A batch of fifteen components is tested for continual use under normal operating conditions until all have failed (by a

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A Batch Of Fifteen Components Is Tested For Continual Use Under Normal Operating Conditions Until All Have Failed By A 1 (63.88 KiB) Viewed 66 times

A batch of fifteen components is tested for continual use under normal operating conditions until all have failed (by a particular mode of failure). The components failed after operating for the following time periods (in hours): 1875, 3375, 1725, 2700, 1050, 3125, 2175, 1550, 3675, 3950, 2450, 2925, 2125, 2625 and 3225 A Weibull model is proposed to describe the distributions of this mode of failure. (a) (b) Determine the median rank (using Benard's approximation) and plot the data on a Weibull plot. From this plot, estimate the two Weibull parameters (n and B) to describe this data. Whilst unsubstantiated, your colleagues think that there is a possibility that the failure mechanism does not start until the components have been in service for some time. They are basing this opinion on a testing process that was conducted some years ago on an earlier design of component. Comment on this assertion with reference to your Weibull plot. Determine an appropriate time location parameter for this model (if it exists). (c) (d) Replot the data and determine the three Weibull parameters (ŋ and B and to). Estimate the reliability R(t) at 3000 hours. (e) (f) Discuss the nature of this distribution of failures in relation with the often discussed "bathtub curve". Do you believe this mode of failure is in the "wear- in", "wear-out" or "constant hazard rate" stage of the components life.