NG BB 26 Control Charts

62
National Guard Black Belt Training National Guard Black Belt Training UNCLASSIFIED / FOUO UNCLASSIFIED / FOUO Module 26 Control Charts

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Transcript of NG BB 26 Control Charts

Page 1: NG BB 26 Control Charts

National GuardBlack Belt Training

National GuardBlack Belt Training

UNCLASSIFIED / FOUO

UNCLASSIFIED / FOUO

Module 26

Control Charts

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CPI Roadmap – Measure

Note: Activities and tools vary by project. Lists provided here are not necessarily all-inclusive.

TOOLS

•Process Mapping

•Process Cycle Efficiency/TOC

•Little’s Law

•Operational Definitions

•Data Collection Plan

•Statistical Sampling

•Measurement System Analysis

•TPM

•Generic Pull

•Setup Reduction

•Control Charts

•Histograms

•Constraint Identification

•Process Capability

ACTIVITIES• Map Current Process / Go & See

• Identify Key Input, Process, Output Metrics

• Develop Operational Definitions

• Develop Data Collection Plan

• Validate Measurement System

• Collect Baseline Data

• Identify Performance Gaps

• Estimate Financial/Operational Benefits

• Determine Process Stability/Capability

• Complete Measure Tollgate

1.Validate the

Problem

4. Determine Root

Cause

3. Set Improvement

Targets

5. Develop Counter-

Measures

6. See Counter-MeasuresThrough

2. IdentifyPerformance

Gaps

7. Confirm Results

& Process

8. StandardizeSuccessfulProcesses

Define Measure Analyze ControlImprove

8-STEP PROCESS

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Learning Objectives

Control chart fundamentals

Use of control charts to identify Common Cause and Special Cause variation

Factors to consider in constructing control charts

Variables control charts

Attribute control charts

Understand the interpretation and application of these charts

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Observation

Indi

vidu

al V

alue

30272421181512963

20

15

10

5

_X=10.58

UC L=18.48

LC L=2.67

Observation

Mov

ing

Ran

ge

30272421181512963

10.0

7.5

5.0

2.5

0.0

__MR=2.97

UC L=9.71

LC L=0

1

I-MR Chart of Pizza Preparation Time

Control Chart Terms

Control Chart = a time plot showing process performance, mean (average), and control limits

The Voice of the Process !!!

Control charts measure the “health” of the process

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Control Chart Terms

Control Limits = statistically calculated boundaries within which a process in control should operate

These boundaries result from the process itself and are NOT customer specifications

Observation

Indi

vidu

al V

alue

30272421181512963

20

15

10

5

_X=10.58

UC L=18.48

LC L=2.67

Observation

Mov

ing

Ran

ge

30272421181512963

10.0

7.5

5.0

2.5

0.0

__MR=2.97

UC L=9.71

LC L=0

1

I-MR Chart of Pizza Preparation Time

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Common vs. Special Cause

Measurements display variation

Variation is either:

Common Cause Variation

This is the consistent, stable, random variability within the process

We will have to make a fundamental improvement to reduce common cause variation

Is usually harder to reduce

Special Cause Variation

This is due to a specific cause that we can isolate

Special cause variation can be detected by spotting outliers or patterns in the data

Usually easier to eliminate

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Process Control

When a process is “in control”

This implies a stable, predictable amount of variation (common cause variation)

This does not mean a "good" or desirable amount of variation

When a process is “out-of-control”

This implies an unstable, unpredictable amount of variation

It is subject to both common AND special causes of variation

A process can be in statistical control and not capable of consistently producing good output within specification limits

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Types of Control Charts

The Control Chart family can be broken into two groups based on the type of data we are charting:

Continuous/Variable

Attribute/Discrete

Since we “prefer” Continuous data we will study this group of Control Charts first

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Continuous Data Control Charts

The theory of all Control Charts can be learned by studying the Xbar (Average) and R (Range) chart for continuous data

We will then explore the I-MR (Individuals - Moving Range) Chart

Xbar-R Charts allow us to study:

Variation “within each subgroup” (precision) on the R chart

Variation “between each subgroup” (accuracy) on the Xbar chart

Note: Look at the R chart first, if it is in control, then look at the Xbar chart

Examples of continuous data: width, diameter, temperature, weight, cycle times, etc.

