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We will start Chapter 2 today.

In this chapter, we focus on the work of three persons whose contributions to

quality design and control and improvement have had a lasting impact on the

world. The main purpose of this course is to explain the Shewhart control chart

point of view of quality improvement. We will first discuss the principle of his

Philosophy of Never-

definition of Quality and his contribution in pushing quality upstream to

engineering design will be discussed.

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Although the Shewhart control charts look fairly simple, many people involved

in trying to manage and improve quality find that its use requires an entirely new

point of view. Briefly stated, the main principles are four:

1. Measured quality of manufactured product is always subject to a certain

amount of variation as the result of chance.

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scheme of production and inspection

3. Variation within this stable pattern is inevitable.

4. The reason for variation outside this stable pattern may be discovered and

corrected.

These principles provide the foundation of statistical process control.

The constant system of chance causes refereed to by Shewhart also has been

called a stable system or defined as statistical stability. Edwards Deming

refereed to these constant or stable systems as common causes of variation.

Variation outside this stable system, called assignable cause variation by

Shewhart and special cause variation by Deming, may be detected using control

charts and its cause or causes eliminated through analysis and corrective action.

Often these actions result in substantial improvement in quality.

Moreover, by identifying certain quality variations as inevitable chance

variation, the control chart tell when to leave a process alone, thus prevent

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unnecessarily frequent adjustments that tends to increase variability rather than decrease

it.

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couple of examples to have a basic idea about these tools.

After hearing a 2-hour lecture on SQC, a production supervisor in a small plant

made an experimental application to one of the operation in the department.

This operation consisted of thread grinding a fitting for an aircraft hydraulic

system. The pitch diameter of the threads was specified as 0.4037+/- 0.0013 inch.

All these fittings were later subject to inspection of this dimension by go and no-

go thread ring gages. This inspection usually took place serval days after

production. In order to minimize gage ware in this inspection operation, it was

the practice of the production department to aim at an average value a little

below the nominal dimension of 0.4037.

In order to make actual measurements of pitch diameter to the nearest ten-

thousandth of an inch, the supervisor borrowed a visual comparator.

Approximately once every hour the pitch diameter of five fittings that has just

been produced was measured. The numbers in the table are expressed in units of

0.0001 inch in excess of 0.4000 in. Example, 36 means 0.4036 in. For each

sample of five, the average and the range were computed. The range is the largest

value minus smallest value in the sample. Without the benefit of taking the 2-

hour SPC course, the supervisor probably would not calculate the range.

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We will exam two type of charts that are NOT control charts first. These chart

sometimes are made from information of this type.

This figure shows individual measurement plotted for each sample. It also shows

the nominal dimension and upper and lower tolerance limits. With the exception

of on fitting in sample 8, all the fittings examined met the specified tolerances.

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This figure shows the average of these samples. A chart of this type may be

useful to show trends more clearly than the previous figure. However, without the

limits provided by Shewhart technique, it does not indicate whether the process

shows lack of control in statistical sense of the meaning of control.

The word control has a special technical meaning in the language of SQC. A

process is described as in control when a stable system of chance causes seems to

be operating. We will have more discussion on the meaning later in the course.

However, the word is often misused and misinterpreted, particularly by those

who have been briefly exposed to the jargon of SQC without having had a chance

to learn its principle.

For example, a government inspection officer in a certain plant was shown a

control limits and plotted them on the chart, showing many points out of control

limits. A few minutes later, the inspection officer was overheard giving advice to

Actually, as a matter of fact no one can tell by inspection a chart like this wheter

or not the process is in statistical control.

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Next, we will look at two control charts. The control char for average called X

bar chart and the control charts for the range called R charts.

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As can be seen, the chart for average X bar chart is the chart shown previously

with the addition of control limits and elimination of the irregular line connecting

adjacent samples. There is a solid line here to indicate the average value of the

statistic that is plotted. The grand average X double bar or the average of the

average is 33.6 (or 0.40336 inch). This is the sum of the averages, 671 divided by

the number of samples ,20. The chart shows two dashed lined marked upper

control limit and lower control limit. The distance of the control limits from the

line showing the average depend on the subgroup size and the average range

R_bar. The methods for calculating such distances are explained later in the

course.

As can be seen from the chart, three points , samples 10,12, and 18 are outside

the control limits. This indicate the process is out of control, or there are

assignable causes of variation in the manufacturing, i.e., factors contributing to

the variation in quality that it should be possible to identify and correct.

Of course not much could be done if no control charts are plotted.

