Abstract:

              Over time, assets lose value, and so does a running project or business. Inaccurate tracking of   these assets could lead to overestimating business value and making it more difficult to secure finance.

In this statistical study, we’re focusing on utilizing depreciation on machinery using depreciation expense calculation methods. we’ll be able to relate the machinery productivity with its asset value.

            This entails how much value project assets lose each year. This value must be recorded and taken into account as a loss and must be subtracted from the revenue. By doing this so, managers will be able to see how much money which is actually been made and be able to manage their financials.

Table of Contents

Abstract:        2

1.        Introduction        4

1.1 Problem definition:        4

2.        Literature review & Necessary background:        5

2.1 Literature review        5

2.2 Definitions        6

2.3 Parameters:        7

3.        Method        8

3.1 The first method is straight-line depreciation.        8

3.2 Second method: Units of production method        8

3.3 Third method: the Sum of Years’ Digits method        9

3.4 The Fourth Method: Double Declining Balance        9

4.        Data        10

4.1 Dataset collection for Data Analysis:        12

∙        Dataset 1        12

∙        Dataset 2        13

∙        Dataset3        13

5.        Experiment Design        15

6.        Performance Evaluation Criteria        19

7.        Results & Discussion        20

1st: Dataset1 (Depreciation): “contains only 3 from our targeted methods”        20

2nd: Dataset2 (Depreciation Methods):        25

3rd: Dataset3 (Predictive maintenance):        28

8.        Conclusions & Recommendations & Future Work Suggestions        30

8.1Conclusions:        30

8.2 Recommendations:        30

8.3 Future Work Suggestions:        31

9.        Appendices        34

List of figures

Figure 1 Changes in salvage value through different accuracy degree        11

Figure 2        12

Figure 3        12

Figure 4        13

Figure 5        14

Figure 6        16

Figure 7        16

Figure 8        17

Figure 9        17

Figure 10        18

Figure 11        19

Figure 12        21

Figure 13        22

Figure 14        22

Figure 15        26

Figure 16        29

Figure 17        29

Figure 18        29

Figure 19        35

Figure 20        35

 List of tables

Table 1 some data about cutting machines        11

Table 2        20

Table 3        20

Table 4        21

Table 5        23

Table 6        23

Table 7        24

Table 8        25

Table 9        25

Table 10        25

Table 11        26

Table 12        28

Table 13        28

Table 14        34

Table 15        34

Table 16        34

Table 17        34

Table 18        35

Table 19        35

1. Introduction

            Normally, equipment fails overtime, which has an impact on production and value and costs factories a huge amount of money. It also has an impact on the companies’ and factories’ reputations, further decreasing business opportunities. By using mathematical equations, we are going to calculate the depreciation rates of machinery, which can assist project managers in determining the way to cover the cost of the machines that were purchased from revenue and help them resolve a plan for the factories to handle their ongoing projects without being affected by sudden equipment breakdowns.

           Equipment depreciation is a metric that shows what quantity the equipment’s value is decreasing annually through regular use. When an older asset breaks down, it should be wiser to get a replacement rather than spend more money on repairs than the asset’s worth.

           Depreciation reduces the quantity of earnings accustomed to calculating taxes, lowering the quantity of taxes owed. The higher the depreciation expense, the lower the taxable income and the tax bill are.

           Our project is searching for a mathematical and numerical way to calculate both depreciation and depreciation rates for equipment to be able to handle any mechanical project properly.

Now, there are some questions that we’re going to answer throughout this project, including:

Why should we care to record depreciation and how should we calculate it?

How can depreciation calculation affect industry in Egypt?

1.1 Problem definition:

            It is known that the performance of machines and equipment deteriorates with time. The operating system contains a replaceable part, the wear of which can be observed over time. However, a period occurs when it becomes too costly to maintain existing machinery, so it is more economical to replace it. Machines are also in danger of becoming obsolete due to the development of technology.

