Toledo Custom Manufacturing (TCM) makes machined steel parts to customer specification. They have a variety of machines that can hold tight tolerances. In this case they have just received an order for 5000 steel pusher rods that are used by the customer to make hydraulic cylinders. Each rod must be machined to .500 ± .005 (five thousands tolerance). The parts must therefore be between .495 and .505 to meet the specification.
Data is provided in the case and shown below for samples made on two different machines with two different operators. Each machine makes a sample of 5 parts for 6 runs or a total of 30 parts. These parts are measured and the resulting measurements are used to make variables control charts, one for operator 1-machine1 and the other for operator2-machine 2. The 30 sample parts for each operator-machine combination are used to establish the grand average mean and the average range, along with UCL, CL and LCL to demonstrate to TCM and the customer that the process is in control for making the parts. If the process is in control, the operator-machine combination can continue to make parts to be shipped to the customer along with the control chart itself to prove statistical control of the process. TCM is asked to continue to take samples every hour and to send the control chart along with the parts that are shipped.
If the process is not in control on a specific machine or both machines, the process must be corrected and another sample of 30 parts taken until process control is achieved. Students are also asked to calculate process capability indices Cp and Cpk and to interpret the results of these calculations.
The purpose of this case is to provide a problem in statistical quality control. Students must apply control chart principles to find the cause of the problem and they are asked to recommend corrective action. They are also asked to calculate process capability measures and to understand the difference between a process being in control and one capable of meeting specifications.
1. Calculate the control charts (UCL, CL and LCL) for each operator-machine combination separately. Do this for both x-bar (average) and range charts. Draw conclusions from the charts about each operator-machine combination.
2. What should be done based on the calculations from question 1?
3. What is the process capability for each operator-machine combination?
4. Can you be sure that all the parts produced by in-control processes will meet the specification?