ISPE OFFICE SPACE ANALYSIS - FARMASI INDUSTRI...35. Short-Term vs Long Term Sigma. Long-Term Sigma. This is the variation is due to both common and special causes. This variation is

Statistical MethodJakarta, 29-30 March,2016

Speaker: Heru Purnomo

1

FITHRUL FARMASIINDUSTRI.COM

Module Outline

• PART 1: Introduction• PART 2: Capability Studies• PART 3: Cp, Cpk and Six Sigma• PART 4: Use of Capability Studies• PART 5: Technical Considerations• PART 6: Control Charts • PART 7: Use of control chart• PART 8: Overview of Statistic Application


PART 1:

Introduction


What is Statistical Process Control?

• A tool that allows us to manufacture products per our customer’s requirements on a consistent basis. This is achieved by preventing defects at each stage of the manufacturing process.

• By itself will not insure our products, processes and services meet our customer’s expectation. Therefore, we assume that all initial work has been done to meet those requirements such as:

– Establishment of specification– Process Characterization– Standards and SOPs– Validation– Training


Where should we use SPC?

• Use as a Method for Preventing Defects

• Use With the Assumptions that Requirements Have Already Been Established: – Customer– Process– Product


So, how do we prevent defects, and build products, processes and provide services with consistently good quality?

To answer this question, we will use a hypothetical filling operation to illustrate various methods of preventing defects.


How Does One Prevent Defects?

?


Two Possible Causes

Cap Fell Off Due to Low

Removal ForceCap Never Put

Onto Vial


CAP NEVER PLACED ONTO VIAL

• This is an Error in the form of an Omission.

• Errors are Prevented by Mistake Proofing.

• Mistake Proofing means ensuring that the defects either cannot occur or cannot go undetected.

ReferenceShingo, Shigeo (1986). Zero Quality Control: Source Inspection and the Poka-yoke System. Productivity

Press, Cambridge, Massachusetts.


Low Removal Forces

• Removal Force is Affected by Many Factors.

• Having low removal forces is an Optimization (Targeting) and Variation Reduction problem.

• Low removal forces are prevented by identifying and controlling the key inputs and establishing proper targets and tolerances.

ReferenceTaylor, Wayne A. (1991). Optimization and Variation Reduction I Quality. McGraw-Hill, New York and

ASQC Quality Press, Milwaukee.


Optimization & Variation Reduction (O.V.R)

Lower Spec Limit

Target

Upper Spec Limit


Typical O.V.R ProblemsLarger the Better

Lower Spec Limit

TargetSmaller the Better Upper

Spec Limit

• microbial level

• particulate level

• contamination level

Closer to the target the Better

TargetLower Spec Limit

Upper Spec Limit

• Vial fill volume

• Potency, Assay


Two Approaches to Preventing Defects

• Mistake Proofing

• Optimization and Variation Reduction


Reducing Variation

“ If I had to reduce my message for management to just a few words, I’d say it all had to do with

reducing variation.”

W. Edward Deming


Tools for SPC

• SPC provides two tools for reducing variation:1)Control Charts2)Capability Study

• The primary tool for managing variation is the capability study.

• An effective program for reducing variation must also incorporate many other tools including: Design Experiments Variation Decomposition Methods Taguchi’s Methods


Statistical Variation

The differences, no matter how small, between ideally identical units of product.

2.3 ml

DIFFERENCES

0.9 ml 1.4 ml


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Displaying Variation

24.023.222.421.6

6

5

4

3

2

1

0

Cap Removal Force in PSI

Num

ber

Mea

s ure

d

Histogram of Removal Force of the cap cover of Sterile Injection


The Bell-Shaped Curve

24.023.222.421.6

Normal Curve

We use the Normal Curve to Model systems having expected outcomes or goals….


The Standard Normal Curve

•Contains an Area equal to One

•Corresponds to 100% of ALL possible Outcomes in a Stable System.

•Has a Mean = 0, and SD = 1

μ

σ

-3Standard Deviations from the Mean

31-1-2 2

• Total Area = 1


A STABLE PROCESS Total Variation


AN UNSTABLE PROCESS • Total Variation


A CAPABLE PROCESS

NOT CAPABLE

CAPABLE

Spec Limits


Objective of SPC

To consistently produce high quality products by achieving stable and capable processes.


WHY REDUCE

VARIATION?


Reducing Variation Reduces Defects

UpperSpecLimit

Lower Spec Limit

UpperSpecLimit

GOOD PRODUCT

GOOD PRODUCT

•Defective Product •No Defective Product

Lower Spec Limit


Reducing Variation Widens Operating Windows

Lower Spec Limit

UpperSpecLimit

Lower Spec Limit

UpperSpecLimit

Initial Operating Window Wider Operating Window


Bad Product

Reducing Variation Improves Customer Value

Lower Spec Limit

Bad Product

Target

GOOD PRODUCT

LOSS

$10

$20

$0

Lower Spec Limit

UpperSpecLimit

Target

LOSS

$10

$20

$0

•Taguchi’s Loss

Loss equals value

Upper Spec Limit


Better Management• Provides facts on process performance to allow: Prioritized improvement projects Tracking progress Demonstrating results

• Provides data on process capability required in product design.

