comprised intervals up to 25 s (except for 20 s), while the second group consisted of intervals exceeding 20 s (including 15 s). In the case of the random type on thinnings, the separation was not as distinct, and there was greater overlap among the groups. The analysis revealed a distinct separation of MAE for fixed intervals on clearcuts. The first group comprised intervals of up to 25 s, characterized by MAE values below 40.7. In contrast, the second group consisted of intervals exceeding 30 s, exhibiting MAE values greater than 63. In the context of random intervals, the distinction between the groups was not that clear, and there was significant overlap between the groups. This phenomenon is analogous to what was observed in the thinnings study.

The mean absolute percentage error (MAPE) is a quantitative metric that calculates the absolute value of the error and expresses it as a percentage of the operations’ duration (Equation (7)). In the majority of cases, the mean absolute percentage error (MAPE) was slightly elevated for random intervals in comparison to fixed intervals of equivalent length (see Figure 2d and Table 2). In a small number of cases, these two types of intervals demonstrated comparable levels of MAPE (19 s for thinning; 6, 7, and 18 s for clearcuts). Only for the longest intervals was the MAPE of fixed-type intervals higher than random ones (20 and 30 s for thinnings and 20 to 30 s for clearcuts).

As anticipated, the value of MAPE exhibited a consistent increase in proportion to the increase in the interval time. However, this tendency was only observed up to the interval length of approximately 14 s in the case of thinning and around 13 s in the case of clearcutting—for random-type intervals. It was at this point that the level of error began to demonstrate some variation. In the case of fixed-type intervals in thinnings, a precipitous decline was observed at an interval of 16 s, followed by a gradual recovery and subsequent substantial increase at 25 s. In the case of clearcut areas, there was a somewhat erratic increase and a marked upward trend from the 20 s mark.

Random-length intervals demonstrated elevated levels of MAPE and exhibited more erratic behavior, especially above the 13 s interval length.

For thinnings, the values of MAPE for fixed-type intervals ranged from 1.64% (for the 3 s interval) to 18.68% (for the 30 s interval). For the random-type intervals, the values were higher, ranging from 3.18% (for the 3 s interval) to as much as 20.55% (for the 35 s interval). For clearcuts, the tendency exhibited a similar pattern but with slightly lower values: 1.58% (3 s interval) to 17.7% (35 s interval) for fixed and from 2.51% (3 s) to 19.01% (35 s) for random intervals.

In both cases of thinning and clearcutting, the length of the interval and its type were found to have a statistically significant influence on the MAPE level (p < 0.005 in all cases). Nonetheless, the interaction was not found to be significant (p = 0.168 and p = 0.077, respectively), which indicates that the changes in MAPE levels followed similar patterns.

The post hoc Tukey test enabled the observations to be separated into distinct groups, which were characterized by similar levels of MAPE. The categorization of intervals into groups exhibiting comparable levels of error suggests that intervals belonging to the group with the lower level of error are equally acceptable. In the case of thinnings, MAPE for fixed-length intervals stratified the observations into two distinct groups—one with MAPE below 9.47% (all intervals up to 19 s, except 15) and the other with MAPE over 10.55% (15 s and all intervals above 20 s). The level of MAPE for random-length snapshots also stratified the observations into distinct groups—one with MAPE below 10.71% (interval lengths up to 20 s, except 18) and the other with MAPE over 13.52% (intervals of 25 s and longer and 18 s).

In the case of clearcuts, the separation was also clear—without any overlaps between groups. Fixed snapshots generated MAPE levels that split into distinct groups: one with MAPE below 8.56% for all interval lengths up to 17 s (except 16) and a second with MAPE exceeding 9.67% for snapshots longer than 18 s (plus 16 s). Random-length intervals resulted in MAPE levels that could be divided into groups overlapping only in one case: for 16 s. The first group was characterized by a MAPE of less than 9.52% (all intervals up to 14 s, plus 16 s), while the second group had a MAPE of more than 9.52% (intervals of 15 s or more, plus 13 s).