            It should be noted that if an existing piece of equipment does not meet the challenges posed by advances in technological development, it must be replaced. Thus, in such cases, even though the equipment has physical value, if it loses its efficiency, thus decreasing its accuracy, it should be replaced because it means that it is not competitive enough.

2. Literature review & Necessary background:

1. Literature review

In 1998, Chu, Proth, and Wolff , relied on predictive maintenance to find out if they should keep the system according to its state. They deal with the case of one-unit system. They came up with a comprehensive approach to the problem and provided a characterization of the optimal maintenance.

In 1995, Shey, Griffith, and Nakagawa founded a numerically efficient algorithm to minimize the long run anticipated costs per unit time of the policy.

In 2007, Cardoso and Gomide suggested the use of predictive data mining techniques, as a systematic approach to explore newspaper company database and improve predictions. The focus of their work is to develop a prediction method that uses fuzzy clustering and fuzzy rules together with performance scores of selling points for prediction.

In 2016 Sahu, Sahu, and Sahu found that uncertainty is always in making decisions and suggested to adopt proper policy in handling the case. They used the concept of fuzzy logic to address  uncertainty in their work.

In today’s competitive environment, because of fast technological development and globalization, replacement of machines and equipment could be a permanent and sophisticated problem, which is a common concern in the minds of the owners of virtually every business firm. The decision regarding replacing machines and equipment helps in determining their economic life so that prior advance planning may be done to interchange their machines and might also consider the spent cost in computing the variable cost per unit and also the damage of the produced product. The presented case favoured the interchange of the lathe machine at the top of the first year with a minimum average expense of Rs. 66,000. If the manufacturer doesn't replace the considered lathe machine after completing the primary year of his operation and proceeds to the second year, third year, and so on, in this case, the firm operates his machine with a high monetary value in spite of the minimum monetary value, which might be easily computed by the presented work. The comparison between the average yearly cost to be spent in the future and, therefore, the minimum yearly cost that may be achieved by the presented work It also shows how much extra money business firms must pay in subsequent years. The authors would love to conclude that, supported by the presented work, merely thanks to a small calculation, it's possible for the business firms to use the purchased machinery via determining the economic replacement time with the minimum cost as compared with other years.” [1]

2.2 Definitions:

Depreciation is a reduction in the value of such a thing due to wear and other environmental conditions. A method used in accounting to recover the cost of assets during their lifetime. [2]

Fixed assets: Any item whose value decreases over time and lasts more than one year.

Useful life: the time during which the assets (equipment) will produce income (how long will it work?

Asset cost: the actual cost of purchased equipment.

Salvage value: the value that the asset will reach at the end of its useful life.

Units produced per year: The number of pieces produced each year.

Goodness to fit: A statistical test show how observed data matches expected data values.in other words it measures how well sample data matches a distribution from a population with a normal distribution is known as goodness-of-fit. Simply put, it determines if a sample is skewed or represents the data that would be found in the population at large. [2]

Production capacity: the number of parts produced throughout the life of the machine.

Chi-Squared: related to the goodness to fit and it also measures how the model compared to actual data it also must be carried out for random, mutually exclusive data that are from a random variable. [3]

2.3 Parameters:

Range: the difference between the largest value and the smallest value is the simplest measure of variability in the data. The range is determined by only the two extreme data values. And it’s calculated by (Range = highest value – lowest value)

Mean: the average of a set of data it’s calculated by the formula

The variance is a measure of variability. It is calculated by taking the average of squared deviations from the mean.

Variance tells you the degree of spread in your data set. The more spread the data, the larger the variance is in relation to the mean. [2]

Standard Deviation: is a measure of how spread-out numbers are.

3. Method

One of the important tools to be observed in our mechanical project is the ability to calculate the depreciation rates on machinery and equipment. Through these means, a good view is provided to show us how well machinery runs.

But, before running a piece of equipment, some tests are applied to evaluate it during and after the assembly process and put it into service. A Factory Acceptance Test (FAT) is carried out, which ensures that the components and controls are working properly according to the functionality of the equipment itself.

