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When calculating MTBF (Mean Time Between Failures), it is important to consider which formula is best suited for your specific situation. Formula a) suggests using the operating time divided by the number of failures in between, with the operating time being the difference between the current date and the date of first production. However, if running hour data is available, it is recommended to use that for a more accurate calculation of MTBF. On the other hand, formula b) involves dividing the difference between the start date of the last failure and the start date of the first failure by the number of failures minus one. This approach excludes the running time before the first failure and after the final failure from the calculation. It poses the question: is there an advantage to omitting this data from the MTBF calculation?

Mean Time Between Failures (MTBF) is a useful metric commonly utilized for a set of similar equipment, such as all the pumps within a refinery. The formula for calculating MTBF is (NUMBER OF EQUIPMENT PIECES X TIME PERIOD) divided by the NUMBER OF FAILURES recorded within that time frame. For instance, if a refinery has 1200 pumps and experiences 387 failures in a year, the MTBF would be calculated as (1200 X 12 months) / 387 = 37 months MTBF. When considering a single item, MTBF can be calculated by dividing the time period by the number of failures. For example, if a pump fails twice in one year, the MTBF would be 12 months / 2 = 6 months MTBF. This metric is essential for assessing the reliability and performance of equipment, helping businesses make informed decisions regarding maintenance and operational strategies.

While I believe in using the first formula for calculating MTBF, there are those who recommend using the second formula due to uncertainty surrounding start and end dates. It's important to note that MTBF pertains to the time between failures, not the duration from start to finish. Can someone clarify which formula is commonly used to calculate MTBF, particularly in the context of published MTBF values for pumps, which may show an increase from 1 year to 3 or 4 years?

During a conversation with an employee, I highlighted the importance of commitment by mentioning the expectation of a minimum of 5 to 7 years of service in our company. If meeting this expectation proves challenging, considering traveling and broadening your network could be a viable option. Exploring different approaches, like training, can also help in achieving long-term career goals.

Sam, do you determine the lifespan of your equipment by subtracting the time it operated before the first failure from the time it operated after the last failure? How do you calculate the 7 and 5-year durability of your machinery?

Quote: MTBF is commonly used to assess a cluster of identical equipment, such as all pumps within a refinery. How do we determine what qualifies as "similar" in this context? For instance, do all pumps at the facility share the same type (reciprocating, centrifugal, diaphragm), size, or other key characteristics?

While there may be varying opinions among peers regarding the definitions of MTTF and MTBF, the attached example demonstrates my long-standing approach to handling operating data effectively. This method has consistently satisfied users and prevented any confusion. From a managerial standpoint, this data can account for any type of failure. Implementation of this method in software is straightforward, and the corresponding indicators can be accessed promptly. Additionally, numerous other indicators can be created at the equipment level to track the achievement of management's goals. Thank you for your attention. See attached file: Indicators.xls (31 KB, 1 version).

I wasn't joking earlier. The wear and tear on machine parts can vary greatly depending on the environment they are in. Just like people, no two machines are exactly the same. While sitting in an office and analyzing data is important, it's equally crucial to get hands-on experience and interact with others in the field. The weakest link in machinery is often the equipment's bearings, which tend to fail first. It's essential to understand the L10 life of the bearings and work towards maximizing Mean Time Between Failure (MTBF). By focusing on proper alignment and maintenance, you can increase the lifespan of your machines and see happier faces around you. Don't just rely on compiled data for recognition - the real reward comes from improved performance and longer machine uptime. Remember, your paycheck should reflect the success of your maintenance program. Stay on top of the latest industry acronyms and advancements to ensure your equipment is running smoothly and efficiently.

The L10 rating often falls short in adequately addressing bearing fatigue, especially considering the impact of contaminants and lubrication. In a recent paper presented at the CMVA conference (the Canadian equivalent of VI), the focus was on fatigue analysis. For more details, refer to the red thumbnail in the final section of http://vibra-k.com/?cat=15. In summary, the longevity of bearing fatigue is heavily influenced by the presence of contaminants in the steel, rather than just the load and cycling. This explains why many bearings continue to perform well beyond their estimated fatigue life. Typically, machines are designed with a target lifespan of 50,000 to 100,000 hours. Electric motors, in particular, may have longer lifespans due to bearing size being proportional to shaft dimensions and torque considerations. While there are cases of bearings lasting even longer, the industry standard estimates of 50,000 hours (standard) and 100,000 hours (upon request) are generally reliable benchmarks to consider.