• Better management of suppliers.


Maximize Process Capability• Replace existing equipment only if necessary.• Improve capability make new product feasible.


Benefits of SPC• Fewer Defects• Wider Operating Windows• Higher Customer Value• Better Management• Maximize Process Capability


PresenterPresentation NotesGive them the product or serviceEx. Maintenance20 minutes for exercise and discussion

PART 2:Capability Studies


Variation Reduction Tools

• There are many tools that help to achieve stable and capable processes: Scatter Diagrams Screening Experiments Multi-Vari Charts Analysis of Means (ANOM) Response Surface Studies Variation Transmission Analysis Component Swapping Studies Taguchi Methods Control Charts & Capability Studies


Capability Study • Determines if a Process or System is Stable and

Capable i.e., can it consistently make good product.• Can Measures the Progress and Success achieved

after changes or improvementPre-Capability

Study

Variation Reduction Tool

Post Capability Study


Capability Study Process capability measures statistically summarize how much variation there is in a process relative to costumer specifications.

Too much variation Hard to produce output within costumer requirement(specification)

Low index value(e.g. Cpk < 0.5)(Process sigma between 0 and 2)

Moderate Variation Most output meets costumer requirement

Middle index value (Cpk between 0.5 and 1.2)(Process sigma between 3 and 5)

Very little variation Virtually all of output meets costumer requirements

High index value(Cpk > 1.5)(Process sigma 6 or better)


35

Short-Term vs Long Term SigmaLong-Term SigmaThis is the variation is due to both common and special causes. This variation is calculated based on all of individual readings (population). Used for Pp and Ppkcalculations

Short-Term SigmaThis variation is due to common causes only. This variation is estimated from the control chart data. Used for Cp and Cpk calculations


36

Cp and Cpk vs. Pp and Ppk• These metrics are calculated the same way, but they

use a different way to estimate standard deviation• Cp and Cpk are considered “short-term” measuresThe estimated StDev (Within) is average of for

each subgroup• Pp and Ppk are considered “long-term” measuresThe estimated StDev (Overall) is calculated using

the standard deviation (n-1) for all the data set points

2dR

The conservative approach is to report whichever set of statistics is smaller. Typical data sets are usually too small to be able say with certainty that one metric is better than the other.


37

Process Capability Ratio – Cp (Cont.)

+3σ-3σ

Process Width

TLSL USL

•orprocesstheofiationNormalspeciationAllowed

var.)(varCp =

99.73% of values

σ6LSL -USL

Cp =

Where σ is “within” rather than pooled


38

Subgroup Measured Values Average Std. Dev.1 52.0 52.1 53.0 52.3 51.7 52.22 1.3

2 51.7 51.5 52.0 51.7 51.3 51.64 0.7

3 51.7 52.2 51.9 52.6 52.5 52.18 0.9

4 51.3 52.2 51.8 52.5 51.4 51.84 1.2

5 50.8 50.9 51.7 51.8 51.4 51.32 1.0

6 52.6 51.4 52.9 52.6 52.4 52.38 1.5

7 53.0 52.9 52.5 52.5 51.8 52.54 1.2

8 52.5 52.7 51.2 53.7 51.3 52.28 2.5

9 51.9 51.6 51.6 52.7 51.7 51.90 1.1

10 52.2 52.7 52.3 51.8 53.2 52.44 1.4

11 52.4 52.6 52.1 51.8 51.9 52.16 0.8

12 51.3 51.2 51.9 53.1 52.9 52.08 1.9

13 51.7 51.6 51.4 51.4 51.1 51.44 0.6

14 51.8 51.0 52.4 51.2 51.6 51.60 1.4

15 52.0 51.7 52.6 51.8 52.7 52.16 1.0

16 52.0 52.3 51.8 52.0 51.5 51.92 0.8

17 51.8 51.8 51.8 51.9 52.0 51.86 0.2

18 52.0 51.9 51.4 51.8 53.3 52.08 1.9

19 51.5 52.6 52.8 52.4 52.0 52.26 1.3

20 51.5 51.8 50.8 51.3 52.5 51.58 1.7

51.99 1.22


Is the process Stable?

21191715131197531

53.0

52.5

52.0

51.5

51.0

Observation

Indi

vidu

al V

alue

_X=51.994

UCL=53.043

LCL=50.945

21191715131197531

1.2

0.9

0.6

0.3

0.0

Observation

Mov

ing

Rang

e

__MR=0.394

UCL=1.289

LCL=0

Control Chart for Average and Range


Is the process Capable?

