I recently came across a documented case on a reliability software company's website about forecasting the replacement of components. However, I have reservations about their solution and would like to gather insights from other professionals in this community. Imagine you need to predict the number of new wheels required to replace worn ones on a cargo-wagon over the next year, on a quarterly basis. The wagon has 24 wheels that have each been in use on rails for 250 days without mileage records. There is extensive failure data available for similar wheels affected by erosion, which, when analyzed statistically, follows a Weibull distribution with a shape parameter of 1.56 and a scale parameter of 1,520 days. How would you forecast the replacement needs for the 1st, 2nd, and 3rd quarters of this 24-wheeled cargo-wagon? Your insights are much appreciated. Thank you, Rui.
What is the purpose of conducting forecasting analysis in maintenance operations? Is it to effectively manage spare parts and resources? In this context, the scale factor provides an average value that can be useful for making predictions, especially when dealing with a large number of assets that have different operational starting times. However, a low shape factor may not accurately define time-to-failure. Additionally, utilizing days instead of miles as a measurement unit can potentially introduce errors in the analysis. Is there any value in conducting this exercise if the underlying data quality is prone to significant inaccuracies?
Hello Vee, the main objective of this forecast is to allocate the necessary funds for purchasing wheels when they are required. It is important to note that the Weibull distribution does not have a closed-form solution, so a numerical method or Monte Carlo simulation must be utilized. In this case, I opted for the Monte Carlo simulation method. Regards, Rui
I scored 1 point in the first quarter, 2 points in the second quarter, and another 1 point in the third quarter. Is there anyone who has a different opinion? - Rui
Rui, if I were in your position, I would recommend conducting a historical comparison analysis. It's crucial that any forecasting method you utilize has proven success with past data. You have access to historical records, so there is no need for speculation. Remember, all statistical predictions are just that - predictions. Have you considered leveraging Edward's Maximum Likelihood Estimate or a Poisson variation in your calculations?
Thank you, Vee, for your insightful comments. It is indeed possible to use historical data as a basis for forecasting, provided that the system remains unchanged over time (e.g., consistent mileage per wagon). However, this general approach may not be specific enough to address individual situations, such as a particular wagon or automotive. In my article, I take a more specific approach, utilizing the Weibull distribution and the Median Ranking Least Square method to estimate detailed needs for specific wagons, locomotives, or bogies. I did not use the Maximum Likelihood method to determine the Weibull distribution parameters, but rather the Median Ranking Least Square method. Could you clarify what you meant by the variation of "Poissan" – did you possibly mean "Poisson"? This distribution is applicable only to random failures. My calculations, based on a Monte Carlo simulation model, indicated a need to replace 1 + 2 + 1 units over the next year. Although there are alternative numerical methods available, I prefer not to rely on empirical attempts for achieving results. The article I referenced, which focuses on 200 wheels in Brazil, provides a detailed history of wheel failures and estimates a monthly replacement of 16 units going forward. However, based on my calculations, I believe the number should be higher at 28 units, distributed differently over the next 12 months. Traditional forecasting methods like Holt or Holt & Winters would not account for the current state of the wheels, particularly if a large number of new wheels were recently introduced. I have shared my perspective with the editor and the community of systems reliability enthusiasts, as I believe this case presents an interesting challenge with the potential for informative solutions. Please refer to the attached article for more details. Best regards, Rui. Attachment(s): Case_Prevendo_Substituicoes.pdf (36 KB) - 1 version
Hey Rui, interesting dilemma you've got there. The Weibull distribution you quoted can be a quite reliable predictor of failure times, given its flexibility to model various levels of failure risks over time. In this case, you could use the survival function of the Weibull distribution to estimate the fraction of wheels that are likely to fail within a certain time range. You extrapolate this to the quarter year you're interested in, and multiply it by the number of wheels on the wagon. For instance, to estimate the number of wheels to be replaced in the 1st quarter, you can calculate the survival function at 250+90 days (90 days for a quarter of the year) and again at 250 days. The difference between these two values would give you the fraction of wheels expected to fail in the 1st quarter. Rinse and repeat for the following quarters. Hope this helps!
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Answer: - To predict the replacement needs for worn wagon wheels, you can analyze failure data and apply statistical methods like the Weibull distribution. By understanding the shape and scale parameters of the distribution, you can forecast the number of new wheels required over specific time periods.
Answer: - The failure data of worn wagon wheels affected by erosion can be modeled using a Weibull distribution. In the provided case, the Weibull distribution has a shape parameter of 1.56 and a scale parameter of 1,520 days, which can help in forecasting replacement needs.
Answer: - The shape parameter of the Weibull distribution affects the failure pattern, while the scale parameter influences the time until failure. Understanding these parameters allows for accurate forecasting of replacement needs for the worn wagon wheels over different time periods, such as quarterly predictions for a 24-wheeled cargo-wagon.
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