Statistical Process Control - AFK

7/31/2019 Statistical Process Control - AFK

1/32


2/32

A.Khan 2

CONTENTS

Page

Summary..................................................................... 2

Module Description.................................................. 3

Learning Sequence Stage 1..................................... 4

Introduction to Statistical Process Control .................. 5

Variability Common and Special Causes ................ 8

Quality Control Charts.............................................. 10

Quality Control Charts for Average and Range....... 12

Stabilization of the Process ........................................ 15

Putting Quality Control Charts into Practice................ 16

Capability of the Process............................................. 17

SPC: Questions and Answers ....................................

18

Exercises..................................................................... 22

Notes........................................................................... 25

Theoretical Self-Evaluation.................................. 26

Answer Sheet..............................................................

29

Bibliography................................................................. 31


3/32

A.Khan 3

SUMMARY

Participants

FacilitatorMSCManager

PrerequisitesStatistical Thinking

DurationTheory: 4 hoursPractice: none


4/32

A.Khan 4

MODULE DESCRIPTION

Objectives

Understand and be capable of transmitting the procedures of the StatisticalProcess Control. Get to know control charts, their interpretation, and purpose.Understand how the statistical control process can bring benefits towardimproving the quality of Gerdau Ameristeel products and processes.

Learning Sequence Page

1- Introduction to SPC

1.1- Present the meaning of SPC and its objectives. Reviewconcepts of variability, common causes, and specialcauses.

5 to 9

1.2- Present the importance of using SPC to identify andeliminate special causes. Present the idea of qualitycontrol charts and explain the operation and analysis ofthe quality control charts according to the variables ofaverage and range.

10 to 14

1.3- Practice filling in the quality control charts and reinforcethe understanding of how SPC works.

15 to 16

1.4- Present the concept of capacity of the process and themain questions and answers concerning SPC.

17 to 21

Criteria of Evaluation

After having studied all of the content presented and correctly finished all ofthe exercises given, you will take a Theoretical Self-Evaluation (pages 26 and28). Following that, you will take the Theoretical Evaluation in which theminimum passing grade is 70%.

If 70% is not reached, you will have to go over the learning stages you hadgreater difficulty. If you need to, ask the Area Manager for help.


5/32

A.Khan 5

LEARNING SEQUENCE

Learning Stage 1

Introduction to SPC

Activities Resources1. Understand the meaning of SPC and its

objectives.1. Module SPC

Pages 5 to 7.2. Study the concepts of variability,

common causes, and special causes.2. Module SPC

Pages 8 and 9.

3. Understand the usefulness of a qualitycontrol chart, how to fill one out, and toanalyze it.

3. Module SPC Pages 10 and 11.

4. Understand quality control charts for theaverage and for the range.

4. Module SPC Pages 12 to 14.

5. Understand the concept of stabilizationof the process.

5. Module SPC Page 15.

6. Practice filling in quality control charts.6. Module SPC

Page 16.7. Understand the basic notions of

capacity of process.7. Module SPC

Page 17.8. Know the answers to the main

questions associated with SPC.8. Module SPC

Pages 18 to 21.

9. Do the Exercises.9. Module SPC

Pages 22 to 24.

10. Do the Theoretical Self-Evaluationthat covers the Learning Stage of this

module.

10. Module SPC Pages 26 to 30.

11, Take the Theoretical Evaluation thatcovers the Learning Stage of this module.

11. With the help of the manager,a grade of at least 70%must be reached.


6/32

A.Khan 6

INTRODUCTION TO STATISTICAL PROCESS CONTROL

Statistical Process Control is a monitoring system that uses samples takenfrom a process with the objective of checking for the occurrence of specialcauses, which are causes that can compromise the quality of the productproduced.

Once the special causes are identified, we can try to solve them, continuallyimproving the quality of the product.

What does SPC stand for?

In the area of quality, the acronymSPC stands for S: Statistical,P: Process C: Control.