555453525150

20

15

10

5

0

H1

Freq

uenc

y

Histogram of H1

• LSL

• USL

Potential Capability Cp = 1.55

Actual Capability Cpk = 1.23


Calculating the Grand Average• If Χ1,Χ2,… ,Χ20 are the subgroup averages, the

grand average is:X = Χ1+Χ2+… +Χ20

20

Grand Average

Time


Calculating the Average Range• If R1,R2,… ,R20 are the subgroup ranges, the

average range is:R = R1+R2+… +R20

20• Estimates the average within the subgroup

variation.


Between and Within Subgroup Variation

Other names for within subgroup variation:• Noise• Unexplained• Inherent• Error

Total Variation

Within Subgroup Variation

Between Subgroup Variation


44

Process Capability Ratio – Cp• Ratio of total variation allowed by the specification to the total

variation actually measured from the process• Use Cp when the mean can easily be adjusted (i.e., plating,

grinding, polishing, machining operations, and many transactional processes where resources can easily be added with no/minor impact on quality) AND the mean is monitored (so operator will know when adjustment is necessary – doing control charting is one way of monitoring)

• Typical goals for Cp are greater than 1.33 (or 1.67 if of considerable importance)

If Cp < 1 then the variability of the processis greater than the specification limits.


45

Different Levels of CpThe Cp index reflects the potential of the process if the mean were perfectly centered between the specification limits.

For a Six Sigma Process, Cp = 2

The larger the Cp index, the better!

−=

6LSLUSL

C p σ

Cp = 1USLLSL

Cp > 1

Cp < 1


PresenterPresentation NotesIf centered process Cp = CpkGoal is to make Cp = Cpk6 sigma process is Cp =2Top +/- 3SigmaMiddle +/- 6 Sigma

46

This index accounts for the dynamic mean shift in the process – the amount that the process is off target.

Calculate both values and report the smaller number.

Notice how this equation is similar to the Z-statistic.

Process Capability Ratio – Cpk

−−=

σLSLxor

σxUSLMinC pk 33 •Where σ is “within” rather than pooled


47

Process Capability Ratio – Cpk (Cont.) • Ratio of the distance to the closest spec to ½ of the estimated process variation • Use when the mean cannot be easily adjusted (i.e., stamping, casting,

plastics molding)• Typical goals for Cpk are greater than 1.33 (or 1.67 if of considerable

importance)• For sigma estimates use:

• R/d2 [short term] (calculated from X-bar and R chart) – use with Cpk

• s = Σ (xi -x) 2 [ “longer” term] (calculated from (n-1) data points) – usewith Ppk

• “Longer” term: When the data has been collected over a sufficient time period that over 80% of the process variation is likely to be included

n - 1


48

Actual Process Performance (Cpk)Unlike the Cp index, the Cpk index takes into account off-centering of the process. The larger the Cpk index, the better.

6σ

LSL USL

6σ

LSL USL

Cp = 1

Cpk = 1

Cp = 1

Cpk < 1


PresenterPresentation NotesIf Cpk = 2 and process is centered then we have plus and minus 6 sigmas (std dev) on each side of the mean. If we look at one side from the mean then we could see that the tail would take up half or 3 sigmas(std dev) with 3 sigmas open to the spec. Cpk is focus from mean to spec - 6 std dev / 3 = 2Cpk = (spec - mean)/3s or Zmin/3

Thus for a Six Sigma process - long term - Cpk = (6 - 1.5shift) / 3 = 1.5 CpkLong term is always in terms of the shift - taking in all the factors of variation.

49

Calculating Cp, Cpk and Pp, PpkHow did Minitab calculate these values?

602601600599598

USLLSL

PPM TotalPPM > USLPPM < LSL



PpkPPLPPUPp

Cpm

CpkCPLCPUCp

StDev (Overall)StDev (Within)Sample NMeanLSLTargetUSL

6367.35 39.19

6328.16

3631.57 10.51

3621.06

10000.00 0.00

10000.00

0.830.831.321.07

*

0.900.901.421.16

0.6208650.576429

100599.548598.000

*602.000

Exp. "Overall" PerformanceExp. "Within" PerformanceObserved PerformanceOverall Capability

Potential (Within) Capability

Process Data

Within

Overall

Cp and Cpk values are calculated based on estimated StDev(Within). The minimum of CPU (capability with respect to USL) and CPL (capability with respect to LSL) is the Cpk.If a target is entered, then Cpm, Taguchi’s capability index, is also calculated.Cp and Cpk values are considered to be “short term.”

•Process Capability Analysis for Supp1


50

Cp, Cpk vs. Pp, PpkHow did Minitab calculate these values?

602601600599598

USLLSL




PpkPPLPPUPp

Cpm

CpkCPLCPUCp

StDev (Overall)StDev (Within)Sample NMeanLSLTargetUSL

6367.35 39.19

6328.16

3631.57 10.51

3621.06

10000.00 0.00

10000.00

0.830.831.321.07

*

0.900.901.421.16

0.6208650.576429

100599.548598.000

*602.000

Exp. "Overall" PerformanceExp. "Within" PerformanceObserved PerformanceOverall Capability


Process Data

Within

Overall

Pp and Ppk values are calculated based on estimated StDev(Overall). The minimum of Ppu (capability with respect to USL) and Ppl (capability with respect to LSL) is the Ppk.Pp and Ppk values are considered to be “longer term.”