The primary application of the snapshot method is the estimation of the proportion of time allocated to different activities during a workday. As the duration of the snapshots decreases, the authenticity of the results increases. Conversely, the investigative burden on the researcher is significantly augmented. Therefore, it is imperative to assess whether the proportions of activities obtained differ with increasing snapshot intervals. For this purpose, a MANOVA model was developed that considered the type of snapshot (fixed and random) and snapshot interval.

The findings indicated that in both thinnings and clearcuts, the interval duration did not demonstrate a statistically significant influence (p values of 0.673 and 0.716, respectively) on the established operation time share. Similarly, there was no substantial impact observed on results based on the selected interval type (p values of 0.975 and 0.862, respectively). The interaction between duration and type also did not reveal a significant relationship (both p values of 0.999), suggesting that the duration and type of interval had equally little impact.

In the case of thinnings, the proportion of time spent on various operations of harvester work demonstrated negligible variations with increasing interval time, both for fixed and random snapshots (Figure 3). A decline in the “driving” proportion was observed in only 19 and 20 s (both fixed and random intervals), favoring an increase in the share of the “other” category.

An examination of the data revealed no statistically significant disparities between the two categories of snapshots, namely random and fixed, with respect to the calculation of operational times (Wilk’s lambda = 0.9929, p = 0.975).

In the case of clearcutting, the results were analogous. There was no significant difference in terms of the time share of various operations (Wilk’s lambda = 0.529, p = 0.716) (Figure 4). A modest increase was detected in the “driving” category, with a fixed interval ranging from 16 to 18 s and a random interval of 17 s. Nevertheless, the investigation revealed that the two types of snapshots (fixed and random) did not yield disparate proportions of operation times (Wilk’s lambda = 0.977, p = 0.682).

In summary, the findings indicate that the shares of operation times in thinnings remained consistent up to an interval of 18 s; above this interval, however, the shares exhibited variations. In the instances of clearcuts, the proportions demonstrated a high degree of consistency throughout, except for fixed intervals ranging from 15 to 20 s, where the “driving” and “other” categories exhibited a slight imbalance.

The stability of the methods was assessed by comparing the levels of error in three variants for each interval type. In the case of fixed-type intervals, the snapshot times were offset by one-third and two-thirds of the interval. For random-type intervals, two other variants were created by employing different sets of random intervals. Statistical tests (one-way repeated-measures ANOVA) revealed no significant differences in the levels of mean error or any absolute error (MAE or MAPE) across different interval types and cutting types.

4. Discussion

The times spent by harvesters on various operations, as determined by conventional continuous time studies, were utilized solely as a standard for comparison with the results of snapshot studies. Nevertheless, they also give some insight into the work process of harvesters.

The findings of this study demonstrated a concurrence with the results of other studies in terms of the obtained shares of operation times in thinning and final felling (Table 1). A number of issues have been identified, stemming from the use of disparate definitions of operations [33] and the subsequent integration of certain operations into composite classes (e.g., positioning, cutting, and felling [41]) or, conversely, the division of operations into smaller components (e.g., positioning divided into swing, felling, and tree securing, as in [8]).

In the study conducted by Szewczyk et al. [42], the average operation times exhibited a high degree of similarity to the results obtained in our study, both in thinning and clearcutting operations. The main distinction observed was in the thinning method, where the duration of cutting and felling activities was shorter by approximately 2.2 s and processing time by over 4 s per tree. Conversely, driving time was found to be longer by an average of 7.2 s. This phenomenon can be attributed to the fact that the thinned stands in Szewczyk’s study were significantly older than those utilized in this study (86 years vs. 40–50 years, respectively). In a study conducted by Pajkoš et al. [27] in a spruce clearfell site, the operation times were significantly longer, especially for felling (45–51 s, compared to 6.5 s in our study) and processing (70–100 s, compared to 25.5 s in our study). This could be attributed to the challenging conditions associated with felling and processing spruce trees in the Czech highlands, as compared to the more favorable conditions experienced in the Polish lowlands during the processing of Scots pine. Additionally, minor discrepancies in the delineation of work operations rendered the comparison less direct.