FAT helps to achieve independent proof of functionality, quality, and integrity with our comprehensive checking process.

Verify all-important documents, such as manuals, instructions, plans, drawings, piping, and instrumentation diagrams (P & IDs).

Ensure that the equipment or plant performs as expected under the testable range of likely conditions, including mishandling and error. [3]

We’ll carry out this test to determine the accuracy of the machine, which we will use in calculating salvage value. The accuracy of the machine is determined by the results that come out of the trial workpieces. The number of trail workpieces must not exceed 100. [4]

Depreciation on equipment and machinery starts when you place the equipment in service for business or production, and you stop depreciating when you’ve fully recovered the cost of the asset, or you take it out of service. [5]

For the mechanical equipment, we’re focusing on calculating depreciation rates mathematically using four methods:

3.1 The first method is straight-line depreciation.

A commonly used technique for its simplicity. To use this method, it’s a necessity to define the used parameters in its mathematical formula.

• Useful life: the time during which the assets (equipment) will produce income (how long will it work?)
• Asset cost: the price of purchased equipment.
• Salvage value: the value that the asset will reach at the end of its useful life.

4. Consequently, the used formula is:

This method is preferable as it is more direct and simpler to use than the others.

3.2 Second method: Units of production method

This one is considered the most accurate method used to calculate the depreciation rates as it is based on the number of units produced per year rather than estimating the useful life of the equipment. Depreciation increases once the number of produced units increases.

• A lifetime of units produced

• Number of units produced

The used formula for calculation is:

3.3 Third method: the Sum of Years’ Digits method

The sum of the years’ digits (SYD) depreciation is a depreciation method that makes you depreciate less as time goes on. It assumes that the asset gets less productive as time goes on, which is why you pay off more during the earlier years and proportionally less each year.

The used formula is:

     For such a method, the remaining useful life is reduced each year.

3.4 The Fourth Method: Double Declining Balance

This one is considered an accelerated method where it is presumed that the asset was more productive in its earlier years. The depreciation rates calculated here are double those calculated using the straight-line method. But before using this formula, some used parameters to be defined as:

• The depreciation rate (R) is the rate at which an asset is depreciated during its useful life.

The formula used is:

Depreciation expense = 2 x Cost of the asset x Depreciation rate. [7]

4.  Data

             Based on the definition of depreciation mentioned earlier, we have to define some basic points:

To calculate depreciation

           We are dealing with the average price of machines. We have compiled several cutting machines with different prices and different performances and calculated the average of their prices to get a number that can be dealt with in the equations.

Equipment doesn’t have a specific lifetime but it has accuracy grades in which we choose the suitable grade according to the required products. The numbers are average approximations since they change from one factory to another and from one material to another. The value mentioned in the table is the number of years that the machine has been operating with the same accuracy. After the end of the period, the machine changes to a lower degree of accuracy.

• Salvage value: the machine price after its degree of accuracy falls below the degree allowed for the product and its inability to produce the same product with the same efficiency (which does not mean it is unusable; it may be suitable for low-accuracy work).

            In order to get the most accurate salvage value, we deal with the number of hours the machine has been working, which is closely related to the accuracy of the machine. 

4.1 Salvage value calculations:

From the expected Salvage value formula:

Where:

• (S) is a salvage value,
• (P) is Cost of asset, and
• (N) are the accuracy degrees that machine decreased by.

Figure 1 Changes in salvage value through different accuracy degree

• We will be dealing specifically with metal working machines (cutting machines) such as bending machines, drills, grinders, lathes, milling machines, and shapers.

Table 1 some data about cutting machines

4.1 Dataset collection for Data Analysis:

• Dataset 1: Depreciation:

The dataset contains:

• Asset information (Rows 2 to 4):    

• Cost (Represents the initial cost of the machine).
• Salvage (Represents the salvage value of the machine).
• Life (Represents the useful life of the machine).

