WEIBULL in WPS Spreadsheet: Shape, Scale and Distribution Modes
Calculate Weibull cumulative probability or density with explicit shape and scale, and derive survival and interval probabilities without confusing them with a mean.
Verification status: See the evidence and test scope described in this guide. How formula examples are checked
WEIBULL evaluates a Weibull distribution using a shape parameter alpha and a scale parameter beta. The final Boolean selects a cumulative probability or a density. Although WPS introduces reliability applications, one CDF or density evaluation does not itself calculate a mean failure time or validate an equipment model.
Syntax and formulas
=WEIBULL(x, alpha, beta, cumulative)
Original examples use positive x, alpha and beta. TRUE returns 1−exp(−(x/beta)^alpha). FALSE returns the density alpha/beta*(x/beta)^(alpha−1)*exp(−(x/beta)^alpha). All four arguments are supplied explicitly.
Beta is a scale in the same units as x, not an event rate. Alpha is dimensionless. Density has inverse-x units, while the cumulative result is dimensionless probability.
Original example at the scale value
Enter x=3, alpha=2 and beta=3 in A2:C2.
- Use
=WEIBULL(A2,B2,C2,TRUE)in D2. - Since x/beta=1, the independent CDF is 1−exp(−1), approximately 0.632120558828558.
- Use
=WEIBULL(A2,B2,C2,FALSE)in E2 for density, approximately 0.245252960780962.
The density is (2/3)*exp(−1). It is not the probability of exactly x=3, which is zero in the continuous model. The scale value corresponds to about 63.2% cumulative probability for any positive shape; it is not generally the mean or median.
Independent controls
| Formula | Expected result, approximately |
|---|---|
=WEIBULL(3,2,3,TRUE) |
0.632120558828558 |
=WEIBULL(3,2,3,FALSE) |
0.245252960780962 |
=WEIBULL(6,2,3,TRUE) |
0.981684361111266 |
=WEIBULL(1.5,2,3,TRUE) |
0.221199216928595 |
=WEIBULL(3,1,3,TRUE) |
0.632120558828558 |
=WEIBULL(6,2,6,FALSE) |
0.122626480390481 |
Doubling both x and beta keeps the standardized position unchanged. At a corresponding point the density halves because its units change; cumulative probability stays unchanged. Shape 1 gives the exponential form identified in the vendor formula image, with rate 1/beta.
Derive survival and an interval
For shape 2 and scale 3, survival beyond x=3 is exp(−1), approximately 0.367879441171442. The probability between 1.5 and 3 is the difference of CDFs, approximately 0.410921341899963.
The model median solves the CDF equal to one half: beta*(ln(2))^(1/alpha). For these parameters it is about 2.49766383347, below the scale value 3. This independent derivation illustrates why a CDF output should not be labeled “average lifetime.” It does not establish a maintenance or safety decision for real equipment.
Official example and limitations
The actual vendor formula WEIBULL(198,40,200,FALSE) displays 0.069226415, agreeing with the printed density equation. The source’s general reliability discussion does not change the function’s returned quantity.
WPS documents #NUM! for nonpositive alpha or beta and negative x, and #VALUE! for nonnumeric numeric arguments. Original examples avoid zero, malformed inputs and extreme shapes. No claim is made about behavior at x=0 when shape is below one, numerical tails, or a dotted modern alias. See EXP for the exponential component and NORMDIST for another function whose Boolean modes distinguish area from density.
Availability and evidence scope
The official WPS lesson is dated 2019-06-21 and explicitly labels WPS Office for Windows Personal. Its numeric build is unspecified. This documents the function by that date; it does not establish first introduction, the last functioning build, other-platform parity or a retirement/deprecation history.
The official lesson was rechecked on October 19, 2026. Original examples are documentation-derived independent calculations, not WPS or other spreadsheet-engine executions. Numeric reference values do not certify application precision or statistical model suitability.