Another study by Szewczyk et al. [41] describes the proportion of operations within a harvester’s workday. These correspond only partially to our results: while positioning, cutting, and felling took a similar proportion of time (33% for thinnings and 31% for clearcuts, compared to 21% and 25%, respectively, in our study), processing took 40%–58% of the time (compared to 30%–33% in Szewczyk), and the driving share was nearly the same for thinnings (31%) but completely different for clearcuts (4% in our study and 32% in Szewczyk). This discrepancy is presumably due to the exclusive analysis of effective work time in our case, as opposed to the total workday in Szewczyk’s study.

A 2017 study by Apǎfǎian [8] on clearcuts showed similar results in terms of cycle time. However, the study’s more detailed approach to the definition of operations makes comparisons more challenging. Processing operations took the bulk of the work time at 68%, while positioning took around 20%. Felling took only around 4%, and driving took around 7% [8]. Nurminen’s [25] study also employed a more detailed operation division, encompassing additional operations such as “boom-in”, “clearing”, and “moving logs, tops, and branches”. The study exhibited moderate concordance with our findings concerning positioning and felling yet significant discrepancy regarding processing and moving/driving. Conversely, some studies have adopted a more general approach to the division of working time, categorizing it only into main work time and supplementary components (complementary work, maintenance, repairs, and non-working time) [13]. This approach also presents challenges in direct comparisons.

It is imperative to acknowledge that the previous research typically shows the proportion of operation times within the context of an entire workday, whereas the configuration of this study describes the proportion of operation time within the effective work-time category; thus, the results may show slight discrepancies.

The calculation of the average cycle time was conducted for the primary purpose of assessing casual synchronization. The results of this calculation yielded cycle times that aligned with those reported in related studies [8,33,42] of approximately 57 s for thinnings and 45 s for clearfell sites.

As demonstrated in the results, the duration of individual operations can be brief, and it can be challenging to record these operations using a standard manual method [29,43]. A further issue pertains to the establishment of an adequately substantial interval time in a snapshot method, a factor that facilitates the detection and accurate representation of brief operations.

Szewczyk’s study [17] posits that the interval between regular snapshots should be a minimum of two to three times the duration of the shortest operation in the cycle to prevent synchronization. In the present study, the shortest operations were “positioning” for thinnings and “driving” for clearcuts, with an average duration of approximately 5.5 s. This would result in recommended snapshot intervals ranging from 11 to 17 s. However, the results obtained from this study demonstrate that intervals of both shorter and longer durations yield analogous outcomes in terms of the share of operation time.

A subsequent analysis of “spikes” in the shares of specific operations, with suspicion of harmonization, did not provide support for this claim. This phenomenon manifests when the operational duration is a precise multiple of the snapshot interval. In this particular instance, the snapshot produces a greater number of “hits” than would be achieved if the operation time were to be marginally extended or reduced. The conditions for such synchronization are the cyclical nature of the work and consistent average operation duration. The high variability of the obtained cycle times (Coefficient of Variation of 33.5 for thinning and 35.7 for clearcutting) indicates that synchronization is not a viable hypothesis, which corresponds with the conclusions of [13].

A method that could be used to mitigate the casual synchronization while also decreasing the researcher’s workload involves the consolidation of numerous short operations into a smaller number of extended classes. Unfortunately, this approach yields less precise results, consequently diminishing their interpretative value. A considerable number of authors opt for meticulous depictions of operational components [8,43], while others consolidate these components into broader classes [27,41]. A key factor to consider when determining the number of work elements to be studied is the required sample size. The application of the Steinhaus formula (Equation (2)) indicates that the number of classes influences the minimum number of observations required for a given level of accuracy.