•Process Capability Analysis for Supp1If the Cp and Pp values are significantly different this is an indication of an out of control process.


PART 3:

Cp, Cpk and Six Sigma


PresenterPresentation NotesPart 4 completed in 15 minutes and will take us up to 215 minutesPart 5 completed in 15 minutes and will take us up to 230 minutes10 minutes for Q&A and class evaluationTOTAL TIME 4 HOURS

Process Should be Stable before Checking Capability

A Stable Process

NOT a Stable Process

UCL

LCL

UCL

LCL


Stable Process are Predictable!Distance from Average

(d) Percentage out of Spec.

-5.0σ 0.3/million

-4.5σ 3.4/million

-4.0σ 31/million

-3.5σ 233/million

-3.0σ 0.135%

-2.5σ 0.6%

-2.0σ 2.3%

-1.5σ 6.7%

-1.0σ 15.8%

-0.5σ 30.9%

0.0σ 50%

0 1σ-3σ 3σ

dLSL

2σ-2σ -1σ

Individuals Distribution

Percent out of Spec


Cp Compares the Specification Range to the Width of the Process, (±3σ each side of the mean):

Cp = USL-LSL6S

LSL

Cp = 1.5 Cp = 2

Cp Does Not Consider Centering

Cp = 1Cp = 0.5

USL


Cp = 1

Allows a ±1.5σ operating window, worse case is 6.7% defective.

LSL USL±1.5σ

6.75% Defective

• -3σ • 3σ• 3 – Sigma Process


Cp = 1.5

Allows a ±1.5σ operating window, worse case is 1350 defects per million.

LSL±1.5σ

1350 Defects/Million

-4.5σ 4.5σ4.5 – Sigma Process

USL


Cp = 2.0

Allows a ±1.5σ operating window, worse case is 3.4 defects per million.

•LSL •USL±1.5σ

3.4 Defects/Million

-6σ 6σ6 – Sigma Process


What has Changed?

6 – Sigma Process

LSL USL±1.5σ

-6σ 6σ

LSL USL±1.5σ

-4.5σ 4.5σ

4.5 – Sigma Process

LSL USL±1.5σ

-3σ 3σ

• 3 – Sigma Process


Operating Windows• Don’t forget to include them in your

process design.• Stable process can hold a ±1.5σ operating

window.• Automated processes may be able to hold

a ±1.0σ operating window.• If a process is not stable, a ±1.5σ window

may not be enough room for the average.Why?UCL, LCL = X ± 3σ/√n When, n = 5then,±3σ/√n = ±3σ/√5 = ±1.34σ


Cp Does Not Consider Centering

LSL USLCp = 2

-6σ 6σ


Determine Cpk

LSLX

Cpk = Distance from X to the nearest Spec

3S

3S

Average - LSL


Cpk = 1

USL

LSL

Cp = 1


Cpk = 2

USL

LSL

• Cp = 2


Cpk When Cp = 2

USL

LSL

• Cpk = 1/2

Cpk = 1/2Cpk = 1

Cpk = 1

• Cpk = 1.5

• Cpk = 1.5• Cpk = 2.0

Fix the variability, then move the average

When the process is perfectly centered, Cpk = Cp.


Interpreting Cpk

Table below gives the corresponding defect level of various Cpk’s with Cp = 2.0:

Cpk Defect Level

1.5 3.4 dpm

1.167 233 dpm

1 1350 dpm

0.83 0.6%

0.5 6.7%


PART 4:Use of Capability Studies


PresenterPresentation NotesPart 4 completed in 15 minutes and will take us up to 215 minutesPart 5 completed in 15 minutes and will take us up to 230 minutes10 minutes for Q&A and class evaluationTOTAL TIME 4 HOURS

Uses of Capability Study• Identifying processes needing improvement.

• Tracking process performance.

• Verifying the effectiveness of fixes.

• Determining the ability of suppliers to consistently make good product.

• Qualifying new equipment.

• Determining the manufacturability of new product.


Identifying Processes Needing Improvement

• Unstable processes of processes with poor Cp’s and/or Cpk’s are target for improvements.

• If the process is unstable it is a good candidate for control chart.

• If the process is stable, but not capable, one should first look for obvious sources of variation.

• If no obvious sources exist, then you should perform designed experiments to uncover them.


Verifying Effectiveness of Fixes• Use a capability study to demonstrate the

effectiveness of fixes.

• New estimates of Cp and Cpk should be at least 15% greater than the pre-fix estimates.

• True changes are unlikely when pre and post capability estimates are within ± 15% of each other.


Assessing the performance of Suppliers• Materials and components from our suppliers make up one

or more inputs in our manufacturing process.

• Our final quality is only as good as our supplier’s quality.

• All suppliers need to provide good product on a consistent basis.

• “Consistency” requires a stable process of manufacturing.