• Depreciation Value (Rows 8 to 18):

• Period (Useful lifetime of equipment divided in years).
• Depreciation value measured in 5 ways:

1. SLN (Straight line method).
2. SYD (Sum of years’ method).
3. DB (Declining balance method).
4. DDB (Double declining balance method).
5. VDB (Variable declining balance method).

*These 5 columns are already calculated by built in excel functions, for example SLN is calculated using a SLN function in excel which takes the Asset information as an input:

• Asset Value (Rows 22 to 33): “Same as Depreciation value except that the asset value (Value of the machine after depreciation is measured instead of the depreciation value; by subtracting the depreciation value from the cost using an excel function”.

• Period (Useful lifetime of equipment divided in years).
• Asset value measured in 5 ways:

1. SLN (Straight line method).
2. SYD (Sum of years’ method).
3. DB (Declining balance method).
4. DDB (Double declining balance method).
5. VDB (Variable declining balance method).

• A Scatter chart showing the correlation between: Period, Asset value (which we will delete to produce our own charts)                                                                                              

*Our main concern from this dataset are methods 1, 2, 4. [10]

• Dataset 2: Depreciation Methods:

The dataset (9 sheets) Contains:

• Asset information.
•  Methods of depreciation over a period of 5 years (Some are left blank), so we’re going to fill them using excel functions. [11]
• Dataset3: Predictive maintenance.

We will use this dataset to evaluate factors (parameters) Affecting the cutting machine useful life against the failure type (Those factors can either be machine factors, ex:  Process temp(K), cutting tool factors, ex: Tool wear(min) or environmental factors which are the factors of the surroundings of the machine that contributes in machine failure, ex: Air temp(K).

Figure 5

The Dataset contains:

1. UDI: unique identifier (An index for the machine number).
2. Product ID:   Describes the machine quality:

• L: low quality.
• M: Medium quality.
• H: High quality.

3. Air temperature(K): The temp. of the air surrounding the machine (measured in Kelvin).
4. Process Temperature(K): The temp of the machine during process (measured in Kelvin).
5. Rotational speed (RPM): The Rotational speed of the cutting tool.
6. Torque (N.M): The output torque from the machine motor.
7. Tool wear(min): The wear in the cutting tool.
8. Target: The value 0 means no failure occurred, 1 means there is a failure.
9. Failure Type:    

• Tool wear failure.
• Heat dissipation failure.
• Power failure.
• Overstrain failure.
• Random failures. [12]

5. Experiment Design

• The first step we take is asking questions.

• How much does the machine value decrease? (What is the depreciation value of the machine?)
• What is the percentage decrease of the machine value over time? (Relative to the initial cost)
• What is the error between the different methods of calculating depreciation? What is the percentage error?
• What are the parameters that affect the machine’s useful life?

•           Now, we need to access our data, visualize and clean it to ensure the data is well structured. Then, we need to perform our analysis to extract important information and statistics. The four methods mentioned in the method section are our main concerns in datasets 1 and 2 (and we can remove the cells containing other methods to avoid confusion).

1. Straight line depreciation method (SNL)

2. Units of production method

3. Sum of years’ digits method (SYD)

4. Double declining balance method (DDB) So the Following are some of the analysis we will do:

 For Dataset 1 (Depreciation):

There are no empty fields. Deleting the scatter plot diagram to create new diagrams expressing the correlation using different methods between:

• Asset value / life (it’s expected that the lines will approximately end at the same point)
• Depreciation value / life (it’s expected that the SNL method will produce a horizontal line while the others will show a negative correlation) We may use a pie chart for each method to show the depreciation value in each period (we may use 2 pie charts for each method (from period 1 to 5 and from period 6 to 10) for clear visualization.)

For the measures of central tendency: (using built in excel functions)

• Getting the mean depreciation value for SYD, DDB (our concern), it’s expected to be approximately equal to the depreciation value of the SNL method (900$)
• Ex:

Figure 6

• Getting the variance and the standard deviation between the final asset value of different methods.
• Getting the Range between depreciation values in each method by using built in functions to get max and min then get the difference between them.
• Measuring the percentage depreciation in each period.
• Ex:

Figure 7

For Dataset 2 (Depreciation methods):

•             There are empty cells that are left to get our output values, but most importantly, our asset values, which are mainly our input values, are available. So, we will use Excel's built-in functions to calculate depreciation values for different methods.