Clarifying RUI: Could you explain the concept of a constant time window and how it relates to the calculation 6*25*8? Why is the number of failures 5 instead of 7 as previously thought? Additionally, can you elaborate on the concept of a moving constant time window?

Understanding how to use MTBF is essential for various applications. In my training, the formula can be intricate and may vary depending on the specific use case. MTBF can be utilized for different purposes: calculating MTBF by critical component (referred to as mttf), by sub-assembly to identify the weakest link in a machine, by Machine to assess overall machine reliability, by process to pinpoint frequent failure points, and by a group of machines to determine total MTBF. The formula for MTBF is calculated by dividing operating time by Breakdown occurrence (BDO), where BDO represents the frequency of failures. Operating time is the difference between loading time and machine downtime. Machine downtime can be due to various reasons, not just failures or breakdowns. For instance, downtime can occur when equipment is being converted to a new product. To further clarify the formula, it can be expressed as MTBF = (Loading Time - Machine DT attributed to failures) / Frequency of Breakdown. Warm Regards, Rolly Angeles Educator

When calculating the Mean Time Between Failures (MTBF) for a machine and a group of similar machines, it is important to begin tracking loading time from the initial production date. This should continue until the present day if the machine is still operational and has not been decommissioned.

MTBF serves as a key metric for assessing the reliability of a machine or group of machines. The timeframe for data collection is flexible, but longer periods yield more accurate results. It is crucial to start from the beginning of reliable breakdown data to analyze MTBF effectively. This metric not only reflects the efficiency of maintenance practices but also highlights areas for potential improvements in reliability. For instance, in my past role as a Machinery Engineer at an older refinery dating back to 1936, we faced high failure rates with an MTBF of approximately 6 months for our 1200 pumps. Through a thorough analysis of recurring failures, we identified common issues such as grease-lubricated gear couplings, outdated packing leading to costly repairs, and poor alignment causing premature bearing failures. Over time, strategic upgrades including replacing gear couplings with membranes, transitioning to mechanical seals, and improving maintenance practices significantly enhanced our MTBF to a robust 37 months. Implementing vibration monitoring, lube oil analysis, and thermography further optimized maintenance scheduling for seamless operations. This comprehensive approach fostered collaboration between Operations and Maintenance, resulting in efficient planning and reduced downtime (Rolly!).

quote: MTBF is commonly used to assess the reliability of a group of similar equipment, such as multiple pumps within a refinery. The calculation for MTBF is (NUMBER OF EQUIPMENT X TIME INTERVAL) / NUMBER OF FAILURES DURING THAT INTERVAL. For instance, if there are 1200 pumps in a refinery over one year with a total of 387 failures, the MTBF would be calculated as (1200 X 12 months) / 387 = 37 months MTBF. When calculating for a single item, the formula is simply the time interval divided by the number of failures. For example, if a pump failed twice in one year, the MTBF would be 12 months / 2 = 6 months MTBF. I am wondering if the time period should only include the running pump (duty) or if standby pumps should also be considered in the calculation of the number of equipment.

Hello Aromatics Thailand, it is important to consider the "total population" of your pumps to ensure they have optimal reliability. The standby units, which are steam-turbine driven and equipped with auto cut-in units, are crucial for maintaining operations in the event of a power failure. In an ideal scenario where all equipment is constantly on stand-by, the mean time between failures (MTBF) would be "infinity" as they would never fail. Goal is to minimize the frequency of pump failures to ensure smooth operations consistently.

In management performance control, setting a moving time window is a common practice to calculate performance indicators (PI) within a specific time frame. The time window is arbitrarily chosen but needs to be long enough to include multiple occurrences, increasing accuracy with more episodes. For example, in Excel, forgetting to update a cell with the product "6 months, 25 days per month, and 8 hours per day" should have simply been entered as 1,200 hours. Only the latest 5 failures matter in the calculation as older data outside the time window are excluded. Using a time interval of 6 weeks as your time window means that the window moves one week at a time with each new calculation. Weighted averages are often applied to data, giving less weight to older data and more weight to recent events, providing insight into potential changes. Graphing the collected PI's over time can reveal trends in performance. Another method called "exponential smoothing" automatically assigns less weight to older data, but is less commonly used compared to the weighted average method. By continuously evaluating performance indicators, you can track progress and make informed decisions.

