VitaComp manufactures nonpharmaceutical pills and pellets from dry ingredients, using a collection of machinery it maintains in a large job shop. Machine AA-23 molds circular pellets to an average diameter of 65 mm, with normally distributed natural variation expressed by a 1 mm standard deviation when the machine is in control. Machine BX-07 molds a nearly identical style of pellet to an average diameter of 62 mm, with a standard deviation of 0.1 mm when the machine is in control. VitaComp has just agreed to mold a batch of plant food pellets of the 65 mm design, but Machine AA-23 is busy with another job, which will not finish for at least a week. The company contracting for the plant food production has set a generous specification width, indicating that pellet size may range from 61 mm to 69 mm.

Questions 

1. Calculate the process capability index value C, to assess whether Machine AA-23 can support plant food pellet production.

2. Calculate the process capability index value Cpk to assess whether Machine BX-07 can support plant food pellet production. Why must BX-07 be assessed with Cpk versus the simpler Cp?

3. Based on your earlier findings, do you recommend that VitaComp wait a week to use Machine AA-23 for plant food pellet production or start sooner using Machine BX-07 instead? Explain. 4. Regardless of your conclusions, now assume that VitaComp decides to wait for Machine AA-23 to finish its current job. To monitor the plant food job, it will sample 100 pellets randomly each hour, and chart their average diameter on a mean chart prepared for this purpose using a z-value of 1.67. What portion of the plant food pellet samples can be expected to fall outside the chart limits, given that Machine AA-23 is operating in control throughout production?