The third parameter, namely the threshold value in 3-p Weibull analysis can bring important information, IF the data are asking for the third parameter. When ln (x) is plotted versus ln(-ln(1-P), if there is a deviation from linear trend at low ln (x) values, then you can no longer assume that threshold is zero. If the deviation is downward, then the threshold is positive and gives a good rule of thumb design value. Moreover the shape of the distribution will change dramatically. If the deviation is upward, then the threshold is negative. This of course has no physical meaning and is an indication of the mixture of two Weibull distributions. I have uploaded two papers of mine on this topic to RG. Good luck.

First, the third parameter t0 represents a period without failures, I mean, t0 represents a period of time for which the reliability is 100%. [If you see this under the cumulative damage model point of view, the damage generated by the stress variable(s) before t0 is not significant to the strenght of the component, I mean the minimum strenght percentile of the strenght distribution of the component is far of the maximum percentile of the stress variable(s) (This is known as the stress-strenght analysis)]. Second, t0 could mean that competitive failures modes are present (in the FMEA could be almost two higher rpn). Third, t0 could mean that the Weibull distribution is not the best function to represent the data; the other possible distribution could be the lognormal distribution. In addition observe that although adding or substracting a constant to the vector time t=(t1,t2,...,tn), is invariant, I mean the variance of the vector t does not change, because the Weibull distribution is based on the ln(ti), adding or substracting a constant, increase (or decrease) the mean of the ln(ti) and its variance. In addition, the fact that the variance of the logaritms change mean that the Weibull shape parameter B change (in particular adding a constant decreses the Rsq index and the variance of the logaritms, but increses B. And substracting a constant increases the Rsq (artifitially improve the plot) index and the variance of the logarithms but decreases B). This effects mean that in order to use the three parameter Weibull distribution first we have to determine a physical explanation of why failures cannot occurs before a time t0. The mentioned relation among B, Rsq and the variance of the logaritms can be found in mi paper uploaded to RG "Weibull accelerated life testing analysis with several variables using multiple linear regression" and how to numerically determine the mentioned effect on the mean and the standard deviation of the logarithms of the life time data can be perform by the aumented matrix given in the uploaded paper to RG "A new theory in multiple linear regression". good luck.

Here probably the crucial thing is to  know / verify all physical reasons to establish

that the component can not fail on the interval [0, t_0]. I would say that establishing the true value of t_0 is not a statistical problem.  I like the advices given in  Manue's reply.

Thank you for the answers. Now I understand why gamma parameter is important.

It is possible to apparently have a negative t0 value in one's data with physical meaning - this could apply to a product that consumed life sitting on shelf before it went into service. If the age is only recorded as zero when it enters service, it will be misrepresenting the true age of a item. However, it is quite likely that in such cases (corrosion perhaps) there will be a variable number of adjustments required to different data points meaning that the concept of a single t0 is meaningless.

I would say, from experience, that  genuine cases of t0 are very rare - almost always there is a mixture issue or similar. I regard t0 as a last resort.

2 Parameter Weibull Distribution can not well define the probability of null velocity (especially in case of wind). However 3 parameter Weibull even takes into account of null velocity thus being more significant than 2 parameter where null values are of high probability.

hi

I want to calculate the components of three weibull parameter? can you help me

what are the name of softwares that i can use for this object?