Weibull analysis
with suspensions
Fit a two-parameter Weibull distribution to life data. Beta (β) is the shape parameter; eta (η) is the characteristic life, by which 63.2 percent of units have failed.
A suspension records a unit that survived at least as long as its recorded time, whether removed or still running unfailed. Dropping suspensions or counting them as failures makes life look shorter. Maximum likelihood uses every unit, including these right-censored observations.
Life data
Failures and right-censored observations
Use the same unit for every observation. Changing this label does not convert times.
One group per line: time, F or S, count. Count is optional and defaults to 1. Use commas, semicolons, tabs, or spaces; letter case does not matter. Blank lines are ignored.
Percent of units failed at Bp.
Optional. Probability of surviving beyond t.
Fitted results
All units contribute to the likelihood
Enter life data to calculate the fit.
Beta describes whether the failure rate decreases, stays near constant, or increases.
- Log likelihood · logL
- —
- Mean life
- —hours
- Standard deviation
- —hours
- B10 life
- —hours
- Median · B50
- —hours
- Reliability · R(500 hours)
- —
Calculated values use 5 significant figures. Unit counts are shown as exact integers. Reliability is a probability, not a percentage.
How to use the calculator
- Set your time unit.Enter a unit label, such as hours. All times must already use that same unit.
- Enter failures and suspensions.Mark failures F and units removed or still running unfailed S. Add a count for grouped observations. Suspensions can come before, between, or after failures.
- Choose your life question.Set p for Bp life and optionally enter a time t for reliability R(t).
- Read the fitted results.Results update as you type. Resolve inline errors and review any warning, especially when the fit rests on only one failure.
Method & formulas
Let cᵢ be each group’s count, tᵢ its time, n the total unit count, and r the failure count. Sums marked F include failures only; other sums include both failures and suspensions.
η = tmax (Σ cᵢ xᵢβ / r)1/β
Standard deviation = η √[Γ(1 + 2/β) − Γ(1 + 1/β)²]
B50 = η (ln 2)1/β
R(t) = exp[−(t/η)β]
A fit needs at least one failure. If every failure occurs at the largest observed time, no finite estimate exists. A root outside the stated search interval is not reported as a fit.
Gamma calculation used for the moments
Start with s = 0. While z < 7, set s = s + ln z and then z = z + 1.
ln Γ = (z − 0.5) ln z − z + 0.5 ln(2π) + 1/(12z) − 1/(360z³) + 1/(1260z⁵) − 1/(1680z⁷) − s.
Γ = exp(ln Γ). Log-space evaluation of the equivalent moment formulas helps avoid numerical overflow and loss of precision.
Frequently asked questions
What does a suspension mean?
A suspension means a unit survived at least as long as its recorded time. It may have been removed or may still be running unfailed. It is a right-censored observation, not a failure.
Why include suspensions in the fit?
Maximum likelihood uses every unit, including suspensions. Dropping suspensions or counting them as failures makes life look shorter.
What do beta and eta describe?
Beta is the shape parameter: below 1 indicates a decreasing failure rate, near 1 a constant failure rate, and above 1 an increasing failure rate. Eta is the characteristic life, by which 63.2 percent of units have failed.
When can the calculator not produce a finite estimate?
At least one failure is needed. If every failure is at the largest time in the data, no finite estimate exists. The calculator also reports an error if the root is outside its search interval of 0.01 to 1000. With one failure, it computes the fit and warns that the estimate rests on that failure.