VF Inc. produces a small coil compression spring used in toys. The process characteristic of interest in testing this spring is the compression distance when a 5-lb. load compresses the spring. The average compression distance of all the springs produced has been specified at 6 cm. The output is normally distributed and the population standard deviation is 0.16 cm. For process control purposes, samples of 16 packs are taken and the sample's average compression distance is checked against a control chart.
(a) What are the three-sigma upper and lower control limits one should use for the control chart?
(b) Jasper Yang, production manager, reviewed the monthly production report for December 2002 and was concerned because the average compression distance was actually 6.1 cm, even though the overall standard deviation was still 0.16 cm. What percent of the sampled springs would fall outside the 3-sigma control limits determined in part (a)?
(c) Jasper Yang set up a taskforce and mandated that within one month, 95% of all the springs produced should be within 6 ± 0.2 cm so as to achieve the desirable design specifications. The taskforce acted immediately and managed to get the process to produce springs with an average compression distance of 6 cm. What else will they have to do to the process to achieve Mr. Yang's specifications?