Case Study 5.1

in

Quality

by Summers, 5

th

Ed. p. 197

-

205

Quality Control for Variables

Part1:

This case study provides some details about the activities of the Whisk Wheel Company, which

is currently

in the process of applying statistical quality control and problem

-

solving techniques

to their wheel hub operation. Whisk Wheel supplies hubs and wheels to variety of bicycle

manufacturers. The wheel hubs under discussion in this case fit on an all terr

ain model bicycle.

Background:

The Whisk Wheel Company has just been notified by its largest customer, Rosewood Bicycle

Inc., that Whisk Wheel will need to dramatically improve the quality level associated with the

hub operation. Currently the operation

is unable to meet the specification limits set by the

customer. Rosewood has been sorting the parts on the production line before assembly, but they

want to end this procedure. Beginning immediately, Whisk Wheel will be required to provide

detailed stati

stical information about each lot of products they produce. (A lot is considered one

days worth of production.) At the end of each day, the lot produced is shipped to Rosewood

just

-

in

-

time for their production run.

The Product

Figure C5.1.1 diagrams the

product in question, a wheel hub. The hub shaft is made of chrome

-

moly steel and is 0.750 inch in diameter and 3.750 inches long. The dimension in question is the

length. The specification for the length is 3.750

+

-

0.005 inches.

The Process

Twelve

-

foo

t

-

long chrome

-

moly steel shafts are purchased form a supplier. The shafts are

straightened and the cut to the 3.750

-

inch length. Several different machines perform the cutting

operation. The data presented here are for the production off one machine onl

y.

Management Strategy

On the basis of new customer requirements, until greater control can be placed on the process,

management has decided to intensify product inspection. This will allow the staff engineers to

complete their study of the problem and

recommend an action plan. Each piece produced will be

inserted in a go/no

-

go gauge to determine if it meets specifications. This will work fairly well by

preventing improperly size shafts from going to the customer. Several managers want to make

this a p

ermanent arrangement, but some of the more forward

-

thinking managers feel that this

will not get at the root cause of the problem. There is also the concern that 100 percent

inspection is costly and not effective in the long run.

In the meantime, the st

aff engineers (including you) are continuing to study the problem

more carefully. The following information is from todays production run. From the finished

parts, an operator samples six hubs 24 times during the day.

Assignment

On the computer create

a histogram from todays data. (Excel Data Sheet, Data for Day 1).

Write a summary of the results. Use the value of estimated sigma and the Z tables to calculate

the percentage of parts produced above and below the specification limits.

Part 2:

Althou

gh process capability calculations have not been made, on the basis of the

histogram, the process does not appear to be capable. It is apparent form the histogram that a

large proportion of the process does not meet the individual length specification. T

he data

appear to be a reasonable approximation of a normal distribution.

During a rare quite moment in your day, you telephone a good friend from your quality

control class to reflect on the events so far. You also remember some of the comments made by

y

ou SQC professor about appropriate sampling and measuring techniques. After listening to

your story, your friend brings up several key concerns.

1.

Product Control. Basically, management has devised a stopgap procedure to prevent

poor quality products from

reaching the customer. This work

-

screening, sorting, and

selectively shipping parts

-

is a strategy consistent with the detect and sort approach to

quality control. Management has not really attempted to determine the root cause of the

problem.

2.

The Engin

eering Approach

-

while a little more on the track, the focus of engineering on

the process capability was purely form the conformance to specifications point of view.

Appropriate process capability calculations should be based on a process that is under

statistical control. No information had yet been gathers on this particular process to

determine if the process is under statistical control. In this situation, process capability

was calculated without determining if the process was in a state of statis

tical control

-

something you now remember your quality professor cautioning against.

Another consideration deals with the statistical significance of the sampling using the best

operator and the best machine. Few or no details have been given about the s

ampling

techniques used or the training level of the operator.

A Different Approach

After much discussion, you and your friend come up with a different approach to solving

this problem. You gather together your fellow team members and plan a course of ac

tion.

The goal of the group is to determine the source of variation in the process if producing

wheel hubs. A process flowchart is created to carefully define the complete sequence of

processing steps: raw material handling, straightening, cutting, and f

inish polish (figure

C5.1.3). Creating a process flowchart had helped all members of the ream to better

understand what is happening during the manufacture of the hub.

At each step along the way, your team discusses all the factors that could be contribut

ing

to the variation in the final product. To aid and guide the discussion, the group creates a

cause

-

and

-

effect diagram, which helps keep the group discussions focused and allows the

team to discuss all the possible sources of variation. There are sever

al of these, including

raw materials (their properties and preparation), the methods (procedures for setup and

machine operation at each of the three operations), the machine conditions (operating

settings, maintenance conditions), and the operator (traini

ng, supervision, techniques). The

diagram created is shown in Fig. 5.1.4.

The team originally focuses on the inherent equipment capability as the key problem.

This approach leads too quickly to the conclusion that new machines should be purchased.

This

approach does not enable team members to learn to use the equipment, processes, and

people already available to their fullest potential.