Why is it necessary to arbitrarily set and adjust the time span over time? Is this concept of a constant time window equivalent to a constant moving average? Instead of this approach, why not calculate the MTBF from the first failure to the present day, especially since more data leads to increased accuracy? It is crucial to compare our MTBF values with industry benchmarks and trends, requiring standardized methods for MTBF calculations. Why is it important to apply weightage to data for equipment undergoing changes? What types of changes are being referred to here - modifications, operational mode changes, operating parameter adjustments, etc.?

Great job on improving the mean time between failures (MTBF) for your refinery pumps, Cheddar! It seems like you took a straightforward approach by calculating the total operating time for all pumps and dividing it by the number of failures, regardless of pump types or failure modes. This overall MTBF calculation gives a clear picture of the improvement trend. To simplify further, did you consider the operating time period starting from the refinery's construction year in 1936, regardless of pump replacements over the years? It also seems like you didn't mention whether any downtime was subtracted from the operating time. I prefer to follow a standard method for MTBF calculations to compare results with published data, like those found in HP Bloch's book. Did you also track the MTBF of individual pump components, such as bearings, seals, and impellers? It would be interesting to see how each component contributes to the overall MTBF improvement.

Upon my arrival at the refinery, it became apparent that there was a significant reliability issue, especially with the pumps. After conducting a thorough analysis of pump failures over the past five years, I identified a pattern within a 6-month timeframe. I prioritized addressing the main culprit of failures, starting with couplings, then moving on to sealing issues and others. To accurately assess the effectiveness of maintenance practices using Mean Time Between Failures (MTBF), it is crucial to have sufficient data to ensure the reliability of readings. The more data available, particularly with good quality data, the more dependable the initial MTBF calculation will be. Reviewing records to determine how far back you can go with accuracy is essential, even if it's just a couple of years. Identifying common failures and investigating the underlying causes, as I did with analyzing bearings, can lead to improvements in MTBF metrics that are highly valued by management.

Greetings, in my previous role at a semiconductor company, I had the opportunity to work with a wirebond machine that placed goldwire in circuits. These machines are comprised of approximately 500,000 electronic parts, with each station containing around 100 or more wirebonds. We used to track the Mean Time Between Failures (MTBF) on a monthly basis, aiming for a perfect MTBF of 168 hours per month. To illustrate, let's look at the MTBF data for 100 wirebonds: - Jan: 49 hrs/month - Feb: 63 hrs/month - Mar: 46 hrs/month - Apr: 31 hrs/month As you can see, the trend is declining, indicating a decrease in MTBF performance. We then proceed to analyze the MTBF at different levels, starting with identifying the specific wirebond machines contributing to the low MTBF. Once identified, we delve deeper into the sub-assemblies and components that are prone to failure. For new employees without prior failure records, it is recommended to begin calculating MTBF from day one and monitor until a failure occurs. In our case, where we analyze MTBF monthly, a zero failure rate results in an infinite MTBF. To address this, we have two options: assume a denominator of one for perfect MTBF or wait for a failure to occur before calculating. When calculating total MTBF for a group of machines, you have three options: 1. Summing the individual MTBF values 2. Calculating the average MTBF 3. Determining the percentage MTBF relative to the ideal 168 hours per month It is crucial to track the trend of MTBF over time, whether on a monthly, quarterly, semi-annual, or annual basis, with the goal of seeing improvement. Warm Regards, Rolly Angeles, Educator

Thank you for the insightful tips and advice. Can you provide a calculated mean time between failures (MTBF) for the scenario involving Rui that was mentioned earlier?

When analyzing historical data, the more data points you include in your calculations to determine an average, the less responsive the result will be to recent changes. However, this approach leads to a more stable indicator over time. To balance these factors, it is necessary to make a trade-off. You can find an example of this concept in the attached Excel file. Despite fluctuations in the data from period to period, a consistent trend may emerge due to ongoing improvements, such as those expected from a Total Productive Maintenance (TPM) program. A shorter time period (defined by a fixed number of events, not a constant timeframe) provides a more responsive result, giving a clearer picture of the actual levels of Mean Time To Failure (MTTF). On the other hand, if there is a significant change in a piece of equipment's reliability, historical data may no longer be relevant, and new data must be gathered to reflect the new reality. Regards, Attachment: MTTF_control.xls (19 KB, 1 version)

Josh, please review the attached file for an updated version of the Excel spreadsheet referenced in my previous post. In this new version, I have included an example demonstrating the use of weighted values. It is worth noting that the indicator displays a higher value compared to simple averages (492 versus 479), indicating a more favorable response. Regards, MTTF_control_1.xls (27 KB) - Version 1.