•            For example, to get the DDB (Double Declining Balance) depreciation values over a period of 5 years, we need to put an absolute reference on each of the following: cost and salvage to maintain the value, while leaving the period without an absolute reference as we want it to change when dragging down to copy the function to the cells below.

Figure 8

•              Except for the Units of production method, which doesn’t have a built-in excel function, we will use a manual excel formula to get it, using the mathematical equation:

 We add an absolute reference to the cost, salvage value, and useful time in years as they’re constant. Then drag down to fill all the empty cells.

Figure 9

And by this, we should’ve filled all the empty cells, then we gathered all the data in one sheet to do our Deceptive Statistics nearly by the same steps as in Dataset1.

For Dataset3 (Predictive maintenance):

• No fields are empty.

• We’re interested in the machines that produced a failure, so we will extract all the rows that have a Target = 1 (which means that a failure has occurred) to extract our information.

• Graph a pie chart for the percentage of each failure type relative to the total number of failures.

• Get the mod of the failure types to know what the critical failure type is.

• Graph a scatter plot diagram between the quality and the tool wear (it’s expected that a lower quality produces more wear, so it’s a negative correlation).

For the validation of mathematical equations against statistical expectations: We already wrote an excel formula manually for the unit production method, but let’s validate, for example, the excel built-in function with the mathematical equation we gathered in the method section (the expected error is 0%).

Let’s compare the depreciation value of a SNL method in excel to our equation using the same inputs of, for example:

• Cost: 10,000 $
• Salvage: 1000 $
• Life: 10 years

Figure 10

6. Performance Evaluation Criteria

 First, we calculated the expected value by calculating the average value and then making a chi-squared test. The result is to calculate the probability values. (p-value is the probability of the appearance of a number different from the calculated values).

 Logically, p-Val equals zero because these equations are used in real life. (Example: zero error).

Figure 11

7. Results & Discussion

The Statistical analysis will concern these four depreciation methods:

1. Straight line depreciation method (SLN).
2. Units of production method.
3. Sum of years’ digits method (SYD).
4. Double declining balance method (DDB).

1st: Dataset1 (Depreciation): “contains only 3 from our targeted methods”

• Deleting the columns concerning other depreciation methods:

Table 2

Table 3

• Taking into consideration that:

1. Table 2 Provides the Depreciation value over the period of 10 years.
2. Table 3 provides the Asset Value over the period of 10 years.
3. Units of production method is not available in this dataset.
4. The example in this dataset uses this data as an input:

Table 4 shows:

-  Cost (The initial cost of the machine).

-  Salvage (The Salvage value of machinery).

-  Life (The period over which we calculate  

   Depreciation “in Years”)

• Checking the Salvage value” Value of the machine after the period of 10 years in this sample”:

Using the equation in Phase 2, Ch.4 (Data): where:    

* Accuracy degrees N is equivalent to the period = 9 years. “As the machine degree of accuracy decreases by 1 each period”.

• S= 10,000 – 0.1×9×10,000 = 1,000  

• Therefore, Salvage Value is correct

• Plotting a Line chart for the Depreciation Value ($) of the machines / Period (Years): To visualize how much the machine value decreases over time.

According to visualization of the line graph (figure12):

-SLN method produced a horizontal line as expected “as the depreciation value is constant over time (900$)”.

-SYD&DDB methods produced a negative correlation as expected “as their depreciation value decreases over time”.

-SYD method shows a uniform decrease in depreciation value “as the formula for calculating the depreciation value using the SYD method includes the remaining useful life in the numerator, which decreases uniformly and causes the depreciation value to decrease uniformly”, the formula is:

• Plotting a Line chart for the Asset Value ($) of the machines / Period (Years): To visualize the final machine value after depreciation.