• If the process is not stable, the products produced will not be stable in quality.

• “Stability” can only be assessed by looking at time ordered samples.


Qualifying New Equipment• Want to demonstrate the equipment can

consistently make good products.

• Should use a capability study to demonstrate “consistency”.

• Consider requesting a capability study when purchasing a new equipment.


Determining the Manufacturability of New Product

• Capability studies measure the match between product specifications and process variation.

• A process may be capable of manufacturing one product, but not another.

• For new products, use capability studies to determine how well the product design adapts to the manufacturing process.


PART 5:Technical Considerations


The Normality Assumption• Common Misconception:

• Control charts work well even when the data are not normally distributed.

• The normality assumption was originally introduced from the control chart constants, i.e. d2, A2, D4, etc,

• Even the control chart constants do not change appreciably when the data are non-normal*.

“The data has to be normally distributed to be control charted”


Why 3 Standard Deviation Limits?• Not established solely on the basis of probability theory.

• Outcomes in most stable processes generally occur between ±3 S.D.’s from the average.

• Originally designed to minimize the time looking unnecessarily for shifts in the process average.

• Additionally concerned with missing an actual process shift as it occurs.


Rational Sub grouping• Organizing the data into rational subgroups allows

us to answer the right questions.

• The variation occurring within the subgroups is used to set the control limits.

• The control chart uses the within subgroup variation to place limits on how much variation should naturally exist between subgroups.


Rational Sub groupingSome Guidelines:

• Try not to place unlike things together into the same subgroups.

• Organize in a way that produces the lowest variation within each subgroup.

• Maximize the opportunity to observe the variation between subgroups.


PART 6:Use of Control Charts


PresenterPresentation Notes10 seconds = 1.6 minutes

79

Control ChartsControl charts are one of the most commonly used tools in our Lean Six Sigma toolbox• Control charts provide a graphical picture of the

process over time• Control charts are both practical and easy-to-use• Control charts help us establish a measurement

baseline from which to measure improvements


80

What Do Control Charts Tell Us?• When the process location has shifted• When process variability has changed• When special causes are present

• Process not predictable• A learning opportunity

• When no special causes are present• Process is predictable• No clues to improvement available; may need to

introduce a special cause to effect a changeControl charts tell you when, not why


Why Use a Control Chart?

81

• Statistical control limits are another way to separate common cause and special cause variation

• Points outside statistical limits signal a special cause• Can be used for almost any type of data collected over time• Provides a common language for discussing process performance

When To Use:• Track performance over time• Evaluate progress after process changes/improvements• Focus attention on process behaviour• Separate “signals” from “noise”


82

Control Chart Selection• Control chart selection should be based

upon:• Data type• Number of observations• Sample size• Subgrouping

• The primary determinant in control chart selection is Data Type


83

Data Types• There are many different types of data• Each type of data has its own unique control chart• The basic format and underlying concepts are the same

across the entire family of control charts• A basic understanding of the different data types is

important to increase the successful use of control charts• How many different types of data are there?


Two General Kinds of Data

84

• Attribute – The data is discrete (counted). Results from using go/no-go gages, or from the inspection of visual defects, visual problems, missing parts, or from pass/fail or yes/no decisions

• Variable – The data is continuous (measured). Results from the actual measuring of a characteristic such as diameter of a hose, electrical resistance, weight of a vehicle, etc.


Continuous Data

85

• Continuous data is a set of numbers that can potentially take on any value

• Also known as variable data• Examples: 0.1, 1/4, 20, 100.001, 1,000,000, -3.26, -10,000• Common Applications

• Dimensions (lengths, widths, weight, etc)• Time (seconds, minutes, hours, etc)• Finance (mills, cents, dollars, etc)

• Distribution Types• Normal• Uniform• Exponential

• Because continuous data has more discrimination, go for continuous data whenever possible


Control Charts for Individual Values

86

Time ordered plot of results (just like time plots)Statistically determined control limits are drawn on the plot.Centerline calculation uses the mean

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53.0

52.5

52.0

51.5

51.0

Index

UCL=53.043

Avg=51.99

LCL=50.945

LCL= X + 2.66mR

Centerline = X

UCL= X + 2.66mR


Attribute Data

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• Attribute data has two main subsets, Binary data and Discrete Data

• Binary Data is a characterized by classifying into only two outcomes• Examples: Pass/Fail, Agree/Disagree, Win/Loss,

defective/conforming• Common uses: Proportions and ratios• Distribution: Binomial • Key assumptions

• Events are independent of each other• Mutually exclusive outcomes• Number of trials and outcomes of each trial is known


Attribute Data (Cont.)