After studying and discussing the complete process flow, the team decides that they do

not know enough about the proc

ess to suggest solutions. They assign team members to more

fully investigate the four areas (raw materials, straightening, cutting, and finishing). Close

contact among the team members will ensure that the discoveries in one area are quickly

shared with

other related areas. After all, in this process making a wheel hub, no one area

can function without the others.

You and your partner have been assigned to the cutting area. To discover the source of

variation, the two of you decide to run

and R charts on the data from the preceding day as

well as the data from this day (an additional 24 subgroups of a sample size 6).

Assignment

Add the new data (Excel Data Sheet, Data for Day 2) for today to your previous file.

Create an

a

nd R chart containing both days data and discuss what the charts look like.

Use all the information available to create a histogram. Use the value for estimated sigma

and the Z table to calculate the percentage of parts produced about and below the

spec

ification limits.

Part 3

To determine the root cause of variation, you and out partner spend the remainder of day

2 studying the cutting operation and the operator. You randomly select a machine and an

operator to watch as he performs the operation and m

easures the parts. You note several

actions taken by the operator that could be sources of variation.

Investigation reveals that the operator runs the process in the following manner. Every

18 minutes, he measures the length of six hubs with a micromete

r. The length values for the

six consecutively produced hubs are averaged, and the average is plotted on a piece of

charting paper. Periodically, the operator reviews the evolving data and makes a decision as

to whether the process mean (the hub length)

needs to be adjusted. These adjustments can be

accomplished by stopping the machine, loosening some clamps, and jogging the cutting

device back or forth depending on the adjustment the operator feels is necessary. This

process takes about five minutes an

d appears to occur fairly often.

Based on what you have learned about process control in SQC class, you know that the

operator is adding variation to the process. He appears to be over controlling (over adjusting)

the process because he cannot distinguish

between common cause variation and special cause

variation. The operator has been reacting to patterns in the data that may be inherent

(common) to the process. The consequences of this mistake are devastating to a control

chart. Each time an adjustmen

t is made when it is not necessary, variation is introduced to

the process that would not be there otherwise. Not only is quality essentially decreased

(made more variable) with each adjustment, but production time is unnecessarily lost.

A glance at the

histogram created the first day shows that over adjustment is indeed

occurring, resulting in the bimodal distribution. Control charts can be used to help

distinguish between the presence of common and special causes of variation. Removing this

source of v

ariation will allow the process to operate more consistently. Removing this

obstacle can also help uncover the root cause of the variation.

The data from day 3 have been gathered and reflect the suggested change. The operator

has been told not to adjust

the process at all during the day. Is the process goes beyond the

previous days limits and out of control, the operator is to contact you.

Assignment

Create an

and R chart for

only the new data from day 3(

Excel Data Sheet, Data for

Day

3). Compare the new chart with the charts from the two previous days. Draw the previous

days limits on the new chart for day 3 by hand. Using only the data from day 3, create a

histogram. Use the value for estimated sigma and Z tables to calculate the p

ercentage of parts

produced above and below the specification limits.

The new chart should allow you to better distinguish between the presence of common

and special cause variation. Compare all of your mathematical and graphical results. What

conclusio

n can you and your partner draw?

Part 4

With one source variation identified and removed, quality and productivity in the line have

improved. The process has been stabilized because no unnecessary adjustments have been made.

The method of over control ha

s proven costly from both a quality (inconsistent product) and a

productivity (machine downtime, high scrap) point of view. The search continues from other

sources of variation.

During day 3, you and your partner watched the methods the operator used to m

easure

the hub. Neither of you feel that this technique is very good. Today you replace the old method

and tool with a new measuring tool, and the operator is carefully trained to use the new tool.

Assignment

-

Continue day 3s control chart to record th

e data for day 4 (Excel Data Sheet, Data for Day 4).

How do the data look overall? Are there any trends or patterns? Comment on the tighter control

limits as compared with days 1 and 2. Create a histogram with the data from only days 3 and 4

combined. Dis

cuss how the overall spread of the process looks using Z table calculations. What

conclusions can be drawn?

Part 5

Now that the two unusual causes of variation have been removed from the process, you and your

partner are able to spend the fourth day stud

ying and resulting stable process. You are able to

determine that the design of the jig used by the operation us causing buildup of chips. Each time

a part is cut, a small amount of chips builds up in the back of the jig. Unless the operator clears

thes

e chips away before inserting the new stock into the jig, they build up. The presence or

absence of chips is causing variation in the length of the hub.

To correct this, during the night

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maintenance shift, a slot is placed in the back of the jig,

allowi

ng the chips to drop out of the jig. Additionally, a solvent flush system is added to the

fixture to wash the chips clear of the jig.

Assignment

-

Create an

and R chart for just day 5s data (Excel Data Sheet, Data for Day 5). Compare the

new chart with the charts form days 3 and 4. Have the control limits changed? How? How is the

process doing now? Compare the percentage out

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of

-

specification found using the Z table

calculations for all the days. Overall, how would you view the process?

Part 6

Assignment

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Revisit the charts you created in part 5. How is the process behaving now that the improvements

have been made? What will you recommend to management that they tell the customer? How

will you support your recommendation?