Question

Toledo Custom Manufacturing (TCM), located in Toledo, Ohio, makes metal parts to customer specifications. They have a variety of machines including lathes, numerically controlled (NC) machines, grinders and drill- ing machines. They can make any metal parts that 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 quality control. They take a Total Quality Management systems approach including use of control charts, ISO 9000 certification, employee training, and teams for continuous improvement of quality. TCM also selects its suppliers based on their ability to provide quality metal blanks and parts that are purchased.

THE PRECISE STEEL ROD ORDER

TCM recently received an order to machine 5000 push rods to be used in the production of hydraulic cylinders. The push rod is a precise steel rod that runs inside of a hydraulic cylinder to build pressure when activated. The push rod has very tight specifications to insure that hydrau- lic leaks do not occur. The particular rod ordered is 6” long and must be .500 inches in diameter (see Exhibit 1 for an illustration). The specifications call for ±.005” (5 one- thousands of an inch) tolerance. Therefore all rods must be machined to a diameter between .495” and .505” to meet the specification and to be acceptable to the customer.

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

QUALITY CONTROL CHARTS

In order to prepare for the order, TCM has decided to make 30 parts on each operator-machine combination. Each operator-machine will run samples of 5 parts and make a total of six samples for 30 parts. Separate control charts will then be constructed using the samples to calcu- late the grand average and average range for each operator. These averages will be used to construct an upper control limit, center line and lower control limit for each of the operators. Then the six samples will be compared to these limits to see if the process is in-control or if there are out- of-control points. If the process is in-control, the operator and machine can proceed to make good parts. Every hour a sample of 5 will then be taken and plotted on the chart of insure that the process is still in-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 fixing the process another six samples of 5 parts each will be taken to see if the process is now in control and this is continued until a satisfactory test is completed.

The customer has asked that the final control charts used to verify the operator-machine combinations be forwarded to them along with the 60 parts produced by the two machines. They also requested, that control charts be maintained by taking hourly samples and sub- mitted along with future batches of the parts. In addition to statistical process control charts, the customer would like to receive a calculation of the process capability index (Cp and Cpk) to insure that the process is capable of meeting the specification.

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

440 Part Seven Case Studies
EXHIBIT 2 Toledo custom manufacturing samples produced.

	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 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 speci cation?

Answer 1

1) Control charts for each operator-machine combination.

Conclusions from the control charts: While Operator 1 - Machine 1 control chart shows that process is in statistical control, Process for Operator 2- Machine 2 is not in control.

2) For operator 2- machine 2, assignable causes of variation must be identified and rectified so that process variability is reduced and the output is more consistent.

3) For sample size, n=5, Control chart constant, d2 = 2.326

Standard deviation for operator1-machine 1, s1 = R?/d2 = 0.0072 / 2.326 = 0.0031

Standard deviation for operator2-machine 2, s2 = R?/d2 = 0.0075 / 2.326 = 0.0032

USL = 0.505

LSL = 0.495

Process capability index (Cpk) for operator1-machine1 = MIN ((USL-X?1)/3s1, (X?1 - LSL)/3s1) = MIN((0.505-0.5001)/(3*0.0031), (0.5001-0.495)/(3*0.0031)) = 0.5269

Process capability index (Cpk) for operator2-machine2 = MIN ((USL-X?2)/3s2, (X?2 - LSL)/3s2) = MIN((0.505-0.5022)/(3*0.0032), (0.5022-0.495)/(3*0.0032)) = 0.2917

4) The capability indices of both operator-machine combination are less than 1.33, therefore, none of the processes are capable of meeting the specification. Even the in-control process is not capable of meeting the specifications.