Yes, but the Excel seems to reverse the roles of alpha and beta, which is why I corrected this on the website. Glad I could help! A small value for k signifies very variable winds, while constant winds are characterised by a larger k. Finally note that MTTF = alpha*Gamma(1+1/beta), and so if you have any two of the values alpha, beta and MTTF the third is determined. Charles, I am trying to learn more about Weibull Distributions and how and where to apply them. can someone help me, Daniel, The problem is now that I need to plug franctions into the x variables. Based on my understanding of the relationship between SEV and Weibull, I took my distribution {Y} and transformed it by taking 10^{Y} . These capabilities will be added when I issue the next software release. By knowing the number of wind speed values within each bin as well as the total number of values for all wind speeds, it is possible to calculate the % frequency of the wind speeds associated with any of the wind speed bins. I’m trying to analyze data in Table 4 of this report on electronic waste (e-waste) in the U.S.: Depending on what you are trying to use the Weibull distribution for the fact that you have multiple failures in the same hour may not be important or it may be very important. The scatter plots described in item #2 should look something like that shown in Figure 1 on the following webpage Best regards, 1) Given a Weibully distributed population with a shape parameter of 3.93 and a scale parameter of 151. Regarding your questions: Not a homework assignment. I calculated the parameters for the Weibull distribution. Perform financial forecasting, reporting, and operational metrics tracking, analyze financial data, create financial models, the function is useful in reliability analysis. Do they get taken out of service or get repaired. , To generate a random data element which follows a Weibull distribution with fixed alpha and beta values you can use the Real Statistics formula, Alternatively, you can use the Excel formula. Thus, if you are given all three you need to make sure that the three values are compatible. Charles. It is equal to: By combining the Equations 2 and 4, an equation with only k unknown is obtained (Equation 5). The referenced webpage shows how to calculate the mean and variance (and therefore standard deviation) from the alpha and beta parameters. I would of expected a Beta value >1 yet, it ended up being .955. For instance, now I need to build the same distribution with an unit variation of 0,5 so that inserting 1, then 1.5, then 2, then 2.5, then 3, then 3.5…until 25,5. Is there anyway to overcome this situation? minutes instead of hours. I used the regression technique you demonstrated to determine Beta: β =SLOPE(ln(-ln(1-F(x))), ln(x)) and Alpha: α =EXP(-βln(α)/β). How to Calculate the Weibull Distribution Mean and Variance. I understand that the shape and scale parameters will change every time. Using MLE, B=2.32, Alpha=7492, MTTF=6638. It appears that WEIBULL.FIT calls beta the shape parameter, but WEIBULL.DIST considers alpha the shape parameter. Before answering your question, let me make sure that I understand your question properly. 2. Fred Albert, Hello Fred, Charles. if the input data are times to repair, how can i calculate the estimation of repair rate as well as the other maintainability’s parameters ? Thank you Charles for the clarification. Your example was very helpful! What sort of help do you need? Glad I could help. ln(1,160,000)-2*ln(1,000) should be ln(1.16), calculated as follows. Weibull Distribution in Excel (WEIBULL.DIST) Excel Weibull distribution is widely used in statistics to obtain a model for several data sets, the original formula to calculate weibull distribution is very complex but we have an inbuilt function in excel known as Weibull.Dist function which calculates Weibull distribution.. I don’t know whether in general that choosing any positive beta value will return the same values, but it wouldn’t be surprising. FYI: Excel’s definitions of alpha and beta seem to be reversed. 1. 4. ), I have mean and the variance value of Weibull distribution then how to i find the values of alpha, beta and Gamma, Sivajothi, I am trying to find the excel formula for variance of the Weibull distribution given you have the alpha, beta, and mean. Thank You. How do you get the predicted Ys so I can compare with the data (or in this case X=hours)? error – Occurs when x, alpha, or beta values provided are non-numeric. By John I. McCool Bernard’s approximation is commonly used and I will address this issue in the next release. Perhaps someone else can help. You then need to estimate the cost of one failure (in terms of repair costs, lost productivity, impact of the rest of the operation, etc.) thank you sir, Thanks for the update, Fred. 12.6% is the probability of being greater than what value? WEIBULL.DIST(x, β, α, TRUE) is only working with x=integer. I need more application by using weibull distribution on health related area. A wind speed distribution created using measured data is a good way to show the frequency of occurrence of different wind speeds for a particular location. For example, the first 3 wind speed bins in a wind distribution may be 0-1 m/s, 1-2 m/s and 2-3 m/s. I have just added Example 2 to the referenced webpage. With those values, I get cumulative discards in years 4 through 7 of: Year 4 = 20% (versus 20%) Daniel, Your help is very appreciated. Year 5 = 42% (versus 35%) Option B: for an average system add 12 Model B widgets If I want to estimate budget for next year maintenance/repair, I would estimate the hours of operations of all machines to determine which ones will reach or pass the MTTF. Charles. The result seems unattractive compared to no failures at all which is modeled as (Prob(no failure in next 3 hours and 15 minutes given survived 200 hours))^3. How to fit the parameters to the data is explained on the following webpage. The scale or characteristic life value is close to the mean value of the distribution. Using WEIBULL(12.6, 4.66, 52, TRUE) I get 0.00135, I am not sure how to get the correct amswer, Gami, You also need to decide what happens with machines that fail in the first year. Regards, Pedro, Pedro, average of [(the difference between each observed value and the average)^3 ] . Mean 27244 Option A: for an average system add 2 Model A widgets it may not be the right place but i hope you could help me. i can sample excel if this helps. On this particular webpage, we are concerned with the mean time between failures, and so there can be multiple failures in the same hour. WEIBULL.DIST function is one of Statistical functions in Microsoft Excel that returns the Weibull distribution. Definition 1: The Weibull distribution has the probability density function (pdf). Charles. , Sir Assuming I haven’t made a mistake in logic or arithmetic, this should take care of the first problem. I believe that the two failures should be calculated as the probability of two failures within 15 minutes of each other given both survived 200 hours, but do not know how to model such, or how to then incorporate the non failure. All Betas >1 Standard Deviation 21478.61039 How can I solve the following problems in Excel using the “WEIBULL.DIST” function? In other words, for the new maintenance schedule, I have to show that the average time of failure if higher than what it is for the current schedule. You don’t need to calculate a confidence interval for the slope, but you can do so. How to plot the confidence interval and prediction interval.” i do not find a clear article on this point as not the data is processed to plot the weibull. Thanks for the response. This is only working for me if I swap alpha and beta between WEIBULL.FIT (or FITM or FITR) and WEIBULL.DIST.