Please find the updated version of your example attached, Rui. I have a few queries regarding the Mean Time To Failure (MTTF) analysis. Is the MTTF always represented by a linear equation (Y=mX + C)? Is this the most accurate way to depict MTTF? Instead of using a linear equation, can we estimate MTTF by averaging Time To Failure (TTF) values at each failure event, as shown in the third chart on the right? My goal is to monitor the monthly MTTF or Mean Time Between Failures (MTBF) value, regardless of failure occurrences. What is the most effective method for calculating the MTTF or MTBF value consistently over time? Find the attachment for reference: 6611007803_MTTF_control_1(1).xls (55 KB, 1 version).

Upon reviewing the attached document, I have recalculated the Mean Time Between Failures (MTBF), Mean Time To Failure (MTTF), and Mean Time To Repair (MTTR) by considering the total operating time from the beginning up to the present day, without utilizing a fixed time window. I am seeking clarification on whether this approach is accurate. Based on the second example provided, it appears that using a constant time window to calculate MTBF may result in higher values when there are improvements made within that timeframe. However, existing MTBF data sources such as HP Bloch books do not mention the use of a constant time window. My concern also lies in determining the most suitable constant time window for comparing MTBF data with others. It seems that calculating MTBF on a monthly basis is appropriate for trend analysis and benchmarking against industry-standard data.

An indicator is crucial for predicting the future behavior of a system based on recent data trends. It's important to find a balance between stability and responsiveness by adjusting the time window periodically. Historical data is only useful for reference purposes, with the focus being on current trends. Management should prioritize tracking trends rather than specific values to make informed decisions. Using weighted data methods can enhance trend awareness. It's essential to choose a suitable time frame for indicator calculation to capture significant events accurately. It's important to consider what is best for each specific case when implementing management performance control systems, rather than blindly following norms that may not align with logic or justification. Ultimately, the decision lies with the user to adopt or reject any suggested norms based on their expertise and understanding of the situation.

When evaluating equipment reliability, the Mean Time Between Failures (MTBF) is a common metric used. However, it is possible to calculate MTBF for individual failure modes as well. For instance, one can calculate the MTBF for specific components such as bearings, pumps, fan belts, and more. This allows for a more detailed analysis of reliability and maintenance needs for each component.

While it is possible to address failure modes at the equipment level, this task is typically left to engineering teams focused on measuring and enhancing the reliability of specific components. Management tends to focus on broader objectives and may not delve into such intricate details. Thank you.

By implementing codes for all potential failure modes at the component level, you can efficiently assess equipment performance at a higher level by analyzing data collected at the lower level. This approach provides valuable insights for enhancing reliability and monitoring management performance. Additionally, translating specific failure modes into computer-readable codes can be challenging. Can anyone share their expertise in failure mode coding? Examples would be greatly valued. Thank you.

Rui, your explanation above is much clearer this time. It seems that calculating MTBF based on the longest time window provides stability but lacks responsiveness. So, how can we strike a balance? It's important to choose a time window length that balances stability (consistency) and responsiveness (adapting to the latest trends). Do we mean to say "..in order NOT to compromise BOTH stability and responsiveness" in the previous sentence? To achieve the optimal balance of stability and responsiveness, how should we select the constant time window for MTBF calculation? While KPIs are typically reported on a monthly basis, a constant 3-month time window, as shown in your example, may lead to improved MTTF. Additionally, how do we determine the appropriate weight for recent data? Are there any English resources that extensively cover this topic?

In SAP Plant Maintenance, each item (failure) record on the Notification screen requires three fields to be filled - Object part, Damage code, and Cause code. For guidance on how equipment is categorized into parts, you can consult ISO14224. Streamline your maintenance process by utilizing these essential fields for detailed breakdown of equipment issues.

After calculating the initial Mean Time Between Failures (MTBF) for the first half-year, how frequently should you update it for Key Performance Indicator (KPI) reporting?

Can you explain the concept of a "moving constant time window"? Is it referring to a specific sequence of months like a) (Jan, Feb & Mar), (Apr, May & Jun), (July, Aug & Sep), (Oct, Nov & Dec) or b) (Jan, Feb & Mar), (Feb, Mar & Apr), (Mar, Apr & May), (Apr, May, Jun), (May, Jun & Jul), (Jun, Jul & Aug), (Jul, Aug & Sep), (Aug, Sep & Oct), (Sep, Oct & Nov), (Oct, Nov & Dec), (Nov, Dec & Jan), (Dec, Jan & Feb)? This query is often asked in data analysis and statistics discussions.