SPC Statistical:

The gathering and analysis of data is done using statistical concepts. Whilethe characteristic under study behaves according to what is expectedstatistically, the priority becomes production. When it is not within what isexpected, then I need to act in order to solve the problem.

Action SpecialCauses

SpecialCauses

Common

CausesAverage

Upper Control Limit = 41.1362

Lower Control Limit 8.0593

Central Line 16.7857

Special Causes


7/32

A.Khan 7


The graph above is an example of a quality control chart. The qualitycontrol charts help you visualize the presence of special causes that areaffecting the performance of the process. On the horizontal line, the numbers2, 3, 4, and 5 represent the samples taken from the process from time to time,while on the vertical line is the characteristic that is being monitored, whichcan be temperature, diameter, ovalization, quantity of defects, etc.

Let's suppose that the variable that is being monitored is temperature. Thecentral line is at 20. This means that, on average, this characteristic is 20.The red lines are the control limits that are calculated according to statisticalprocedures. These limits indicate the natural behavior of the averagetemperature. While the average temperature remains within these limits, theprocess is behaving naturally.

However, when the average temperature goes outside of the control limits,

this means that we are facing some form of a special cause and actionsshould be taken to solve the problem.

So, SPC indicates when corrective actions should be taken or improvementsmade, serving as a base for the continual improvement of the process,reducing wastes, scrap, and rework.

When you reduce the special causes one by one, this makes the processmore stable, lowering the number of defects and the end result is lessstress.

SPC Process

Process is the set of equipment, people, and procedures needed for theproduction of goods or the provision of services. Examples of process:process of receiving raw material, rolling process, thermal treatment process,shipping process, etc.

When we speak of processes, the focus should be continual improvement.Actions should be taken to correct eventual deficiencies in the process. Thisway, slowly but surely, the improvements will make the process more robust,free of defects.


8/32


SPC Control:

The word control refers to themonitoring of the process, which is acontinuous activity of gathering andanalyzing the data that characterizesthe performance of the process.

This monitoring allows the process to be controlled, which means thatwhenever necessary, actions can be taken in order to maintain the expectedperformance. The control is done by using samples taken from time to time.With each sample taken from the production, important characteristics can bechecked, such as temperature, diameter, ovalization, or the quantity of defectsobserved in that sample.

What are the objectives of the SPC?

In simple terms, the SPC's objective is to provide a statistical signalwhenever there is evidence of the presence of special causes.

Because of these signals, the team can work towards eliminating the specialcauses. This reduces the variability present in the process. The reduction ofthe variability will bring reductions of rework and of scrap. Therefore, thequality of the process increases and at the same time costs are lowered.

As you can see, speaking in general terms, the objectives of the SPC are toimprove the product's quality and to reduce manufacturing costs.

What is a characteristic of quality?

They are variables (levels measured by an instrument) or attributes (result ofcounting or percentages) that reflect the quality of the process.

For example, for the rolling process, to check if the rolling was done correctly,we should evaluate some characteristics of quality, such as: size, ovalization,length, overfill, fin, folds, etc.

Now let's make sure you got it ...Answer key on page 29.

Give the name of a process that you are familiar with and list its mostimportant characteristics of quality.

Process: _____________________________________________________

Variables: _____________________________________________________

Attributes: _____________________________________________________


9/32

A.Khan 9

VARIABILITY COMMON AND SPECIAL CAUSES

What is variability?

The variability is represented by the differences (variations) that occur, forexample, among rolled bars. Due to variability, the bars are not exactlyidentical.

Variability (or variation) is always present in all of the processes. Therefore,the individual measurements are different one from the other, but in a group

they tend to form a standard. Many times this standard is similar to a modelthat we call a "Normal Model".

averageaverage-3 deviations

average+3 deviations

Unexpectedbehavior

(SPECIAL)

Expectedbehavior

(COMMON)

When a variable stays within the normal model, 99.73% of the observationswill be within its natural limits, which means the average plus or minus threestandard deviations.

Thus, the expected is that the measurements stay within these natural limits.Any item outside of these limits is most likely due to special causes ...

