Section 3 Control Charts

Lesson S03-09

Text: Section 3 pages 53 – 54

Duration: 6 minutes

Reaction to Chart Signals

All chart signals should be investigated for identification of the root cause of the apparent process change (e.g. trend, shift, variation change). It is not a good strategy to “wait and see” as the opportunity to detect and uncover a detrimental root cause may be lost.

Tips to Improve Your Reaction Effectiveness

Monitoring your process closely to look for correlated events to signals is just one idea discussed here.

Updating Control Limits

A common question is, “When Should Control Limits be Updated?” Some software will allow for dynamically updated control limits in which the control limits are regularly updated based on the most recent data. This is a dangerous practice as process shifts and trends can be masked by control limits that adjust along with the trend. The only justifiable reason to update control limits is to reestablish a valid control chart following a process change (the change may be by design or an unexpected change that becomes the new norm).

Section 3 Control Charts

Lesson S03-08

Text: Section 3 pages 46 – 52

Duration: 32 minutes

X̄ Specific Out of Control Rules

X̄ specific signals of strong evidence of a special cause shifting the process mean.

• 4 out of 5 points in top or bottom third of the chart
• 2 out of 3 consecutive points in the top or bottom sixth of the chart
• 15 points in a row in the middle third of the chart
• 8 point in a row outside the middle third of the chart

The above signals apply to X̄ charts but not range charts. More generally, they depend on the statistic being plotted following a normal distribution so any charts of statistics or values that follow a normal distribution may utilize these rules.

Zone Rule Violation 4 out of 5 in Outer Third

Zone Rule Violation 2 out of 3 in Outer Sixth

Zone Rule Violation of 15 in the Middle Third

Zone Rule Violation 8 Outside the Middle Third

Minitab examples of Out of Control Examples

Minitab Rule Settings and Customization

Section 3 Control Charts

Lesson S03-07

Text: Section 3 pages 34 – 45

Duration: 22 minutes

Decisions

As in almost all decision making processes, the interpretation of control charts is gambling. In fact, any time a decision must be made, and the truth is not known with certainty, we are gambling.

First a brief discussion on sampling error, then a set of descriptions of signals that provide strong evidence of a special cause of a process change.

Points beyond the control limits, runs, trends, and cycles apply to all control charts discussed in this course. They do not depend on the statistic being plotted following any particular distribution.

Type I and Type II Errors

When sampling we are gambling the results will reflect the actual full dataset. It is possible that the data will mislead us, yet being aware of these errors permits us to minimize their impact.

The purpose of this section is to review the signals and patterns that should be identified on X̄ and R (or s) charts. The most important concept is that these signals and patterns provide strong evidence that the process is out of control. However, they do not provide a guarantee that the process is out of control. Thus, we should always be aware of the risks we take when we draw incorrect conclusions. Furthermore, understand that there is always a risk of making an erroneous decision, but we can minimize that risk.

Points Beyond the Control Limits

Even when a process is stable, it is possible to see points beyond control limits. This event has already been alluded to, and it occurs 27/10,000 times. However, points beyond control limits are much more likely to come from an unstable process than a stable one. Hence, we are better off concluding that the process has changed.

Runs — 7 consecutive above or below the center line

What is the probability of experiencing a run?

Discussion on Calculating the Probability of a Run

Trends — 7 consecutive points stepping up or down

Cycling — 14 points alternating up then down

Section 3 Control Charts

Lesson S03-06

Text: Section 3 page 33, Section 9 page 10

Duration: 11 minutes

Introduction to Exercise 5

Exercise 5

Batches of Blended Rubber to be used for O-Rings are tested for tensile strength. One sample was taken and tested from 30 consecutive batches. The data is shown below and is also included in file Exercise05.MTW.

Construct Individuals and Moving Range Charts and assess the stability of the process.

Note: The values have been shown to be normally distributed.