According to visualization of the line graph (Figure13):

-         All lines nearly ended at the same point as expected “Asset value of the machine for the 3 methods ended with approximately 1000$ at year 10”.

-        The line of the SLN (Straight-line method) is a straight line as expected “because the decrease in value of the machines using this method is uniform (900$ in this case).

-        DDB&SYD methods produces a higher decrease in Asset Value than SLN method at the beginning of the period (Approximately 1st 5 years), then lower decrease at the last 5 years.

-        DDB method produces a slightly higher decrease in asset value than SYD method at nearly the 1st 6 years then slightly lower at the last 4 years.

• Plotting a pie chart for each method showing the Depreciation value over the 10 years period: To visualize the depreciation amount in each period of accuracy.

According to visualization of the pie chart (Figure14):

-SLN method showed equal portions of depreciation value “as the depreciation value is constant over the period”

-SYD, DDB methods showed that portion 1 “depreciation in period1” is the largest, then the portion decreases till portion 10 “period 10 (Least depreciation value)”.

• Getting the mean for the depreciation values: (in this step, we needed to move the asset values downward in the excel sheet to make our statistical results fit): To check the Average depreciation amount of the machine in each period of the 10 years.

-SLN method showed a 900$ mean depreciation value as expected “as its depreciation value is already calculated by dividing the (cost-salvage value) by the period “useful lifetime”, which is the same way of calculating the mean value.

-SYD method showed a 900$ mean depreciation value as expected as it uses the same final asset value as SNL method (1000$).

-DDB method showed a slightly different mean depreciation value as it has a slightly different final asset value (1073.74$).

• Getting the range between final Asset values of the machinery for the 3 methods: To check the reliability of the methods.

Conclusion:

• Since the range is too small compared to the Asset values, therefore there is no massive difference between the 3 methods in calculating the depreciation for machinery, but this difference is due to that: Final asset value of DDB method is not the same as the given salvage value “should be the same”, So the DDB method may have a little bit of inaccuracy.

• Getting the Range between depreciation values for each method: To get how much are the depreciation values in each period dispersed “A large dispersion indicates that the depreciation may be concentrated in a specific period”.

Table 7 Shows:

-SNL method showed a range of 0$ “as all the depreciation values are the same”.

-DDB method showed the biggest range between depreciation values.

*Although the Range is not an accurate measure of data because there may be outliers, but since we can visualize that there are no outliers in our data, therefore we can rely on the Range as a measure of dispersion.

• Measuring Depreciation percentage by using this formula for each period, each method:

 & Getting the largest and smallest depreciation percentage for each method.

-        SLN has the same %Depreciation as the depreciation value of machinery is constant.

-        SYD Produced different depreciation percentages that varies between 0.02 & 0.16

-        DDB produced different depreciation percentages that varies between 0.03 & 0.2 “Largest difference between depreciation percentages, which is expected, as it has the biggest range between depreciation values”.

• Finally, an answer to the research questions: How much does the machine value decrease? (What is the depreciation value of the machine?) & The period it takes, what is the percentage decrease of the machine value over time? (Relative to the initial cost)

• In this example, the machine value has decreased approximately 9,000$ from a total cost of 10,000$ which is a percentage of approximately 90% over a period of 10 Years (9 Periods “9 degrees of accuracy”), which is a very huge portion of the machine’s value, which means that the machine’s value decreases very fast.

2nd: Dataset2 (Depreciation Methods):  

Our Target from this dataset is Analyzing the fourth method of depreciation for machinery.

(Units of production method) which was not available in the 1st dataset as the machine useful life   in units was not available.

• Fill in the missing cells using built in excel functions for all depreciation methods, except for the Units of production method which has no built in excel function, so we typed it manually. Then creating another Asset value table, which shows the final asset value of the machine for each period.