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Control Chart Assumptions

Normally Distributed Data

Control limits approximate +/- 3 sigma from the mean

These control limits are based upon a normal distribution

If the distribution of the data is non-normal, you must use one of the x-bar charts, because the x-bars are likely to be normally distributed due to the effects of the Central Limit Theorem

Rule of thumb for x-bar charts is subgroups of at least 4. Rarely is the underlying distribution so far from normal to require larger subgroups to achieve normality in the x-bars.

Independent Data Points

“Independence” means the value of any given data point is not influenced by the value of any other data point (it is random)

Violation of this assumption means the probability of any given data value occurring is not determined by its distance from the mean, but by its place in the sequence in a data series or pattern

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Continuous Data Control Charts

Subgroup Size of 1

I-MR

Subgroup Size < 3-9

Xbar-R

Subgroup Size > 9

Xbar-S

Measurement(Continuous/Variable Data)

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Continuous Data Control Charts

Utilize probabilities and knowledge of the normal distribution

I-MR chart is used:

When you are learning about a process with few data points

When sampling is very expensive

When the sampling is by destructive testing and

When you are building data to begin another chart type

Xbar-R Chart is used with a sampling plan to monitor repetitive processes. The sub-group sizes are from 3 to 9 items. Frequently practitioners will choose subgroups of 5. All of the theory of Control Charts can be applied with these charts

Xbar-S Chart is used with larger sample groups of 10 or more items. Statisticians sometimes state that the standard deviation is only robust when the subgroup size is greater than 9 (These charts are similar to the Xbar-R Chart)

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Introduction to Xbar-R

Xbar-R Charts are a way of displaying variable data

Examples of variable data: width, diameter, temperature, weight, time, etc.

R Chart: a look at “Precision”

Displays changes in the „within‟ subgroup dispersion of the process. Often called “Short-Term Variation.”

Asks "Is the variation in the measurements „within‟ subgroups consistent?”

Must be “in control” before we can build or use the Xbar chart

Xbar Chart: a look at “Accuracy”

Shows changes in the average value of the process and is a visualization of the “Longer-Term Variation”

Asks "Is the variation „between‟ the averages of the subgroups more than that predicted by the variation within the subgroups?“

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Mechanics of an Xbar-R Chart

Control charts track processes by plotting data over time in the form:

Center Line (X)

Upper Control Limit

Upper Control Limit Averages

Chart = X Double Bar + A2 R Bar

Center Line Averages Chart =

Average of the Subgroup Averages

Lower Control Limit Averages

Chart = X Double Bar - A2 R Bar

X Chart

Lower Control LimitCenter Line (R)

Upper Control Limit

Upper Control Limit

Range Chart = D4Rbar

Center Line Range Chart =

Average of the Subgroup Ranges

Lower Control Limit

Range Chart = D3Rbar

Range Chart

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Example: Xbar-R Chart

Stat > Control Charts > Variables Charts for Subgroups > Xbar-R

Open the worksheet data file called ORDER TAKING.MTW

In this file, orders are taken by order entry clerks. The data is the average hold time a customer waits before speaking with a person to take their order.

The delays are a problem, as many customers give up and we have a dropped call and lost order

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Example: Xbar-R Chart

Double click on C-1 Ave Hold TimeThis places it in the

Variables box5

Type in 5 for yourSubgroup size

Our response is Ave. Hold Time and we choose 5 cells to represent our Subgroup size

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How Do We Interpret This Chart?

Always Look at the R Chart first ! Only if it is in control, is the Xbar chart usable !