The SPC works based on this logicsmallvariations are acceptable since this is a part of anyprocess. However, large variations, out of thenatural standards of the process, are immediatelydetected and require corrective action.


10/32

VARIABILITY COMMON AND SPECIAL CAUSES

What are special causes again?

They are causes of variability whoseeffect cannot be foreseen, because they do

not follow a known rule. They cause greatvariations in the result of the process. Hereare some examples of special causes:

Operator without training for the task

Errors in machine set up

Problems with the equipment or with the tools

Defective raw material, etc.

00

10

20

15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34

Standbytime

Special Causes

And what are common causes?They are the various causes of variation thatare always present. For example, smalldifferences in the chemical composition of theraw material, small variations in the processtiming, variations in temperature and humidity ofthe day, variations in the temperature anddilatation of the rolling cylinders, etc.

Common Causes!!!

In order to control the process, it is important to investigate its causes. Thefirst step is to distinguish between common causes and special causes.

Indicates the presence of special causes


11/32

QUALITY CONTROL CHARTS

What is the tool that we can use to distinguish common causes fromspecial ones?

For monitoring the processes, SPC uses Quality Control Charts. TheQuality Control Charts indicate up to what point we can consider a variation asa result of common causes or special causes.

Special Causes

How do we calculate the control limits?

The lines of the graph (control limits) are calculate in the following way:

Upper control limit: average + 3 deviations Central line: average Lower control limit: average - 3 deviations

An example:

Suppose the average temperature of a water tank is being monitored. Weknow that the average level is 40 degrees Celsius and that the standarddeviation is 5 degrees. In this case, the control limits for the averagetemperature are the following:

Upper control limit: 40 + (3 x 5) = 55 degrees

Central line: 40 degrees

Lower control limit: 40 (3 x 5) = 25 degrees

So, the top line of the graph would be 55, the central line 40, and the bottomlimit 25, which is demonstrated in the graph below:

30

40

50

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Average

Top Control Limit = 54.8535 Central Line = 40.Bottom Control Limit = 25.1465


12/32


13/32

A.Khan 13

CONTROL CHARTS FOR AVERAGE AND RANGE

Quality control charts for variables are those that we monitorcharacteristics that can be measured. For example, an operator can bemonitoring the size of rolled parts. He is gathering samples of 5 parts andchecking the average. For the first sample, the average was 48.13, then

48.17, 48.09, 48.15, 48.15, 40.18, etc.

There are various types of quality control charts for variables. The ones thatare known the most are the limits for averages and ranges. Average is written

with the symbol x (read: X bar) and range with an R.

Now, let's take a look at an example of a data gathering spreadsheet andquality control charts for average and range.

QUALITY CONTROL CHARTS FOR x and R

Name of part Retainer Specifications 30 to 90 microns

Part number 9983-5 Instrument Micrometer

Operation Top fold Sample/Freq. 5 / 2 hours

Machine 030 Unit Microns

Characteristic Cracks Level No. 01

Date 6/3 7/3 8/3

Hour 8 10 12 14 16 8 10 12 14 16 8 10 12 14 16

Operator A A A B B A A A B B A A A B B

1 65 75 80 65 80 75 80 70 85 65 75 85 70 70 75

2 70 70 70 65 60 70 75 65 85 65 60 65 75 65 80

Measur. 3 75 80 70 65 80 60 65 75 75 65 75 75 75 85 85

4 60 90 80 80 80 85 75 65 65 80 85 75 70 60 80

5 80 70 80 65 75 75 70 85 80 60 90 80 70 75 90

Total 350 385 380 340 375 365 365 360 390 335 385 380 360 355 410

Average 70 77 76 68 75 73 73 72 78 67 77 76 72 71 82

Range 20 20 10 15 20 25 15 20 20 20 30 20 5 25 15


14/32

A.Khan 14


Quality control charts for the average:

60

70

80

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Average

Upper Control Limit = 84,5716 Central Line = 73,8

Lower Control Limit = 63,0284 Special Causes

Quality control charts for the range:

0

10

20

30

40

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15

Range

Upper Control Limit = 39,468 Central Line = 18,6667

Lower Control Limit = 0 Special Causes

Let's take a look at an example...