• Calculating total depreciation and percentage depreciation: To assure the answer of the research question: How much does the machine value decrease? (What is the depreciation value of the machine?) & the period it takes, what is the percentage decrease of the machine value over time? (Relative to the initial cost)

• In this example, the machine value has decreased 40,000$ from a total cost of 50,000$ which is a percentage of 80% over a period of 5 Years, which is the same as dataset1 example: a very huge portion of the machine’s value, which assure that the machine’s value decreases very fast.

“Since the DDB method produced the same total depreciation as the other methods in this example, therefore the deduction that it may not be 100% accurate and may be false, and there may be a fault in the inputs of the 1st dataset which were : Cost, Salvage, Life if we assume that the excel function that calculates the DDB depreciation is alright, so we now have 2 assumptions based on the results : 1.The DDB method is not accurate, 2.The DDB method is accurate, and we can’t find an answer with these datasets because we’re doing inferential statistics with a small sample of machining equipment”, We can take a bigger sample in the future work to answer this question.

• Since The Units of Production method is independent of the period that the machining equipment operates and dependent on Units produced by machine, based on the following equation from Ch4.Data:

Therefore, we need a line graph of the Depreciation Value in the units of production method against the Units actually produced using the machine: To ensure the expected outcome that the depreciation value increases when the machine produces more units.

Visualization of the Graph (Figure15):

As expected, as the units of production increases, Depreciation value “on the vertical axis” increases “As logically, when the machine operates more to produce more units, it will get consumed and will depreciate “. Therefore, we need to pay attention to the produced units & calculate them precisely to keep in mind the depreciation amount they caused to machinery.

• The Standard deviation and Variance of the depreciation values: to know how dispersed the data is relative to the mean (Average depreciation value).

Figure 16 Shows:

 -The Standard deviation& Variance of the depreciation values for each method

-When the Standard deviation for the depreciation values of the Sum of years digits for example = 4216.37$, that means that most of the depreciation values for the Sum of years’ digit method are within 4216.37$ of the Average depreciation value “Mean”.

-The Standard deviation for the depreciation values of the Straight-Line method= 0$, which means that all the depreciation values are equal to the mean value “8000$” which is correct.

-The Variance gives us a bigger visualization of the spread of the depreciation values.

3rd: Dataset3 (Predictive maintenance):  

• Another research Question was: What are the parameters that affect the machine’s useful life?

Therefore, in this dataset we analyze some of the parameters that causes the machining equipment to depreciate and analyze the failure they produce, if they do.

Ex:

1. Machining equipment type (L” low”, M “medium” , H “high”)
2. Air Temperature [K]
3. Machining Process Temperature [K]
4. Rotational speed [rpm]
5. Torque [Nm]
6. Tool wear [min]

• Filtering the dataset by filtering Target column to 1 only “Means that a failure occurred”: to focus on the failure cases in this sample and analyze it.

• Visualize the number of failures for each failure type ascendingly& Get to the mode “most repeated” for the Failure types: To know which failure type occurs the most and which failure types that occur frequently and try to increase the time to reach these failures in the future.

Table (13) Shows:

• The mode failure is Heat Dissipation Failure.
• Total Failures are 330.
• Power Failures are the second most critical failure.

Plot a histogram& a pie chart with percentages for the failure types against the number of failures: To better, visualize the difference in the no. of occurrences of each failure type.

  Figures 17 & 18 Show:                                                                                                                        

• Heat dissipation failure occurs the most, so we need to focus on this type of failure in the future work and try to increase the useful life of the machine until this failure occurs.
• Power failures
• Power Failures are the second most critical failure with a lower percentage of 5% than heat dissipation failure.
• Overstrain& Tool wear failure failures are less critical with percentages of 23% and 14% respectively.

• Plot a histogram for the Type “quality” against the Tool Wear: To prove the expectation that a lower quality produces more wear.

Figure (18) Shows:

• Expectation is correct, as the lowest material quality (L) produced the highest wear, the highest quality (H) produces the lowest wear and medium quality (M) produced a wear in between them, so it is preferred to use High quality machining equipment.

