978-0077835439 Toledo Custom Manufacturing Quality Control Case

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Toledo Custom Manufacturing: Quality Control

Teaching Notes

Synopsis and Purpose

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.

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

specification?

Analysis

Question 1:

The analysis for TCM is shown below. The first step is to compute the sample average and the

Question 2:

As can be noted from the spreadsheet operator1—machine 1 is in control in both average and

range. All of the sample averages and ranges fall within the control limits. The samples can

therefore be used to continue production and shipped to the customer. The customer has asked

Question 3:

Process capability for each operator-machine combination is shown at the bottom of the

Question 4:

A sharp student will recognize that the process capability calculated below is less than 1 and

therefore future parts are likely to be out of spec, even though the process is in control. The

Teaching Strategy

When teaching this case I start by asking a student to conduct a statistical analysis of the data.

Other students are then asked to comment on the analysis until several variations and

assumptions have been discussed.

When the data has been thoroughly analyzed, I then turn to a discussion of how the situation can

be corrected. Some students will miss the point that the process must first be brought under

control before statistical control charts can be used. That is several samples must be found to be

within the control chart limits to establish the grand average and the average range used. In this

case we require 6 samples of 5 each to insure we have a stable process. After that the control

chart can be used to continue production.

sample sample

Operator 1 machine 1 average range

sample 1 0.500 0.498 0.502 0.499 0.503 0.500 0.005

sample 2 0.496 0.497 0.500 0.502 0.499 0.499 0.006

sample 3 0.504 0.503 0.503 0.496 0.495 0.500 0.009

sample 4 0.503 0.501 0.498 0.497 0.500 0.500 0.006

sample 5 0.500 0.502 0.503 0.498 0.495 0.500 0.008

sample 6 0.505 0.496 0.504 0.503 0.502 0.502 0.009

Operator 2 machine 2

sample 1 0.495 0.497 0.495 0.502 0.500 0.498 0.007

sample 2 0.505 0.510 0.503 0.511 0.504 0.507 0.008

sample 3 0.504 0.503 0.502 0.502 0.501 0.502 0.003

sample 4 0.500 0.501 0.497 0.496 0.504 0.500 0.008

sample 5 0.501 0.512 0.510 0.508 0.504 0.507 0.011

sample 6 0.503 0.500 0.497 0.496 0.504 0.500 0.008

operator 1 operator 2

machine 1 machine 2

Grand Average 0.50013 0.50223

Average Range 0.00717 0.00750

Number of points out of control

Average Chart 0 2

Range Chart 0 0

σCp

Cpk

Standard deviaton of individual parts operator 1 machine 1 0.00298 0.559 0.544

Standard deviaton of individual parts operator 2 machine 2 0.00468 0.356 0.197