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This is control chart for the range, called R chart. We also have a solid line

representing the average of the ranges. The control limits are not equidistant from

the average range of 6.2. The upper limit is 13.1, and lower limit is 0. We have

two samples out of control limits (samples 9 and 13) which further proved that

the process is lack of control.

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Since the lack of control was evident to the production supervisor who prepared

this chart.

A continuation of the chart permitted the identification of the assignable causes

of variation in the average mostly related to machine setting

Assignable cause of in the range mostly related to carelessness a particular

operator.

An effort to prevent their recurrence resulted in a substantial improvement in

product uniformity.

It was found that if control could be maintained, the natural tolerance appear to

be about +/- 0.0006 inch from the process center, well within specified tolerance

of +/- 0.0013 in.

Whenever natural tolerance are within specification tolerance, consideration

should be given to the advisability of eliminating 100% inspection using go no-

go gage and substituting sampling inspection with the use of control charts. With

will also save time and cost.

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sometimes include a number of misconceptions, it is worthwhile to make serveal

comments on the example directed at these misconceptions.

One misconception is that the statistical method can only be applied only where

there is a long period record. It should be noted that the necessary data for a

successful application in this case were obtained in 20 hours.

Another misconception is that the methods are highly mathematical. Actually this

application only involved simple arithmetic.

A common misconception is that the techniques are good to use only when you

are conscious that you are in trouble. While it is true that the places where one is

conscious of trouble are likely to provide the best opportunities for improvement.

Yet in our example, the supervisor applied the technique without the awareness

of the lack of control of the process.

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Another example. A rheostat knob, produced by plastic moldling, contained a

metal insert purchased from a supplier. A particular dimension determined the fit

of this knob in its assembly. The dimension was specified by the engineering

department as 0.140+/- 0.003 inch. Many molded knobs were rejected on 100%

inspection with a go and not-go gage fore failure to meet the specified tolerances.

Later, the company decided to apply SQC technique and started to take 5

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The dimension values are expressed in units of 0.001. e.g. 140 means 0.140 inch.

The engineering specification of the dimension is 0.140+/- 0.003 inch. Again, the

average and the range of the 5 measurements in the sample are calculated and

listed in the last two columns.

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The individual measurements within each sample are shown here. Where

horizontal axis is the sample number, vertical axis is the dimension in inch. The

upper and lower tolerance limits are also plotted. It is obvious that a fairly large

portion, more specifically 42 out of 135 knobs measured failed to meet the

specification tolerance and should be rejected.

The first impression to viewer of the chart is that the process is very poor in

to find out until we plot the control charts.

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The control limits for X bar and R charts can be calculated very easily. It only

involves simple arithmetic operations. We started with computation of the grand

average of X double bar and average of the range R_bar. All the control limits are

functions of these two quantities. We will study the details in the later lectures.

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Now we have the control limits and the average and range of each sample, we

can plot the control charts. b) and c) are the control charts for X_bar and R,

respectively.

Do you see any data point fall outside of the control limits?

No. So the process was evidently in statistical control, even though it was in

control with a spread that was unsatisfactory from the standpoint of the specified

tolerance of 0.003 inch.

No assignable causes of variability were identified. The variation from hour to

hour were chance variation; they could not be reduced by hunting for changes

that took place from one hour to the next.

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In a situation of this type, improvement is not likely to be obtained by plant

So what can do about it.

The first one is to make fundamental change in the process, which is usually

costly and time consuming. The quality engineers studied the situation, and

found the spread was mostly due to the inherent variability of the variability of

the metal insert from the outside supplier. But the part was essential for an

important contract and available suppliers were scarce, nothing could be done

immediately about it.

Another immediate alternatives is to widen the tolerances. The quality control

engineer requested the engineering department to review the tolerances. The

review showed that the specified tolerance of 0.003 in were much narrower than

necessary for the satisfactory functioning of the rheostat knob. After trying

different value of this dimension and judging when the fit was good, the

tolerance were changed to +0.010 and -0.015. This will make every part

examined fall with the new specification tolerances.

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http://www.youtube.com/watch?v=ckBfbvOXDvU

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Lessons to be learned from the red bead experiments.

1. Understand the stability of a system. Is the system stable? The answer is yes.

2. Where does the variation come from? The variation among the willing

workers are due to the system itself.

3. Where to look for improvement? It is futile to ask people to do better, to

work harder, and then reward or punish them accordingly, when their

performance is solely driven by the system itself

4. What is a proper management of a system?

5. Treat causes, not symptoms.

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