EXAMPLE

An operator is monitoring the production of rolls of wire with a nominal weightof 30.0 kg. From each production order a sample of four rolls is taken and an

evaluation of weight is done.For the first sample, the four measurements were the following: 31.0 30.930.8 30.2 kg. For this sample and for the subsequent ones, calculate theaverage and range and make sure that they are within the quality controllimits.


15/32

A.Khan 15


Average =measuresofnumber

measuresofSum

Average =4

230830930031 ,,,, +++ = 31.75

Central Tendency (average)

Range = Maximum Minimum

Range = 31.0 30.2 = 0.8 Dispersion (variability)

The control charts make it possible to evaluate if the process is understatistical control and point out the presence of special causes in orderto be able to take corrective actions.

If only common causes are present, the averages should be maintained withinthe quality control limits, as occurs with the average weight of the rolls:

30.0

30.5

31.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Average

UCL 31.1516 CL = 30.6138 LCL 30.0759

Average weight

Variations due to onlycommon causes.

Points outside the quality control limits indicate the presence of specialcauses, as can be seen in the limits of ranges.

0.0

0.5

1.0

1.5

2.0

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

Range

UCL = 1.7116 CL = 0.75 LCL = 0

Range

Detected the presenceof a special cause.

Sample 16 points out the presence of a special cause because the dispersionobserved was greater than naturally was expected. The team needs to takeaction in order to correct the problem (identify the cause and take action).


16/32

A.Khan 16

STABILIZATION OF THE PROCESS

If the special causes are eliminated, the subsequent averages willcontinue to stay within the quality control limits. This is the expectedbehavior when only the common causes are present.

In this case, we can say that the process is stable or that it is under statisticalcontrol. As can be seen, the quality control chart is an important tool for thestabilization of the processes.

How the SPC works on a daily basis

Monitoring is a day-to-day task (routine). Data continues to be gathered andare plotted on the quality control chart. While only common causes arepresent, the expected result is that the plotted points continue within thecontrol limits.

One point outside of the control limits is an indication of the probablepresence of special causes and should be investigated. The special causesshould be identified and eliminated. They represent an opportunity for

improvement.

If the actions are being carried out, the process will improve its performance,as illustrated in the following graph:

Process outside

static control

Process within

static control

Actions driven by Quality Control Charts

Sample

X

31

35

35 40 45 50 55

Sample

31.8

35.2

15 20 25 30 35


17/32

A.Khan 17

PUTTING QUALITY CONTROL CHARTS INTO PRACTICE

SPC = Data + ACTION

SPC is based on facts and data.Action is only taken when there arereasons to do so, which is when thebehavior of the process deviates fromthe natural.

Action should take place in two steps: First the causes of the problem areidentified and then action is taken on these causes. The action can be any of

the following: Change the work method.

Standardize activities.

Give training in critical activities.

Do maintenance or improvement of equipment.

Change the raw material used, etc.

A point outside the control limits requires ACTION.Consider some of the causes that could haveoriginated the problem. Once the causes areidentified, come up with a solution!

If the solution is within your reach ...

Solve the problem.

If the solution is not within your reach ...

Form a team to analyze the problem, and

notify your manager.

If you would like to practice now with quality control charts, go to page 22 anddo the exercise there.

Then return to page 17 in order to finish this Learning Stage.


18/32

A.Khan 18

CAPABILITY OF THE PROCESS

Evaluation of the Capability

After eliminating all of the special causes,

the process is stable. Then we canevaluate the real capability of theprocess, comparing the variability that itpresents with the specifications given.

In the case of a stable process, the variability that it presents is due to onlycommon causes. If this variability is lower than the range of the specifications,we say that the process is capable.

For example, the characteristic of interest in a process can be surfacehardness. If all of the levels of surface hardness are within the specificationlimits, then this process is capable.