Solution / Discussion of Exercise 5

A Few Hints for Using Minitab

Section 3 Control Charts

Lesson S03-05

Text: Section 3 pages 21 – 32

Duration: 23 minutes

X̄ and S Charts

The s chart can be used instead of the R chart. In fact, the standard deviation is a superior measure of variation than the range is. Ranges were used historically based on the ease of calculation. However, the standard deviation is superior since it does not “throw away” data when it’s computed.

Constructing the X̄ and s chart combination is nearly identical to the method for the X̄ and R chart combination. The only difference is in the way we estimate control limits. We will reuse the data from our X̄ and R chart discussion, and we will compare the X̄ / R pair of charts with the X̄ / s pair of charts.

Download the  X̄ and S Charts Calculations Worksheet. Or view workbook page Section 3: Page 26.

Individuals and Moving Range Charts

Although sampling subgroups for control charting has many advantages, it is not always feasible.

When testing is destructive or expensive, a subgroup may be too costly. In this instance, it may only be possible to acquire a sample of size one (n = 1). The importance of rational sampling for charts of subgroups will be discussed shortly but the point here is that the inability to obtain rational samples may dictate a sample size of 1. In this case we may create individuals and moving range charts.

Here, we review only the traditional individuals and moving range charts.

Download the  Individuals and MR Charts Calculations Worksheet. Or view workbook page Section 3: Page 30.
 

Section 3 Control Charts

Lesson S03-04

Text: Section 3 pages 20 & Section 9 pages 6 – 9

Duration: 22 minutes

Minitab demonstration on creating control charts

Introduction to Exercise 3 and 4

Exercise 3 is optional yet is good practice.

Exercise 3

30 samples of size 4 (n = 4) have been collected. The average of the averages is 130mm. The average range is 10mm.

a. What are the control limits for the X̄ chart?
(Hint: use the worksheet for X̄ and R chart calculations. Download the  X̄ and R Charts Calculations Worksheet and graph paper. Or view workbook pages Section 3: Page 11 and 12.)

b. What are the control limits for the R chart?

Solution / Discussion of Exercise 3

Exercise 4

A Key Characteristic of an O-Ring is the Radial Cross Section. 26 samples of size n=5 were taken. The data is shown below and may be found in the file Exercise04.MTW

a. Construct X̄ and R Charts (or X̄ and S Charts) and assess the process stability.

Solution / Discussion of Exercise 4 a

b. Assume that the out of control point in the chart constructed above is a Type I Error (the process is actually stable) and answer the following questions.

What is the estimated process average?

What are the control limits for the X̄ Chart?

What is the average Range?

What are the control limits for the Range chart?

Solution / Discussion of Exercise 4 b

Section 3 Control Charts

Lesson S03-03

Text: Section 3 pages 17 – 20

Duration: 11 minutes

The Purpose of Charts

Let’s start with a couple of questions.

Quick Quiz

 

Does the process appear to be in control or out? View the next video for answers/discussion.

Is the Process Stable Discussion

Quick Quiz

Does the process produce units that meet specification consistently? Will the process produce units in spec at least 95% of the time? Click the Discussion button for a short note. View the next video for answers/discussion.

Meeting Specifications Discussion

Keep in mind that the standard deviation of the averages (standard error) is smaller than the standard deviation of the individuals.

$$ \displaystyle\large {{\sigma }_{{\bar{x}}}}=\frac{\sigma }{\sqrt{n}}$$

Quick Quiz

Click the Discussion button for a short note. View the next video for answers/discussion.

How about Plotting Individual Values?

There are some tradeoffs between plotting averages versus individuals where averages provide some distinct advantages.

One of the Most Important Points!

The purpose of control charting is to learn when the process
has done something unexpected (and that does not mean “out of
spec”). With that information, we can quickly learn how the process
is affected by various factors potentially affecting it.

