Curved Data on Weibull Probability Plots
When the points graphed on a Weibull probability plot appear to curve, the selected distribution is considered a poor fit. The causes for this poor fit can be due to poor quality data or to the origin of the age scale not being appropriately located, as explained below:
• Concave downward plots–May reflect the manufacturer’s failure to include the early failures that occurred during burn-in, stress screening or production acceptance. May also suggest the existence of a guaranteed failure-free period, where it is physically impossible for the failure mode to produce failures instantaneously or early in life. For example, a bearing cannot fail due to spalling or imbalance until bearing rotation has caused sufficient damage.
• Concave upward plots–Much more unusual and difficult to explain, may reflect either shelf life or shipping deterioration of spare parts or the mixture of failure modes.
When curved data appears on a Weibull probability plot and the cause is that the origin of the age scale is inappropriately located, a three-parameter Weibull distribution can be used to shift the scale by the value entered for the location parameter, t-zero (t0). To estimate the t0 value that is needed to straighten the Weibull probability plot, you can “eyeball” a curve through the two-parameter Weibull probability plot and use the point where it intersects the horizontal time scale.
Computerised three-parameter Weibull analysis iterates on the t0 value until the correlation coefficient is maximised. The t0 value will always be less than the first failure time and either be added to or subtracted from the failure values. Providing that the t0 value is correct, the plot resulting from the three-Weibull distribution should follow a straight line. If shifting the origin does not correct the curved data on the Weibull probability plot, the lognormal distribution, which is not a member of the Weibull family, may be better suited for analysing this particular set of life data.