Sample

Sa

mp

le M

ea

n

54321

16

14

12

10

8

__X=10.88

UC L=14.97

LC L=6.79

Sample

Sa

mp

le R

an

ge

54321

16

12

8

4

0

_R=7.10

UC L=15.01

LC L=0

1

Xbar-R Chart of Ave. Hold Time

Xbar Chart

R Chart

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Control Chart Data Requirements

Data requirements for control chart applications:

Must be in time series order

Minimum of 25 consecutive (no time gaps) subgroups or

Minimum of 100 consecutive observations

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I-MR Chart

The Individuals and Moving Range chart is also for continuous data

It can be used for many transactional applications:

Revenue or cost tracking

Customer satisfaction

Call times

System response times

Wait times

Most common continuous measures – time and money!

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Individuals and Moving Range (I-MR) Chart

The top chart is a plot of individual pizza preparation times

The bottom chart is the Moving Range, in this case, the Range of two adjacent pizza preparation times

Observation

Indi

vidu

al V

alue

30272421181512963

20

15

10

5

_X=10.58

UC L=18.48

LC L=2.67

Observation

Mov

ing

Ran

ge

30272421181512963

10.0

7.5

5.0

2.5

0.0

__MR=2.97

UC L=9.71

LC L=0

1

I-MR Chart of Pizza Preparation Time

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Control Limit Calculation

The UCL (Upper Control Limit) and the LCL (Lower Control Limit) are calculated by Minitab using the sample/process data

The control limits approximate +/- 3 standard deviations (99+% of the data)

Here, 99+% of the pizzas are prepared between 2.6 and 18.7 minutes

Be careful not to confuse control limits and specification limits! If a data point appears outside of the control limits, there is less than a 1% chance that this was part of the normal process. Since it is very unlikely that this value occurred by chance, it is called “Special Cause” variation.

Observation

Individ

ual V

alue

30272421181512963

20

15

10

5

_X=10.58

UCL=18.48

LCL=2.67

1

I Chart of Pizza Preparation Time

UCL

X

LCL

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Control Limit Interpretation

Another type of Special Cause variation occurs when there is a predictable pattern in the data

The predictable pattern of the data means the data is not random and that there is an underlying reason for this pattern – a Special Cause

The Western Electric rules are helpful in identifying patterns in the data (these are in the appendix)

Observation

Indiv

idual

Value

272421181512963

20.0

17.5

15.0

12.5

10.0

7.5

5.0

_X=9.87

UCL=15.29

LCL=4.453

3

3

3

3

3

1

3

3

3

1

I Chart of Pizza Prep Time 2

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Exercise: Begin Building an I-MR Chart

Let‟s begin building an I-MR chart for a Pizza Preparation process. Begin by using the 5 Pizza Preparation Time measurements below to start the calculations for a Control Chart on a flip-chart.

Individuals Chart

Plot each individual time measurement

Calculate the Centerline

The centerline on an Individuals chart is the overall average

Verify that the average is 9.6

The control limits will be calculated by a formula in Minitab. They approximate +/- 3 standard deviations of the pizza prep times

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Pizza Exercise

Moving Range Chart

Calculate the ranges

The first range is between points 1 and 2

Range = Max - Min

12 - 7 = 5

The next range is between points 2 and 3

Range = Max - Min

11 - 7 = 4

Continue for the next 2 ranges

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Pizza Exercise (Cont.)

Moving Range Chart

Calculate the Centerline

The centerline is the average of the moving ranges, called R

For these 5 points (4 range calculations), verify that R = 3

The Control Limits will be calculated in Minitab. In this case they approximate +/- 3 standard deviations of the range values.

We expect the Control Limits to be tighter for the Moving Range chart than for the Individuals chart

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Build I-MR Chart in Minitab

Let‟s continue with our exercise:

1. Open the exercise Exercise9.mtw

2. Choose: Stat> Control Charts> Variables Charts for Individuals> I-MR

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I-MR Input Window

3. Double click on C1 Pizza PreparationTime. This places it in the Variables box.

4. Click OK

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Individual and Moving Range (I-MR) Chart

Is our Pizza Prep process in statistical control?Is the process likely to be acceptable to our customers?