Dear Josh, I believe the example I have provided is self-explanatory. The attached document contains 26 Time to Failure (TTF) data points gathered over a period of time. One page displays simple averages while the other includes weighted averages. The 27th event is yet to occur, but the Mean Time to Failure (MTTF) can already be calculated. The values in cells D34 and E34 serve as an estimate of the MTTF at the time of the 27th event. However, if you are focused on reporting past events, then cells D33 and E33 are the main points of interest. The techniques utilized for management performance control in this scenario closely resemble those commonly used in forecasting. For a brief description of these techniques, you can refer to the e-book available at http://home.ubalt.edu/ntsbarsh/stat-data/Forecast.htm#rhowma. Best regards, Attachment(s): MTTF_trend_example.xls (38 KB) - 1 version

When making forecasts, MAD (mean absolute deviation) is a crucial metric that indicates the accuracy of your predictions. The goal is to minimize MAD as it signifies how closely your forecasts align with reality. It is a widely used indicator for comparing forecasting methods. Best regards,

Dear Rui, I am writing to you with great pleasure as I recently acquired a copy of your book "Decision Support in Maintenance Management." I have been reading the messages in this thread and I must admit I am feeling a bit puzzled. I manage a production line with 10 different types of equipment, and I have been recording all the downtime for each, technician wait times, and repair durations. I am eager to understand which formula to use for calculating MTBF, MMTR, Reliability, and Availability, as there are many formulas out there. I have attached an Excel file (I believe it was shared by you on this forum), but it seems to only apply to a group of identical equipment. My goal is to calculate the Reliability of each individual equipment as well as the entire system (which operates in a series-parallel configuration). I appreciate your attention and assistance. Best regards, Joaquim Silva it@gewiss.pt

In many instances, a unit or system can be promptly repaired following a breakdown. The mean time between failures (MTBF) represents the average time until the device is no longer repairable. For systems with an exponential failure rate, the MTBF is equal to 1 divided by the failure rate, signifying the average time between equipment failures. It is important to note that MTBF does not dictate how long the equipment is expected to function before failure. For example, if the equipment is expected to operate for a period equivalent to its MTBF, there is a roughly 40% chance of it lasting that long without failing. The likelihood of survival increases if the equipment is used for a shorter period. To calculate MTBF in practical terms, one can divide the total operating time of a population by the number of failures that occurred. For instance, if there are 100 identical pieces of equipment each operating for around 8000 hours, totaling 800,000 hours for the population, and 80 failures occurred during this time and were repaired after running for 8000 hours each, the MTBF would be calculated as 800,000/80 = 10,000 hours. The failure rate, which is the reciprocal of the MTBF, would be 0.0001. This emphasizes the importance of understanding the MTBF as the average time between failures for efficient equipment maintenance and performance evaluation in various systems.

Check out the attached example of a rolling Mean Time Between Failures (MTBF) calculation for a unit. This calculation is particularly beneficial when the start and end dates and times of failure are uncertain. It is important to ensure that the analysis is conducted on identical equipment under the same operating conditions. Download the file "Rolling_MTBF_calculation_example.xls" to see the example in action.

Dear [Recipient], I am in possession of the system as shown in the attached file and am interested in calculating the following metrics for both the equipment and the system: - Mean Time Between Failures (MTBF) - Mean Time To Repair (MTTR) - Mean Wait Time (MWT) - Mean Time To Failure (MTTF) - Availability - Reliability Is it feasible to calculate these metrics for both the equipment and the system as specified? Best regards, Silva Attachment: production_line.xls (23 KB) - Version 1

Dear partners, I am curious to know if it is possible to perform these calculations. Thank you, Silva

What is MWT and how does it relate to calculating Availability and Reliability? Can you provide the formula used for these calculations?

Hello, Mean Wait Time (MWT) refers to the amount of time that elapses between a machine breakdown and the initiation of intervention. Availability and Reliability calculations involve the utilization of statistical formulas. Thank you, Silva.

