Over the last year, a company that manufactures golf clubs has received numerous complaints about the performance

Question:

Over the last year, a company that manufactures golf clubs has received numerous complaints about the performance of its graphite shafts and has lost several market share percentage points. In response, the company decided to monitor its shaft production process to identify new opportunities to improve its product. The process involves pultrusion. A fabric is pulled through a thermosetting polymer bath and then through a long heated steel die. As it moves through the die, the shaft is cured. Finally, it is cut to the desired length. Defects that can occur during the process are internal voids, broken strands, gaps between successive layers, and microcracks caused by improper curing. The company's newly formed quality department sampled 10 consecutive shafts every 30 minutes, and nondestructive testing was used to seek out flaws in the shafts. The data from each 8-hour work shift were combined to form a shift sample of 160 shafts.

Number of Defective Shafts Proportion of Defective Shafts Shift Number .05625 6. .03750 3 .05000 .08750 .04375 .03125 4

Data on the proportion of defective shafts for 36 shift samples are presented in the table shown at the bottom of the previous column.
a. Use the appropriate control chart to determine whether the process proportion remains stable over time.
b. Does your control chart indicate that both common and special causes of variation are present? Explain.
c. Data on the types of flaws identified are given in the table below. To help diagnose the causes of variation in process output, construct a Pareto diagram for the types of shaft defects observed. Which are the "vital few"? The "trivial many"?
Type of Defect ____________________Number of Defects
Internal voids ........................................ 11
Broken strands ....................................... 96
Gaps between layer ................................. 72
Microcracks .........................................150