Observation

In

div

idu

al

Va

lue

30272421181512963

20

15

10

5

_X=10.58

UC L=18.48

LC L=2.67

Observation

Mo

vin

g R

an

ge

30272421181512963

10.0

7.5

5.0

2.5

0.0

__MR=2.97

UC L=9.71

LC L=0

1

I-MR Chart of Pizza Preparation Time

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Remember the tests that we used in Run Charts? These are used in Control Charts as well.

The additional tests are called the “Western Electric Rules”

They can be found under Stat>Control Charts>Variables Charts for Individuals>I-MR>I-MR Options>Tests

Western Electric Rules

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Point outside of the limit:Control limits are calculated to measure the natural variability of a process. Any point on, or outside, the limit is consideredabnormal and requires investigation.

Run:A “run” is a series of points occurringcontinually on one side of the center line. A “run” of seven points is considered abnormal. Also considered abnormal: 10 out of 11,12 of 14, or 16 of 20 points on oneside of the center line.

Trending:Seven points in a continuous upward or downward direction.

Upper Control Limit

Lower Control Limit

Center Line

Upper Control Limit

Lower Control Limit

Center Line

Upper Control Limit

Lower Control Limit

Center Line

Control Chart Tests

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Approaching the center line (hugging):When most points lie within the center line and 1.5s it is not a controlled state and usually means the mixing of data from different populations. This makes the control limits too wide and stratification of data is usually necessary.

Cycling (periodicity):Any repeated up and down trend is abnormal and requires investigation.

Approaching control limits:2 of 3 points lying outside the2s line is considered abnormal.

Upper Control Limit

Lower Control Limit

CL

Upper Control Limit

Lower Control Limit

CL

LCL

UCL

CL

Control Chart Tests

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Special Causes Are Clues to the Process

A control chart is a guide to improving your process

Take advantage of every clue

Identify and investigate all special causes – they teach us how things affect the process

Some special causes are good!

For example, in our pizza delivery case, a delivery time out of control on the low side would be good. We could investigate this case to try to discover a new best practice.

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Process for Identifying Special Causes

Check all the W.E. rules each time you plot a point

Look across the entire chart

Circle all special causes

Investigate immediately – this is especially important. Do not lose the opportunity to learn as much as possible about the conditions that caused this special cause variability.

Take notes on the investigation

You must investigate and eliminate the special cause!

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Next Steps

Identify assignable causes

Establish that the data are normally distributed without the special cause data points

Circle the special causes

Eliminate special causes from the control limit calculation

Recalculate control limits

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Observation

In

div

idu

al

Va

lue

30272421181512963

20

15

10

5

0

_X=10.69

UC L=18.86

LC L=2.52

Observation

Mo

vin

g R

an

ge

30272421181512963

10.0

7.5

5.0

2.5

0.0

__MR=3.07

UC L=10.04

LC L=0

1

1

1

I-MR Chart of Pizza Preparation Time

New Control Limits

If you can investigateand determine what

caused these „Out of Control‟

points, you can then delete them and recalculate your

control chart limits

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Attribute Control Charts

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Attribute Data Charts

Two categories of attribute data:

Count data (outcomes: 0, 1, 2, 3, 4, 5, etc.)

Good/bad product data (only 2 possible outcomes)

Four common attribute charts:

C and U charts are used for count data of

Errors in the process, either a step in the process or the overall process, or

Defects in the process‟ or steps‟ deliverables

NP and P charts are used for good/bad process, service, or product data (items or process steps that are defective or flawed)

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Which Chart to Use?

C Chart “defect count“

U Chart, “defects / unit”

NP Chart, “no. defective”

P Chart, “proportion ”

Count or Classification(Discrete/Attribute Data)

Defects

Fixedsample sizes

Variablesample sizes

Defective Units

Fixedsample sizes

Variablesample sizes

Discrete/Attribute DataTo select an attribute chart, first choose between plotting defects or defective units. Then decide between fixed or variable opportunity. The variable opportunity charts are used more frequently.

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Deeper into Attribute Charts

Many transactional processes and manufacturing processes only record data as to the service or the products being either bad or good, defective or not defective

There are two sub-families in the Attribute control charts:

If we count defects (usually with any item having more than one opportunity for a defect) we use the C or Ucharts

If the sample size is always the same, use a C-chart. If the sample size varies, use a U-chart.

