Toledo Custom Manufacturing (TCM), located in Toledo, Ohio,makes metal parts to customer specifications. They have a varietyof machines including lathes, numerically controlled (NC) machines,grinders and drill- ing machines. They can make any metal partsthat require use of these machines. TCM employs 65 work- ers,supervisors, and managers in its facility.

TCM is very customer-oriented and prides itself on qualitycontrol. They take a Total Quality Management systems approachincluding use of control charts, ISO 9000 certification, employeetraining, and teams for continuous improvement of quality. TCM alsoselects its suppliers based on their ability to provide qualitymetal blanks and parts that are purchased.

THE PRECISE STEEL ROD ORDER

TCM recently received an order to machine 5000 push rods to beused in the production of hydraulic cylinders. The push rod is aprecise steel rod that runs inside of a hydraulic cylinder to buildpressure when activated. The push rod has very tight specificationsto insure that hydrau- lic leaks do not occur. The particular rodordered is 6” long and must be .500 inches in diameter (see Exhibit1 for an illustration). The specifications call for ±.005” (5 one-thousands of an inch) tolerance. Therefore all rods must bemachined to a diameter between .495” and .505” to meet thespecification and to be acceptable to the customer.

In order to meet the customer’s delivery schedule, TCM willutilize two machines, each with its own opera- tor. The machinesare similar, but operator 1 has more experience than operator 2.TCM must also insure that the supplier of blank steel rods willprovide consistently good material for machining.

QUALITY CONTROL CHARTS

In order to prepare for the order, TCM has decided to make 30parts on each operator-machine combination. Each operator-machinewill run samples of 5 parts and make a total of six samples for 30parts. Separate control charts will then be constructed using thesamples to calcu- late the grand average and average range for eachoperator. These averages will be used to construct an upper controllimit, center line and lower control limit for each of theoperators. Then the six samples will be compared to these limits tosee if the process is in-control or if there are out- of-controlpoints. If the process is in-control, the operator and machine canproceed to make good parts. Every hour a sample of 5 will then betaken and plotted on the chart of insure that the process is stillin-control. If either machine-operator combination is out-of-control based on the first six samples of 5 parts each, the

process will need to be fixed before proceeding. After fixingthe process another six samples of 5 parts each will be taken tosee if the process is now in control and this is continued until asatisfactory test is completed.

The customer has asked that the final control charts used toverify the operator-machine combinations be forwarded to them alongwith the 60 parts produced by the two machines. They alsorequested, that control charts be maintained by taking hourlysamples and sub- mitted along with future batches of the parts. Inaddition to statistical process control charts, the customer wouldlike to receive a calculation of the process capability index (Cpand Cpk) to insure that the process is capable of meeting thespecification.

The data collected from the first six samples of 5 each areshown in Exhibit 2 for operator 1–machine 1 and operator 2–machine2. These are the samples of 30 each required to insure that bothoperator-machine

440 Part Seven Case Studies
EXHIBIT 2 Toledo custom manufacturing samplesproduced.

	Operator 1–machine 1
Sample 1	0.500	0.498	0.502	0.499	0.503
Sample 2	0.496	0.497	0.500	0.502	0.499
Sample 3	0.504	0.503	0.503	0.496	0.495
Sample 4	0.503	0.501	0.498	0.497	0.500
Sample 5	0.500	0.502	0.503	0.498	0.495
Sample 6	0.505	0.496	0.504	0.503	0.502
	Operator 2–machine 2
Sample 1	0.495	0.497	0.495	0.502	0.500
Sample 2	0.505	0.510	0.503	0.511	0.504
Sample 3	0.504	0.503	0.502	0.502	0.501
Sample 4	0.500	0.501	0.497	0.496	0.504
Sample 5	0.501	0.512	0.510	0.508	0.504
Sample 6	0.503	0.500	0.497	0.496	0.504

processes are in control before proceeding with full pro-duction of the 5000 unit order.

Discussion Questions

1. Calculate the control charts (UCL, CL, and LCL) for eachoperator-machine combination separately. Do this for both x-bar(average) and range charts. Draw

conclusions from the charts about each operator-machinecombination.

2. What should be done based on the calculations from question1?

3. What is the process capability for each operator-machinecombination?

4. Can you be sure that all the parts produced by in-controlprocesses will meet the speci cation?