This problem uses the data on time to wear out of shave dies in Problem 4.1 of Chapter 4.

(a)  Plot the product-limit estimate of the cumulative distribution function on Weibull paper and assess the validity of the data and the fit of the Weibull distribution. Use the following STATPAC output. CENTER denotes the Weibull (Y and SPREAD denotes ß

.

(b) Does the ML estimate of the shape parametel 3uggest that the failure rate of the dies increases or decreases with die age?

(c) Do the confidence limits for the shape parameter provide convincing evidence that the failure rate increases or decreases with die age?

 (d) On the Weibull plot from (a), plot the fitted distribution and confidence limits for the percentiles

Problem 4.1

Shave die. The following are life data (in hours) on a shave die used in a manufacturing process. Operating hours for shave dies that wore out: 13.2 67.8  76  59  30 26.7 26 68 30.1 76.3 43.5. Operating hours on shave dies that were replaced when the production process was stopped for other reasons: 45.1  27  49.5  62.8  75.3  13  58 34 48  49  31.5  18.1  34  41.5  62  66.5  52  60.1  31.3 39 28.6 7.3 40.3 22.1 66.3  55.1

(a)  Calculate hazard (or probability) plotting positions for dies that wore out.

(b)  Plot the data on Weibull hazard (or probability) paper.

(c)   Assess the validity of the data and the fit of the Weibull distribution.

(d)  Graphically estimate the Weibull shape parameter. Does it suggest that the instantaneous failure rate increases or decreases with die life? An increasing one indicates that dies over a certain age should be replaced when the production process is stopped for other reasons, as die wear out stops production and is therefore costly.