The utilization of the formula provided by [6] (Equation (1)) resulted in a comparable minimum number of observations in this study. It was demonstrated that intervals as long as 20 s or more were adequate to ensure the requisite level of accuracy. Furthermore, shorter intervals yielded a substantially higher required number of snapshots. This finding indicates that the utilization of either formula would be permissible in research concerning the time structure of harvester work.

This study employed a variety of calculation formulas (e.g., Equations (4)–(7)) to determine the magnitude of errors in the estimation of operation time. The types of errors that do not utilize absolute values (ME and MPE) have been shown to possess limited analytical value. As these encompass both positive and negative discrepancies, the average of the two types of discrepancies tends toward 0. This creates an illusion of an accurate method, even if the values of the individual discrepancies are substantial. Also the results are highly volatile—rapidly changing from positive into negative with only a minor shift in the interval time, especially for random-type intervals (see Figure 2b). Statistical analyses indicated that the interval type does not exert a significant influence on the levels of both mean error (ME) and mean percentage error (MPE). In the context of evaluating the accuracy of the snapshot method, it is advantageous to consider errors that employ absolute values of discrepancies. This is due to the fact that these errors are not canceled out, which is a beneficial characteristic for the analysis. The absolute percentage error is of particular significance, as it quantifies the discrepancy in terms of a percentage of the operation time.

In the context of the study, the analysis of the mean absolute percentage error (MAPE) levels obtained with various interval lengths and types indicates that fixed-type intervals result in MAPE levels that are lower and more consistent than for random-length intervals. The results of the HSD Tukey test for MAPE level separated the observations into homogeneous, distinct groups. In the thinning scenario, the group exhibiting the lowest levels of MAPE included intervals up to 19–20 s (resulting in MAPE values around 10%–11%), while in the clearcutting scenario, these intervals extended up to 16–17 s (MAPE values around 9%). This finding indicates which interval lengths and types yielded analogous error levels, potentially serving as a valuable reference point for determining the optimal interval setting when conducting research in analogous conditions. An analysis of the changes in the proportions of operating times with increasing interval length revealed that, for fixed intervals, these remained relatively constant up to approximately 17 s for thinnings (see Figure 3) and around 15 s for clearcuts (see Figure 4). For longer interval lengths, some proportions exhibited fluctuations, particularly “driving” and “other.”

Most sources suggest that observations should be taken randomly [4,6,7,10,15,42] during the work shift. This statement is particularly valid when considering field sampling over extended periods. For analyzing the video recordings, another approach seems favorable. Using a fixed interval duration facilitates skipping of the video, thus making the analysis faster. The findings of the present study demonstrate that random intervals resulted in elevated levels of errors. Furthermore, these errors exhibited heightened instability. This phenomenon can be attributed to the distribution of operating times, the average duration of instances of work phases, and the delineation of operations. In the context of field studies, particularly those conducted over an extended time, the implementation of alternative interval configurations, such as the incorporation of random or lengthier intervals, has the potential to yield precise outcomes, provided that the sample size is adequately large.

5. Conclusions

• The minimum number of observations required, calculated using the general formula (Equation (1)) and the Steinhaus formula (Equation (2)), were very close: 368 for thinnings and 376 for clearcuts compared to 298 using the Steinhaus formula.
• Within the time constraints of this study (the length of recorded videos), only snapshot intervals shorter than 25 s yielded the number of observations that fulfilled the criteria of the required sample size.
• The type and length of interval had an impact on the level of mean absolute percentage error (MAPE). Random-length-type intervals usually produced elevated levels of MAPE compared to fixed-length intervals of the same length.
• Type of snapshot interval: Fixed- or variable-type intervals did not have an impact on the resulting proportions of work operation time. The duration of intervals within the same type also did not influence the proportions of work operation times.
• The practical recommendation from the results of this study is to use the longest fixed-type interval that falls into the group with a lower MAPE. In this particular instance it would be a fixed interval of up to 19 s for thinning and 17 for clearcuts.