It appears that more data is needed to accurately analyze the statistics for certain equipment. Without any failures, it is impossible to calculate the Mean Time Between Failures (MTBF). In this case, an estimation of realistic failure rates can be made based on judgment. In order to determine system statistics, more information about the system is necessary, such as the presence of redundancy. For example, does the system require both components D and E to be operational, or is one sufficient? It is important to consider if there is spared redundancy, and whether components run continuously or only when others fail. Given that equipment runs constantly based on the number of work hours, it is noted that D is equal to E, F is equal to G, and H is equal to I. However, there have been more failures of I than H, and more failures of G than F, suggesting differences in reliability or preferential usage. Once enough data is collected or estimated failure rates are determined, the system can be assessed. One method is to simplify the configuration by combining parallel branches and analyzing the resulting series configuration. Various texts are available to guide this process.

Hello David, thank you for your response. Both equipment sets D&E are being used simultaneously throughout the year to meet our production quantity needs, along with equipment sets F&G and H&I. The varying number of failures is due to the difference in age of the equipment, even though they are identical. For instance, if a piece of equipment only fails once in a year, the Mean Time Between Failures (MTBF) would be the time it was operational. If there are zero failures, the MTBF would be zero. I calculate the MTBF for each piece of equipment on my production line, and the overall MTBF for the system is the average of all individual MTBF values. Is it correct to include preventive maintenance time in the MTBF calculations? Could you please review the attachment to confirm the accuracy of my calculations? Thank you, Joaquim. Attachment: 9171031443_production_line.xls (26 KB) Version 1.

Quoting the MTBF (Mean Time Between Failures) calculation can be tricky when dealing with zero fails. If the number of failures is zero, then the MTBF is technically infinity, resulting in a #Div/0! error in your worksheet. When trying to determine the MTBF of a system or production line by averaging all MTBF values, caution is needed. Averaging fails when elements equal infinity. For a system where any equipment failure is considered a system failure, the MTBF is calculated by dividing the total work hours by the total number of failures across all equipment. Assumptions made include that all failures are independent, that only one equipment failure is fixed at a time without addressing others, and that all equipment failures are counted as system failures. In this scenario, the MTBF is equal to 100 hours based on 1832 work hours and 18 total failures.

Hello David, I want to express my gratitude for your assistance with understanding the "philosophy" behind the system calculations. Are the calculations for the individual equipment properly executed? Thank you, Silva.

To accurately calculate MTBF, utilizing the Weibull distribution is recommended. It is crucial to gather historical data on equipment failures, up times, and down times for analysis. This method yields both the BETA factor and MTBF, which are essential for determining the necessary maintenance for the equipment. For assistance with MTBF calculations using various distributions, please refer to the attached file VALRAMOR4.xls. This document is 544 KB in size and is the first version available for download.

Hello, thank you for assisting. However, the file is displaying an error when attempting to perform calculations. Thank you, Silva.

Hello there, do you include machine downtime from process upsets when calculating MTBF? Thanks, Karthik.

Hello, I am Silva.

Hello everyone, I'm in need of assistance in determining the equation for calculating Mean Time Between Failures (MTBF). Can someone provide guidance on how to calculate MTBF?

Zaidi, by reading approximately 20% of this discussion, you will discover the solution to your query. Best regards,

Can anyone provide insights on the standard practices for calculating MTBF and Availability in the Oil and Gas Industry, specifically for Rotating Equipment? I'm curious about how major Oil Companies calculate and report these key performance indicators.

In my experience with MTBF, the formula I have been taught is MTBF = OT/F, where MTBF stands for Mean Time Between Failure, OT represents Operating Time, and F denotes the number of failures within a specified time period (such as per day, week, or month). If this formula is inaccurate, please advise on how to calculate it on a monthly basis.

Does anyone have a reliable source for the formula used to calculate Mean Time Between Failures (MTBF), which is (date of last failure - date of first failure) divided by (number of failures - 1)? This formula is commonly used in the calculation of equipment reliability and downtime.

**Answer:** - Answer: When choosing a formula for calculating MTBF, factors to consider include the availability of operating time or running hour data, the number of failures, and the specific context of the equipment or system being analyzed.

**Answer:** - Answer: Operating time is calculated based on the difference between the current date and the date of first production, while running hour data provides more precise information on the actual time the system or equipment has been in operation.

**Answer:** - Answer: Formula a) is preferable when operating time data is readily available and provides a comprehensive view of the equipment's performance over time. Formula b), on the other hand, excludes certain time intervals and may be more suitable for specific scenarios where such exclusions are deemed necessary for accurate MTBF calculations.

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