Defects in graphite shafts. 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 SHAFT1 SHAFT2 Shift Number Number of Defective Shafts Proportion of Defective Shafts 1 9 .05625 2 6 .03750 3 8 .05000 4 14 .08750 5 7 .04375 6 5 .03125 7 7 .04375 8 9 .05625 9 5 .03125 10 9 .05625 11 1 .00625 12 7 .04375 13 9 .05625 14 14 .08750 15 7 .04375 16 8 .05000 17 4 .02500 18 10 .06250 19 6 .03750 20 12 .07500 21 8 .05000 22 5 .03125 23 9 .05625 24 15 .09375 25 6 .03750 26 8 .05000 27 4 .02500 28 7 .04375 29 2 .01250 30 6 .03750 31 9 .05625 32 11 .06875 33 8 .05000 34 9 .05625 35 7 .04375 36 8 .05000 Source: W. Kolarik, Creating Quality: Concepts, Systems, Strategies, and Tools. Copyright © 1995 by William J. Kolarik. Used by permission of William J. Kolarik. 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. 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. [Note: Each defective shaft may have more than one flaw.] 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