Remember that the specification limits are defined according to the needs ofthe customer. For example, in a certain process, the specifications of thecustomer may be 60.33 0.64 mm.

So, the lower specification limit is LSL = 60.33 - 0.64 = 59.69

And the upper specification limit is USL = 60.33 + 0.64 = 60.97

0.00

0.01

0.02

0.03

0.04

0.05

0.06

30 40 50 60 70 80 90

f(x)

x: Size

Limits of SpecificationTarget

Distribution of Size

Capable Process

The variability is small comparedwith the specification limits and the

production of defective productspractically does not occur.

0.00

0.01

0.02

0.03

0.04

0.05

0.06

30 40 50 60 70 80 90

f(x)

x: Size

Limits of Specification

TargetDistribution of Size

Incapable Process

Excessive variability compared withthe specification limits and thereare many defective units.

0.00

0.01

0.02

0.03

0.04

0.05

0.06

30 40 50 60 70 80 90 100

f(x)

x: Size

Limits of SpecificationTarget

Distribution of Size

Incapable Process

Acceptable variability, but theprocess is not centralized and alsosome defective units may beproduced.


19/32

A.Khan 19

SPC: QUESTIONS AND ANSWERS

What is the difference between SPC and

Inspection?

SPC is different from inspection. Inspection works with a great quantity ofparts (sometimes 100%) and has the objective of making sure that nodefective parts reach the customer. The focus is the detection of defects.

SPC, on the other hand, focuses actions on special causes, which put inanother way are the origin of the problem. This happens because the datais gathered during the process, exactly at the time that the problem happens.

This way you can immediately identify what is happeningsome problem withthe machine, with the raw material, in the procedure, etc. So the chance tosolve the problem is much greater.

During how long does SPC operate?

SPC uses small samples collected at regular intervals. The idea is not tosolve all of the problems in the first day. However, due to the regularity ofcollecting the data, the existing problems will be detected sooner or later.

SPC operates over a longer period of time.

The special causes go being identifiedand eliminated one by one, over time,with patience and persistence.

And finally, SPC ends up doing somethings that apparently was not its originalobjective, such as:

a process free of defective units

that fully meets the specifications

and whose performance does not depend on the activities of inspection.


20/32

A.Khan 20


How can SPC help me?

I learn about quality.

I become a better-trained professional. Quality and productivity increase.

The chance of receiving awards forperformance is greater.

Also, if the company grows in competitiveness,

The jobs are more secure.

What are the results from SPC

By using SPC, a problem on the production line can be identified at themoment it occurs. It is not necessary for the product to reach the end of the

production line to realize that something is wrong.

SPC makes it possible for the operators themselves to control the process. Ifthe solution is difficult, the facilitator and/or manager can be called in to help.

The correct use of the control limits gives a clear distinction between commoncauses and special causes. This way, it serves as a guide for local actions ormanagerial actions.

SPC helps the process to reach a high quality level, a low cost per unit,consistency, and results can be foreseen.

Has SPC come to control people?

No: SPC is to control the process!

People want to do things right. If they are doinganything wrong it is due to lack of training or

lack of clear standards.


21/32

A.Khan 21


Who is the base of the SPC?

The operators!

The monitoring of the process iscarried out by the operators. Theoperators are the ones that initiate theimprovement actions. The success ofthe SPC depends on the operators.

What is the biggest change thatSPC brings?

A change in culture.

The focus ceases to be on inspectionand begins to be on improving theproduction process. The operatorstake on the most important role ofmonitoring and Quality Assurance.

What should I write down on thespreadsheet?

You should write down exactly what ismeasured. Nothing more, nothing less.

To hide defects is to take away theopportunity for the team to solve theproblem.

To write down defects that do not exist is

to force the team to investigate ghostcauses.


22/32

A.Khan 22


Is the presence of a defect bad?

No. It is neither good nor bad.

The presence of defects should beseen as an opportunity to improve.

SPC will help identify the specialcauses.