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• Discrete Data is a set of finite outcomes, usually integers, and is measured by counting• Also known as Ordinal data• Common uses and examples:

• Number of product defects per item• Number of customer requirements per order• Number of accounting errors per invoice

• Distribution: Poisson• Poisson characteristics and assumptions

• Unlimited number of defects per item• Constant probability of defect per item• Probability of defect per unit is low• Defects are independent of each other


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Control Chart Selection TreeTYPE OF DATA

•Poisson Distribution

Count or Classification(Attribute Data)

Count

Defects orNonconformance

FixedOpportunity

C Chart

VariableOpportunity

U Chart

Classification

Defectives orNonconforming Units

FixedOpportunity

NP Chart

VariableOpportunity

P Chart

Subgroup Size of 1

I-mR

Subgroup Size < 9

X-bar R

Subgroup Size > 9

X-bar S

Measurement(Variable Data)

•Binomial Distribution •Normal DistributionNormal DistributionBinomial DistributionPoisson Distribution


PresenterPresentation NotesStay on the right of the chart. Go to continuous data. Attribute charts work some of the time, but there are a bunch of statistical assumptions that often don’t hold true. For small subgroup sizes, standard deviation will downplay variability. For larger sample sizes, you want standard deviation because it uses all of the data points to make the estimation. Range only uses the max and the min. For x-bar and R and s - interpretation is the same, limits calculated slightly differently.Count data - defects - 15 defects on a car, but I can still ship. If the number of opportunities varies then you need to calculate a ratio. If the number of opportunities is fixed, you can just plot the number of defects. We will give you some time to read up on these in the Minitab documentation.

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Individuals and Moving Range Charts• Display variables data when the sample subgroup size is

one (And in certain situations, attribute data)• Variability shown as the difference between each data

point (i.e., moving range)• Appropriate Usage Situations:

• When there are very few units produced relative to the opportunity for process variables (sources of variation) to change

• When there is little choice due to data scarcity• When a process drifts over time and needs to be monitored

• I-mR is a good chart to start with when evaluating continuous data


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Calculations for Individuals Charts

1. Determine sampling plan 2. Take a sample at each specified interval of time3. Calculate the moving range for the sample. To calculate each moving

range, subtract each measurement from the previous one. There will be no moving range for the first observation on the chart

4. Plot the data (both individuals and moving range)5. After ‘30' or more sets of measurements, calculate control limits for moving

range chart6. If the Range chart is not in control, take appropriate action7. If the Range chart is in control, calculate limits for individuals chart8. If the Individuals chart is not in control, take appropriate action


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Why Use Subgroups?

It allows us to examine both within sample variation and between sample

variation


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X-Bar & R Chart• The X-bar & R chart is the most commonly used control chart due to its use of

subgroups and the fact that it is more sensitive than the ImR to process shift• Consists of two charts displaying Central Tendency and Variability• X-bar Chart

• Plots the mean (average value) of eachsubgroup

• Useful for identifying special cause changesto the process mean (X)

• X-bar control limits based on +/- 3 sigmafrom the process mean are calculatedusing the Range chart

• R Chart• Displays changes in the "within" subgroup dispersion of the process• Checks for constant variation within subgroups


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Calculations for X-Bar & R Charts1. Determine an appropriate subgroup size and sampling plan2. Sample: (Take a set of readings at each specified interval of time)3. Calculate the average and range for each subgroup4. Plot the data. (Both the averages and the ranges)5. After ‘30' or more sets of measurements, calculate control limits for the

range chart6. If the range chart is not in control, take appropriate action 7. If the range chart is in control, calculate control limits for the X-bar chart8. If the X-bar chart is not in control, take appropriate action


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Rational Subgrouping• An important consideration in using the X-bar & R (and X-bar & S) chart

is the selection of an appropriate subgroup size• Rational Subgrouping is the process of selecting a subgroup based

upon “logical” grouping criteria or statistical considerations• Subgrouping Examples

• “Natural” Breakpoints: • 3 shifts grouped into 1 day; • 5 days grouped into 1 week, • 10 machines grouped into 1 dept

• Wherever possible, both natural breakpoints and homogenous group considerations should be combined together in selecting a sample size


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Attribute Control Charts• Attribute control charts are similar to variables

control charts, except they plot proportion or count data rather than variable measurements

• Attribute control charts have only one chart which tracks proportion or count stability over time

• Chart Types• Binomial: P chart, NP chart• Poisson: C chart, U chart


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Attribute Control Charts• Binomial Distribution Charts

• Use one of the following charts when comparing a product to a standard and classifying it as being defective or not (pass vs. fail):• P Chart – Charts the proportion of defectives in each subgroup• NP Chart – Charts the number of defectives in each subgroup

• Poisson Distribution Charts• Use one of the following chart when counting the number of defects

per sample or per unit• C Chart – Charts the defect count per sample (must have the same

sample size each time)• U Chart – Charts the number of defects per unit sampled in each

subgroup (using a proportion so sample size may vary)


PART 7:Use of Control Charts



Uses of Control Charts

• Evaluation

• Improvement

• Maintenance



• Evaluation: Determine if the process is both stable and capable, as part of a capability study.

• Improvement

• Maintenance



• Evaluation

• Improvement: Identify changes to the process so that the causes may be investigated and eliminated.

• Maintenance


Improvement• Control Charts search for differences over time.