If we count defective units instead of defects, we use the NP or P charts

If the sample size is always the same, use a NP-chart. If the sample size varies, use a P-chart.

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Charts for Attribute Data

Most of the Attribute Control Charts are identical in interpretation and very similar to create in Minitab

The equations used are slightly different, but still based on the theory we learned with the Xbar Chart

One of the most commonly used attribute charts is the P-Chart which plots Proportion Defective

If you calculated Proportion Defective as your baseline capability metric – this chart is for you!

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P-Chart

P-Charts should be used whenever we are monitoring proportion defective (percentage defective is just another proportion)

Some uses of the P-Chart in transactional applications would be:

Billing errors (proportion of total bills that had errors)

Defective loan applications

Proportion of invoices with errors

Proportion of missing reservations

Defective room service orders

Missing items

Proportion of customers who were dissatisfied with service

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P-Chart Pizza Exercise

Anthony's Pizza wishes to monitor defective pizzas

Each day for a month the cook keeps a count of the number of defective pizzas for that day and also the total number of pizzas that day

Let‟s use the first 5 days data below to start the P-Chart on a flipchart

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P-Chart Pizza Exercise (Cont.)

Calculate the proportion defective

Recall the formula for proportion defective:

In this example:

For the first day:

Calculate the proportion defective for days 2-5

UnitsTotal

UnitsDefectiveofNumberDefectiveProportion

PizzasTotal

PizzasDefectiveofNumberDefectiveProportion

0.021420

9DefectiveProportion

Note: Percentage Defective, in this case, would be 2.1% defective

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P-Chart Pizza Exercise (Cont.)

Next, calculate the center line

The center line is the proportion of Total Defectives (for all samples) to Total Units (for all samples)

Verify that this is 0.019

The Control Limits are calculated in Minitab

The equations are slightly different, but the Control Limits are still calculated from the actual values, predicting the range of 99% of the data

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Minitab - Attributes Control Charts

1. Open worksheet: Exercise9.mtw

2. Choose Stat>Control Charts>Attributes Charts>P

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P-Chart Input Window

3. Double click on C-4 Defective Pizzas. This places it in the Variables box.

4. Place cursor in the Subgroups sizes box and then double click on C-5 Number of Pizzasto move it there

5. Click OK

Note: Minitab calculates the proportion defective for us. We enter the defective units in the Variable box. Then we enter the total units over

that time period in the Subgroup sizes box.

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P-Chart

Note: Minitab recalculates the control limits every time the subgroup size changes.

To get a straight line, you can enter a constant value under “Subgroup size.”

In this example, the best constant would be the average of the “Number of Pizzas.”

What are your thoughts around our defective pizzas?

Sample

Pro

po

rtio

n

30272421181512963

0.05

0.04

0.03

0.02

0.01

0.00

_P=0.01932

UCL=0.03689

LCL=0.00174

1

P Chart of Defective Pizzas

Tests performed with unequal sample sizes

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Exercise: Create a Control Chart

Now Anthony's Pizza wants to investigate sales history and billing errors for the same month

In teams, continue with Exercise9.mtw. Use an I-MR Chart to monitor sales for the month.

Use a P-Chart to observe the proportion of defective bills

Prepare to teach back to the class on your findings

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Quick Review - Control Chart Reminders

There are several types of control charts:

Determine type of data: continuous or attribute

Be clear on the purpose and value you wish to gain from the chart

Control limits are derived from process data

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Control Chart Uses and Benefits

Demonstrate stability and predictability of a process over time

Range of variation within the “control limits”

Distinguish between common vs. special cause variation

Provides more information than Run Charts

Can be used to demonstrate changes in performance

Provide a common language for process performance

Offer early warning of problems

BUT…..

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Control Chart Challenges

Must use correct type of chart for the data

Must meet normality and independence assumptions

Non-normal, continuous data must use x-bar chart to meet normality requirement

Control limits vs. customer requirements

Remember that the control limits are providing the Voice of the Process

We need to look at specification limits to see the Voice of the Customer

A process “in control” may be ineffective, inefficient, or both!