The elimination of the special causes,one by one, will drive the process to ahigher level of quality.

Remember

SPC does not want to control people. SPC does not want to inspect production.

SPC provides data to guide the improvement actions of the process.

SPC = Data + Improvement actions

SPC = More reliable process

The success of the SPC depends on three key factors: The operators monitoring the

process and firing off theimprovement actions.

The actions of the quality supportteam that slowly but surely goeliminating the special causes.

Time for the improvement process tooccur gradually.


23/32

EXERCISES

Let's see if you got it...

With the numbers given below, calculate the average and range, put thepoints on the graphs, and check to see if there are any points out of control(special causes).

The data below refers to the length of bars, measured after being cut. Fromeach batch processed, 4 bars were measured. The control limits for the chartof averages are [661; 673] and for the chart of ranges [0; 18].

1 2 3 4 5 6 7 8 9 10 11 12

Meas. 1 666 669 663 667 668 662 667 669 669 665 675 664

Meas. 2 659 664 663 661 676 672 668 672 668 673 662 676

Meas. 3 670 673 663 668 675 672 662 668 667 666 673 668Meas. 4 669 670 665 662 679 666 661 666 665 669 666 660

Average 666,0 669,0

Range 11 9

1st) Calculate the average and range of sample 1:

( ) 0,6664

669670659666=

+++=XAverage

( ) 11659670 ==RRange

2nd) Plot the first point on each graph:Chart of averages Chart of ranges

655

660

665

670

675

1 2 3 4 5 6 7 8 9 10 11 12

Samples

Length

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10 11 12

Samples

Length

3rd) For the next data gathering time, repeat the operation for sample 2:

( ) 0,6694

670673664669=

+++=XAverage

( ) 9664673 ==RRange


24/32

A.Khan 24

EXERCISES

4th) Put the second point on each graph and draw a straight line to join thepoints:

655

660

665

670

675

1 2 3 4 5 6 7 8 9 10 11 12

Samples

Length

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10 11 12

Samples

Length

5th) Make sure that no point is outside of the control limits (red lines). If thishappens, then there are special causes that must be identified and dealtwith. If not, if all points are within the control limits, than the productioncan continue on normally.

Now continue to fill in the graph and see the results on the answer sheet onpage 29.

655

660

665

670

675

1 2 3 4 5 6 7 8 9 10 11 12

Samples

Length

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10 11 12

Samples

Length


25/32

A.Khan 25

EXERCISES

1) With the numbers given below, calculate the average and range forsamples 12, 13, and 14. Are there any special causes? The control limits forthe average are [80.7; 84.3] and the control limits for the ranges are [0.0; 6.6].

Sample 12 Sample 13 Sample 14Obs. 1 81 80 82Obs. 2 83 79 84Obs. 3 83 83 83Obs. 4 82 82 82Obs. 5 84 82 84

2) Check the correct alternative:At first instance, what should guide the SPC actions?

a. ( ) Not produce any defective units.b. ( ) Meet the specifications.c. ( ) Eliminate the special causes.

3) Check the correct alternative (multiple choice):A stable process is one where:

a. ( ) All of the levels measured are within the control limits.b. ( ) All of the levels measured are within the specifications.c. ( ) There are no special causes causing variability.d. ( ) There are no common causes causing variability.

4) Check the correct alternative (multiple choice):

A capable process is one where:

a. ( ) All of the levels measured are within the control limits.b. ( ) All of the levels measured are within the specifications.c. ( ) There are no special causes causing variability.d. ( ) There are no common causes causing variability.

5) Mark True or False:

a. ( ) The presence of defects should be seen as an opportunity to improve.b. ( ) SPC provides data to guide the improvement actions of the process.c. ( ) SPC will only bring results to the company if actions are taken on the

special cases identified on the control graphs.

d. ( ) SPC helps to control the people and make sure that they areworking during the entire shift.