• Observing a change on the control charts means a key input variable has changed.

• The pattern observed on the control chart provides clues about the key variable that changed:• Timing of the change

• Shape or pattern• Trends

• Jumps or shifts


Maintenance

• Control charts can help us to decide when to make adjustments to the process.

• Using control charts we can make better decisions, and minimize the chance of making two possible errors:.• 20% - Failing to adjust when the process needs adjustments

• 80% - adjusting when the process does not need adjustment

• When maintaining processes using control charts, try to center the average around the desired target.


Statistical Step to Establish Control Limit1. Collect the data 30 or more

2. Prepare Individual moving range chart (I-MR) using appropriate statistical software

3. Review the moving range chart, if any data point beyond are beyond the UCL, the data the data point must be evaluated and excluded if there is an assignable cause, then replot the moving range chart.

4. Review the individual chart, if any data point beyond are beyond the UCL and LCL, the data the data point must be evaluated and excluded if there is an assignable cause, then replot the individual chart.


Real Time Evaluation

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Rule 1 The data outside of control limit: One point of outside the control limit

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56

55

54

53

52

51

Index

UCL=53.043

LCL=50.945

Avg=51.99



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Rule 2 Trend Shift: 8 consecutive point on same side of center line

272421181512963

53.0

52.5

52.0

51.5

51.0

Index

UCL=53.043

Avg=51.99

LCL=50.945



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Rule 3 Trend drift: 6 consecutive points that trend in the same direction (all increasing or all decreasing)

2421181512963

53.0

52.5

52.0

51.5

51.0

Index

UCL=53.043

Avg=51.99

LCL=50.945


PART 8:Minitab Exercise



Opening a new project in Minitab

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Menu bar

Toolbars

Session window

Data window

Project Manager window (minimized)


Overview of Minitab

Worksheet• Each Minitab worksheet can contain up to 4,000

columns, each column is identified by a number• The letter after the column number indicates the

data type:D : date / timeT : text (alphanumeric)

If no letter appears, the data are numeric

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Example 1

ProblemSupervisor of medical company is preparing a sales report for a new line of facial cream that the company intends to distribute nationally. In a pilot launch, the company sold facial cream at various stores in Jakarta and Bandung for three months.

Data Collection The supervisor recorded the daily revenue for two locations during the three months and stored them in minitab project

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Example 1

Tools• Dotplot• Time Series Plot• Graphical Summary• Display Descriptive Statistics• Layout Tools

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Open Project1. Choose File > Open project2. Choose ISPE_Example 1.MPJ.3. Click open.

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Creating Dotplots• Choose Graph > Dotplot• Complete the dialog as shown below, then click OK

• In graph variable, enter ‘Jakarta Sales’ and ‘Bandung Sales’ by highlighting them and double clicking each variable, then click OK

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Interpreting your resultThe graph shows the sales data during the three month period for both location. On average, Bandung sales appear higher than Jakarta sales.

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Correcting the Outlier After checking with the person who entered the data, your discover that the sales information for data n=20 is missing. Instead of entering 0, you should enter an asterisk (*) to indicate that the value is missing.• Click project manager toolbar• In the Bandung column, highlight the cell in column 3 and

row 20 as show below.

• Press [DELETE]

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Updating a graph• To choose the dotplot, click in the project manager toolbar• Click the graph to make it the active window• Choose Editor > Update > Update graph now

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Time Series Plot• Choose Graph > Time Series Plot• Choose Multiple, then click OK• In series, enter ‘Jakarta Sales’ ‘Bandung Sales’• Click Time / Scale• Complete the dialog as shown below

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Graphical Summary• Choose Stat > Basic Statistic > Graphical Summary• Complete the dialog as shown below

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Display Descriptive Statistic• Choose Stat > Basic Statistic > Display Descriptive

Statistics.• In variable, enter ‘Jakarta Sales’ ‘Bandung Sales’• Click statistics• Complete the dialog box as shown below, then click OK

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Creating a multiple graph• Click graph folder, then click the dotplot in the project

manager. Click the graph to make it the active window.• Choose Editor > Layout tool• Double click all graph have been created to place the graph

in the layout window.

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ProblemThe validation supervisor want to evaluate the consistency of the fill weight for hydrocortisone cream. The cream is packed in tube. The target weight is 1150grams. The specification limit are 1100 and 1200 grams.Earlier evidence indicate this process is stable with a mean of 1150 grams and a standard deviation of 8.6 grams

ToolsI-MR

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Example 2


I-MR• Open ISPE_Example 2.MPJ• Choose Stat > Control Charts > Variable Charts for

Individuals > I-MR• Complete the dialog box as shown below

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I-MR• Click Scale, under X scale, choose stamp• Under Stamp columns, enter date/time. Click OK• Click I-MR Options.• In Mean, type 1150; in standard deviation type 8.6, then click

OK

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Individual chart shows that the process is clearly not in statistical control also process operated consistently above the mean.