The purpose of control charting is NOT to identify parts out of
print (specification). In fact, since X̄ charts monitor averages,
they do not indicate whether parts are out of tolerance.

Section 3 Control Charts

Lesson S03-02

Text: Section 3 pages 7 – 16

Duration: 19 minutes

Individuals and Averages & construction of the X̄ & R Charts Manually

A quick review of individuals and averages followed by a step by step walkthrough of the steps to create two basic charts.

Download the  X̄ and R Charts Calculations Worksheet and graph paper. Or view workbook pages Section 3: Page 11 and 12.

How to create the X̄ & R Charts using Minitab

If you are using Minitab, let’s run through the steps to create the same two charts.

Section 3 Control Charts

Lesson S03-01

Text: Section 3 pages 1 – 6

Duration: 23 minutes

Control charting can be done for both variable and attribute data types, but the mathematics involved depends on the data type. Furthermore, sample size considerations vary dramatically depending on whether the information is variable or attribute.

When the data is discrete, but the number of possible values is reasonably large, the data can be treated as variable type data. You may notice that in the first numeric example of this topic, the data is discrete (integer valued), but it will be handled as variable type data.

This topic mostly deals with variable type data but most of the concepts apply to attribute charts as well. The common charts for attribute data are discussed in Appendix II.

Recall that control limits are limits of expected variation. Hence, before attaining these limits, we must have a sense of what to expect. The question is, how much data is required before we have an idea of what to expect?

Introduction to Section 3 Control Charts

A quick overview of the section on control charts. An introduction to the process capability flowchart.

The Process Capability Flowchart

An introduction to the process capability flowchart.

An Overview of the Creation of   X̄ & R charts

Control charting can be done for both variable and attribute data types, but the mathematics involved depends on the data type. Furthermore, sample size considerations vary dramatically depending on whether the information is variable or attribute.

Once enough data has been collected, an estimate of the overall process average and the average range can be made. The estimates only have meaning if the process has been stable, so stability is assumed initially. If the process has not been stable, then we do not know what to expect, and there are no limits of expected variation.

Section 3

An important prerequisite for assessing Process Capability is to first establish process stability (i.e. process control). Furthermore, since changes in materials, equipment, people, and the environment are bound to occur, methods are needed to detect such changes which may produce harmful consequences if not detected and addressed. This section focuses on the use of control charts to assess process stability and establish process control.

This section includes details on:

• Constructing control charts for variable data
• Chart signals for special cause variation
• Interpreting chart signals
• Sampling procedures and frequency
• Chart sensitivity and sample size determination
• Control chart selection
• Reaction plans

Section 2 Variation Fundamentals

Lesson S02-12

Text: Section 9 pages 5

Duration: 27 minutes

A quick introduction to Minitab including essential information to allow the completion of exercise 2

Introduction to Mintab and Exercise 2

a. George collected annual return percentages for the seven largest portfolios managed by his firm. Assume these are variable type data and compute the sample standard deviation. Here is the data:

23%
37%
4%
125%
210%
52%
10%

Solution/Discussion Exercise 2 a

b. A company monitors paint thickness. Xbar and R charts based on n = 3 indicate that the process is stable. The average range is 2.5mm.

What is an estimate of the standard deviation among individual paint thickness measurements?

Solution/Discussion Exercise 2 b

Section 2 Variation Fundamentals

Lesson S02-11

Text: Section 2 pages 72 – 96

Duration: 29 minutes

A statistic is a one number summary of a group of numbers. In other words, a statistic is one number which describes some characteristic of the data.

Some basic mathematical notation must be understood before attempting to estimate these three important aspects of a process.Many of the formulas used to compute statistics require the use of special notation, and it is this notation that is described next.

It is important to discriminate between a population and a sample. A population is a group that consists of everything being researched. For example, if the interest is on television viewing habits of American teenagers, then the population is all American teenagers.