26/32

A.Khan 26

NOTES


27/32

A.Khan 27

THEORETICAL SELF-EVALUATION

1) Imagine that you are controlling the thickness of the zinc layer on theprocess of wire galvanization. Considering the situations below, mark whichof them possibly are due to common causes (CC) and which ones are due tospecial causes (SC):

a. ( ) A displacement of the scrapping mechanism has occurred, causinga decrease in the thickness.

b. ( ) The line was not adjusted as specified on the technical guide,causing an increase in thickness.

c. ( ) Variations in the temperature of the zinc tank caused smalldifferences in the thickness levels.

d. ( ) Small variations in the time of the process generated differences inthe levels of thickness.

2) Mark True or False for the sentences below:a. ( ) SPC works with samples that are periodically taken from production.

By using these samples, it is possible to check the quality of what isbeing produced.

b. ( ) The gathering and analysis of the data for the SPC is done usingstatistical concepts. While the characteristic being studied iswithin the limits calculated statistically, the priority is production.

c. ( ) The control charts help to verify the presence of special causes.d. ( ) We should learn to accept the special causes because they will

always be present in all of the processes.

3) Calculate the average for the 10 samples presented below. Then plotthese averages on the control chart and answer if there is some evidence of aspecial cause.

SamplesObs.

1 2 3 4 5 6 7 8 9 10

Obs. 1 170 170 168 168 174 163 168 168 168 168

Obs. 2 171 168 171 166 172 171 170 167 169 171

Obs. 3 169 168 167 169 172 174 169 167 166 169

Average


28/32

A.Khan 28


165.0

170.0

175.0

1 2 3 4 5 6 7 8 9 10

Samples

Averages

4) Calculate the range for the 10 samples presented below. Then plot these

ranges on the control chart and answer if there is some evidence of a specialcause.

SamplesObs.

1 2 3 4 5 6 7 8 9 10

Obs. 1 418 418 414 416 424 413 416 416 418 415

Obs. 2 420 417 414 413 422 420 417 420 415 420

Obs. 3 417 416 414 417 421 420 413 417 416 416

Range

0

3

6

9

12

1 2 3 4 5 6 7 8 9 10

Samples

Range


29/32

A.Khan 29


5) Check which of the processes below can be considered to be capable. Thevertical lines represent the lower specification limit, the nominal level, and the

upper specification limit.

a. ( )

b. ( )

c. ( )

d. ( )

e. ( )

f. ( )

g. ( )

h. ( )


30/32

A.Khan 30

ANSWER SHEET

EXERCISES

Answers

PG. 7 Process: Manufacturing of steelVariables: chemical composition of the steel, tapping temperature, etc.Attributes: number of heats in sequence, % of off-specification heats

PG. 22

Chart of averages Chart of ranges

650

655

660

665

670

675

680

1 2 3 4 5 6 7 8 9 10 11 12

Samples

Length

0

5

10

15

20

1 2 3 4 5 6 7 8 9 10 11 12

Samples

Length

Answers

PG. 24 1. Averages = 82.6 81.2 83.0Ranges = 3.0 4.0 2.0There are no special causes of variation.

2. C

3. a and c

4. a, b, and c

5. T T T F


31/32

A.Khan 31

ANSWER SHEET


1) SC, SC, CC, CC

2) T, T, T, F

3) One special cause sample 5 4) No special causes

165.0

170.0

175.0

1 2 3 4 5 6 7 8 9 10

Samples

Ave

rages

0

3

6

9

12

1 2 3 4 5 6 7 8 9 10

Samples

Ranges

5) Processes b, c, d, and h.


32/32

BIBLIOGRAPHY

[1] Fundamentals of Managerial Development Managing the Day-to-DayRoutine Tasks Vicente Falconi

[2] (Fundamentals of Managerial Development Basic Statistical Tools forManagerial Processes Maria Cristina

[3] Statistics Applied to Administration Stevenson, W. J[4] Statistics - Costa Neto, P. L. O.

[5] Statistical Methods for Improving Quality Kume, H.

[6] Understanding Variation Donald Wheeler

Documents

Statistical Process Control - AFK