Question

Ten items are put on the test, until all have failed. The first faliure occures at 35 000 operating cycles. Regression analysis of the times to faliure shows a good fit to a two-parameter Weibull distribution, and the distribution parameters are derived. The specification states that the item should have a B₁₀ life of 30 000 cycles. Discuss the practical implications assuming that the test shows complience with the specification.

In a previous problem, how might your judgment be influenced if the items is;

a) a seek bolt subject to fatigue loading

b) a plastic component in a child s toy

c) a lighting unit

d) a bearing in a gerbox

e) a light-emitting diode

Answer 1

in the above example =

mean=30,000

x=35000

standard error for this example=5000

let take we have to be 99% confitent in manufactured items

t value at 99% at 9 degrees of freedom = 3.250

3.250= 35000-30000/se/√n    ;where se is standard erroror standard deviation of sample

3.250= 35000-30000/se/√10

3.250*se/√10 =5000

5000/3.250*√10=se

se=4865.043

as standard error calculated at 99% confidence interval is less than in the given example we can say that completing 35000 cycles is a good for an item.

a) the bolt should be able to load 35000 units of load to give it a yes to sell

b) the child's toy should work 35000 that will use plastic component to give it a yes to sell

c) it should light for 35000 units of time to give it a yes to sell

d) the bearing should revolve 35000 times to give it a yes to sell

e) it should light for 35000 units of time to give it a yes to sell