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Next StepRemove mean then replot the I-MR Chart


ProblemWith previous data analyse normality and capability process

ToolsProbabilityCapability Six Pack

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Example 3FITHRUL FARMASIINDUSTRI.COM

Probability Plot• Open ISPE_Example 2.MPJ• Choose Grap > Probability Plot > Single • Complete the dialog box as shown below• Complete dialog as shown below

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Normality Check• Check normality data (P>0.05)

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12001190118011701160115011401130

99.9

99

9590

80706050403020

105

1

0.1

Mean 1164StDev 8.576N 60AD 0.293P-Value 0.591

Fill Weight

Perc

ent

Probability Plot of Fill WeightNormal - 95% CI

Normal Data P > 0.05


Capability Analysis

• Open ISPE_Example 2.MPJ• Choose Stat > Quality Tools > Capability Analysis • Complete the dialog box as shown below• Complete dialog as shown below

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Capability Analysis

• Cp/Cpk > 1.33

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1200118511701155114011251110

LSL 1100Target *USL 1200Sample Mean 1163.58Sample N 60StDev(Overall) 8.57554StDev(Within) 8.34686

Process Data

Pp 1.94PPL 2.47PPU 1.42Ppk 1.42Cpm *

Cp 2.00CPL 2.54CPU 1.45Cpk 1.45


Overall Capability

PPM < LSL 0.00 0.00 0.00PPM > USL 0.00 10.81 6.39PPM Total 0.00 10.81 6.39

Observed Expected Overall Expected WithinPerformance

LSL USLOverallWithin

Process Capability Report for Fill Weight


Summary

• Understand basic principle statistic• Know important parameter• Know variation and trending• Know proper tools for data evaluation• Combine data statistic and product

knowledge

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Statistical MethodModule OutlineSlide Number 3What is Statistical Process Control?Where should we use SPC?Slide Number 6How Does One Prevent Defects?Two Possible CausesCAP NEVER PLACED ONTO VIALLow Removal ForcesOptimization & Variation Reduction (O.V.R)Typical O.V.R ProblemsTwo Approaches to Preventing DefectsReducing VariationTools for SPCStatistical VariationDisplaying VariationThe Bell-Shaped CurveThe Standard Normal CurveA STABLE PROCESS AN UNSTABLE PROCESS A CAPABLE PROCESS Objective of SPCSlide Number 24Reducing Variation Reduces DefectsReducing Variation Widens Operating WindowsReducing Variation Improves Customer ValueBetter ManagementMaximize Process CapabilityBenefits of SPCSlide Number 31Variation Reduction ToolsCapability Study Capability Study Short-Term vs Long Term SigmaCp and Cpk vs. Pp and PpkProcess Capability Ratio – Cp (Cont.) Slide Number 38Is the process Stable?Is the process Capable?Calculating the Grand AverageCalculating the Average RangeBetween and Within Subgroup VariationProcess Capability Ratio – CpDifferent Levels of CpProcess Capability Ratio – CpkProcess Capability Ratio – Cpk (Cont.) Actual Process Performance (Cpk)Calculating Cp, Cpk and Pp, PpkCp, Cpk vs. Pp, PpkSlide Number 51Process Should be Stable before Checking CapabilityStable Process are Predictable!Cp Cp = 1Cp = 1.5Cp = 2.0What has Changed?Operating WindowsCp Does Not Consider CenteringDetermine CpkCpk = 1Cpk = 2Cpk When Cp = 2Interpreting CpkSlide Number 66Uses of Capability StudyIdentifying Processes Needing ImprovementVerifying Effectiveness of FixesAssessing the performance of SuppliersQualifying New EquipmentDetermining the Manufacturability of New ProductSlide Number 73The Normality AssumptionWhy 3 Standard Deviation Limits?Rational Sub groupingRational Sub groupingSlide Number 78Control ChartsWhat Do Control Charts Tell Us?Why Use a Control Chart?Control Chart SelectionData TypesTwo General Kinds of DataContinuous DataControl Charts for Individual ValuesAttribute Data Attribute Data (Cont.) Control Chart Selection TreeIndividuals and Moving Range ChartsCalculations for Individuals ChartsWhy Use Subgroups?X-Bar & R ChartCalculations for X-Bar & R ChartsRational SubgroupingAttribute Control ChartsAttribute Control ChartsSlide Number 98Uses of Control ChartsUses of Control ChartsUses of Control ChartsImprovementMaintenanceStatistical Step to Establish Control LimitReal Time EvaluationReal Time EvaluationReal Time EvaluationSlide Number 108Opening a new project in MinitabOverview of MinitabExample 1Example 1 Slide Number 113Slide Number 114Slide Number 115Slide Number 116Slide Number 117Slide Number 118Slide Number 119Slide Number 120Slide Number 121Slide Number 122Slide Number 123Slide Number 124Slide Number 125Example 2 Slide Number 127Slide Number 128Slide Number 129Slide Number 130Example 3� Probability PlotNormality CheckCapability AnalysisCapability AnalysisSummarySlide Number 137

Documents

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