Control charts require effective, ongoing data collection. To be effective for determining root causes of special cause variation, they must be reacted to immediately!

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Steps in Control Charting

Select process characteristic to control, the key x or Y

Collect data and calculate appropriate statistics

Assess data distribution normality

Construct preliminary control charts

Establish control (find and eliminate special causes)

Construct final control charts

Establish stability (find and reduce common causes)

Use for ongoing control purposes

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What Do Control Charts Tell Us?

When the process mean has shifted

When process variability has changed

When special causes are present

Process is not predictable

Opportunity to learn about the process

When no special causes are present

Process is predictable

No clues to improvement available; may need to introduce a special cause in order to understand cause and effect, and then to effect a change

Control charts tell you when, not why!!

Observation

In

div

idu

al

Va

lue

30272421181512963

20

15

10

5

0

_X=10.69

UC L=18.86

LC L=2.52

Observation

Mo

vin

g R

an

ge

30272421181512963

10.0

7.5

5.0

2.5

0.0

__MR=3.07

UC L=10.04

LC L=0

1

1

1

I-MR Chart of Pizza Preparation Time

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Process Control Chart Template

The current baseline delivery time is stable over time with both the Moving Range (3.22 days) and Individual Average (29.13 days) experiencing common cause variation

255 data points collected with zero subgroups, thus the I&MR control chart selected

Observation

In

div

idu

al

Va

lue

2442171901631361098255281

40

35

30

25

20

_X=29.13

UC L=37.70

LC L=20.56

Observation

Mo

vin

g R

an

ge

2442171901631361098255281

10.0

7.5

5.0

2.5

0.0

__MR=3.22

UC L=10.53

LC L=0

I-MR Chart of Delivery Time

Required As Applicable- Example -

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Exercise: Prepare a Control Chart

Objective

Create control charts for the GGA's Budget Department

Instructions

Identify Primary Y metric

Determine best control charts to use

Run proper control chart for that data

Time = 15 Minutes

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Takeaways

Control limits are calculated from a time series of the characteristic we are measuring

Different formulas are available, depending on the type of data

Control limits should not be recalculated each time data are collected

The control limits are a function of the sampling and subgrouping plan

Variation due to "assignable cause" is often the easiest variation to reduce/eliminate

Control limits are not related to standards! Nor are they specifications! Control limits are a measure of what the process is doing/has done. It is the present/past tense, not the future (what we want the process to do or what it has the potential to do)

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What other comments or questions

do you have?

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References

Wheeler, Donald J. & Chambers, David S., Understanding Statistical Process Control, Second Edition, SPC Press, Knoxville Tennessee, 1992

Pruit, James M. & Snyder, Helmut, Essentials of SPC in the Process Industries, Instrument Society of America, 1996

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APPENDIX

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Western Electric Rules

1. One point beyond Zone A

Detects a shift in the mean, an increase in the standard deviation, or a single aberration in the process. For interpreting Test 1, the R chart can be used to rule out increases in variation.

2. Nine points in a row in Zone C or beyond

Detects a shift in the process mean

3. Six points in a row steadily increasing or decreasing

Detects a trend or drift in the process mean. Small trends will be signaled by this test before Test 1.

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Western Electric Rules (Cont.)

4. Fourteen points in a row alternating up and down

Detects systematic effects, such as two alternately used machines, vendors, or operators

5. Two out of three points in a row in Zone A or beyond

Detects a shift in the process average or increase in the standard deviation. Any two out of three points provide a positive test.

6. Four out of five points in Zone B or beyond

Detects a shift in the process mean. Any four out of five points provide a positive test.

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Western Electric Rules (Cont.)

7. Fifteen points in a row in Zone C, above and below the center line

Detects stratification of subgroups when the observations in a single subgroup come from various sources with different means

8. Eight points in a row on both sides of the center line with none in Zone C

Detects stratification of subgroups when the observations in one subgroup come from a single source, but subgroups come from different sources with different means