A sample is a subgroup. Because it is usually impossible to acquire information on every unit in a population, it is more cost effective to select a subgroup. So, a sample is a subset of the population, and hopefully, the sample represents the population of interest.

Measures of Central Tendency include mean, median, and mode.

Measures of variation include range, standard deviation, and variance.

Basic Statistics

Note: we had some technical issues with the audio and there are some unwanted skips or audio artifacts. We are working to clean up the audio and will post updates as soon as possible.

Notation

Average & Central Tendancy

Measures of Variation

Section 2 Variation Fundamentals

Lesson S02-10

Text: Section 9 pages 1 – 4

Duration: 18 minutes

In the workbook, find and work the questions in exercise 1. The following videos include suggested answers and discussion. You will also find the text of each question above the corresponding answer/discussion video.

Introduction to Exercise 1

a. Key Characteristic Data always follows a normal distribution (true/false).

Solution/Discussion: Exercise 1 a

b. For a Normal distribution, what percentage of the population falls within one standard deviation of the mean?

c. For a Normal distribution, what percentage of the population falls within three standard deviations of the mean?

Solution/Discussion: Exercise 1 b & c

d. What is the difference between control limits and specification limits?

e. Who determines control limits?

Solution/Discussion: Exercise 1 d & e

f.  What term do we use to describe sources of variation that cause unexpected changes in a process?

Solution/Discussion: Exercise 1 f

g. Which distribution do individual values follow?

Solution/Discussion: Exercise 1 g

h. Which distribution do averages from a stable process follow?

Solution/Discussion: Exercise 1 h

i. Does “in control” imply “in spec?”

j. What is another word for the term “out of control?”

Solution/Discussion: Exercise 1 i & j

k. Please define Quality.

l. How does variability among individuals compare to variability among averages? Please state the relationship mathematically and in words.

Solution/Discussion: Exercise 1 k & l

m. The process below is “in-control.” (True, False, Cannot Tell)

n. Does the following graphic represent an “in control” process?

Solution/Discussion: Exercise 1 m & n

o. Does the following graphic represent an “in control” process?

p. A stable process implies that the process is also capable (true/false).

q. Describe the difference between process stability and process capability.

Solution/Discussion: Exercise 1 o, p & q

Section 2 Variation Fundamentals

Lesson S02-09

Text: Section 2 pages 68 – 71

Duration: 10 minutes

Assessing Process Capability is a major component of this training program. We introduce the concept of Process Capability here.

Process Capability refers to the ability of the process to meet specification. Typically we quantitatively evaluate the capability by estimating the number of defective parts per million (or another similar statistic) or utilize common process capability indices (such as Cp or Cpk).

In section 4 we will focus on quantitative assessment of process capability. Here, we simply aim to introduce the concept.

Introduction

Process Stable and/or Capable Exercise (continued)

Process Stable and/or Capable Exercise (continued)

Process Stable and/or Capable Exercise (continued)

Process Stable and/or Capable Exercise (continued) and Summary

Section 2 Variation Fundamentals

Lesson S02-08

Text: Section 2 pages 59 – 67

Duration: 22 minutes

There are two primary objectives in this section. The first is to identify the sources of variation. Once we know the sources of variation, the largest contributors to the output can be determined (with the assistance of other statistical methods).

The second objective is to learn whether each source of variation is a natural and expected source of variation or whether the source can lead to unexpected outcomes in the output.

Common cause sources of variation are sources of variation that influence the process in an expected or predictable manner. In other words, if we observe a stable process, we conclude that the relevant sources of variation are common cause sources. “In control” processes are subject to common cause sources of variation only by definition.

Special cause sources of variation are factors that cause unexpected changes to the process. Phrased differently, special causes imply an “out of control” condition. They may affect the process average by causing a shift in the location. They might also cause the amount of variability in the process to increase or decrease significantly.

What are we going to control?

The Signature Exercise

The Signature Exercise (continued)

Common and Special Causes