8. Conclusions & Recommendations & Future Work Suggestions

  8.1Conclusions:

• When using the DDB ("Double declining balance") or SYD ("Sum of years’ digits") methods to calculate machining equipment depreciation, the result is that the machine depreciates more in the earlier years (its value decreases significantly earlier).

• When using the SLN "straight-line" method, the result is that the machine depreciates the same amount every period.

• The SLN method is probably called the Straight-line method because the depreciation value/period graph produces a straight line as the depreciation is constant over the whole period.

• When using the units of production method to calculate depreciation, the depreciation value for each period varies according to the units produced and is independent of the period that the machine operates. "There is a positive correlation between them, which means when the units produced increase, the depreciation value increases, and therefore a negative correlation between the units produced and the final asset value of the machines."

• So, we conclude that the machining equipment’s value decreases when the period that the machine operates increases AND when the units produced increase.

• As the quality of the machining equipment decreases, tool wear increases.

• Heat dissipation failure is probably the most common failure among machines.

8.2 Recommendations:

• Factory owners should stick to calculating the depreciation of the machining equipment they own, as these machines lose their value very fast.

• Factory owners should keep in mind predictive maintenance to avoid sudden failures by predicting them through the operating machine parameters.

• To avoid sudden failures due to tool wear, high quality machining equipment is preferred to be used.

• Factories with machining equipment should be built in a location with suitable environmental conditions (especially for the weather conditions) that satisfy the machine operating conditions "parameters," as temperature and humidity should be the focus.

• The period that the machine operates, and the units produced by the machine must be calculated precisely to get an accurate measure of machine depreciation.

8.3 Future Work Suggestions:

• working with larger samples of data for depreciation and machine failure analysis to decrease the error percentage in the analysis and increase the analysis’ accuracy.

• focusing on heat dissipation failure, performing a detailed analysis to determine the main causes, attempting to avoid them, and predicting when the machining equipment will produce such a failure.

• Searching for more datasets that concern machine depreciation and machine failure to find more parameters that affect both.

• Analyzing other parameters that cause the machines’ values to decrease, e.g., humidity,

• Plotting more graphs using the Predictive maintenance dataset, ex: rotational speed [rpm]/Wear, torque [Nm]/Wear, to find relations between these parameters and get to conclusions of what causes machine depreciation and failure, by what percentage.

9. References

10.  Appendix A

• The following are some excel functions& manually written formulas &tools added in phase3:

1st Dataset: Depreciation:

• Getting the Total depreciation for each method using the SUM function.

• Getting the Range between depreciation values using MIN function to get the minimum depreciation value, MAX function to get maximum depreciation value, and then subtracting MAX-MIN in a written formula. (The same sequence was done to the asset value table).

2nd Dataset: Depreciation-Methods:

• We filled the 2 tables (Depreciation Values table & Asset values table) manually, so for the Asset values table:

• Asset value for each period is  calculated by a manual formula : Subtracting the corresponding cell in the Depreciation Value table “depreciation value for this period” from the above cell “previous Asset Value”

• Getting the STANDARD DEVIATION & VARIANCE of the depreciation values for each method.

-By using the function: STDEV.S

-VARIANCE is Calculated using the function: VAR.S

-.S is used in both functions because where analyzing a Sample of data.

3rd   Dataset: Predictive maintenance:

• Using a FILTER to remove the rows that will not add to our analysis.

We filtered the failure type to remove the machining equipment with no failure and focus on the machines that produced failure and depreciated.

• Making a PIVOT TABLE to visualize critical machine failure types, which calculates how many machines produced each type of failure.

11. Author contraptions

Author 1: Ahmed Osman

Author 2: Ahmed Ezzat

Author 3: Alaa Mahmoud

Author 4: Andrew Adel

Author 5:  Aya Ibrahim

Author 6: Kholoud Sharaf

Author 7:  Reem Hany

Author 8: Shahd Gamal

Author 9:  Amr Khaled

Author 10: Mohammed Hosny

Author 11:  Mohammed Khaled