ISPE-Statistical Method

Statistical Method

Jakarta, 29-30 March,2016

Speaker: Heru Purnomo

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 1:

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

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 Force

Cap 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.

Reference

Shingo, 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.

Reference

Taylor, Wayne A. (1991). Optimization and Variation Reduction I Quality. McGraw-Hill, New York and ASQC Quality Press, Milwaukee.

Optimization & Variation Reduction

(O.V.R)

Typical O.V.R Problems

Larger the Better

Lower Spec Limit

Target

Smaller the Better Upper Spec Limit

• microbial level • particulate level • contamination level

Closer to the target the Better

Target Lower Spec Limit Upper Spec Limit

• Vial fill volume • Potency, Assay

Two Approaches to Preventing

Defects

• Mistake Proofing

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.”

Tools for SPC

• SPC provides two tools for reducing variation:

1) Control Charts 2) 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

Displaying Variation

Cap Removal Force in PSI

Nu m be r M ea su re d

The Bell-Shaped Curve

The Standard Normal Curve

• Corresponds to 100% of ALL possible Outcomes in a Stable System. • Has a Mean = 0, and SD = 1

μ

σ

-3

Standard Deviations from the Mean

3 1

-1

-2 ₂

Slide 20

A STABLE PROCESS

Total Variation

Slide 21

AN UNSTABLE PROCESS

• Total

Slide 22

A CAPABLE PROCESS

Slide 23

Objective of SPC

To consistently produce high quality

products by achieving stable and

Slide 24

WHY

REDUCE

VARIATION?

Slide 25

Reducing Variation Reduces Defects

Upper Spec Limit Lower Spec Limit Upper Spec Limit GOOD

PRODUCT _PRODUCTGOOD

•Defective Product •No Defective Product

Lower Spec Limit

Slide 26

Reducing Variation Widens

Operating Windows

Slide 27

Bad Product

Reducing Variation Improves

Customer Value

Loss equals value

Upper Spec Limit

Slide 28

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.

Slide 29

Maximize Process Capability

• Replace existing equipment only if necessary.

• Improve capability make new product feasible

.

Slide 30

Benefits of SPC

• Fewer Defects

• Wider Operating Windows

• Higher Customer Value

• Better Management

Slide 31

PART 2:

Slide 32

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

Slide 33

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 improvement

Pre-Capability Study Variation Reduction Tool Post Capability Study

Slide 34

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)

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 calculated based on all of

individual readings (population). Used for Pp and Ppk

calculations

Short-Term Sigma

This variation is due to common causes only. This

variation is estimated from the control chart data. Used for

Cp and Cpk calculations

36

C

_p

and C

_pk

vs. P

_p

and P

_pk

• These metrics are calculated the same way, but they

use a different way to estimate standard deviation

• C

and C

are considered “short-term” measures

 The estimated StDev (Within) is average of for

each subgroup

• P

and P

are considered “long-term” measures

 The estimated StDev (Overall) is calculated using

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

points

2

d R

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 – C

_p

(Cont.)

+3σ -3σ Process Width T LSL USL

•or

NormalAllowedvar variation (spec.)

C_p = 99.73% of values

σ

6

LSL

-USL

C

=

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

Slide 39

Is the process Stable?

21 19 17 15 13 11 9 7 5 3 1 53.0 52.5 52.0 51.5 51.0 Observation In di vi du al V al ue _ X=51.994 UCL=53.043 LCL=50.945 21 19 17 15 13 11 9 7 5 3 1 1.2 0.9 0.6 0.3 0.0 Observation M ov in g Ra ng e __ MR=0.394 UCL=1.289 LCL=0

Slide 40

Is the process Capable?

55 54 53 52 51 50 20 15 10 5 0 H1 Fr eq ue nc y Histogram of H1 • LS L • US L Potential Capability Cp = 1.55 Actual Capability Cpk = 1.23

Slide 41

Calculating the Grand Average

• If

Χ

,

Χ

,… ,

Χ

are the subgroup averages, the

grand average is:

X =

Χ

+

Χ

+… +

Χ

20

Slide 42

Calculating the Average Range

• If R

,R

,… ,R

are the subgroup ranges, the

average range is:

R = R

+R

+… +R

20

• Estimates the average within the subgroup

variation.

Slide 43

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 – C

_p

• Ratio of total variation allowed by the specification to the total

variation actually measured from the process

• Use C

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 C

are greater than 1.33 (or 1.67 if of

considerable importance)

If C_p < 1 then the variability of the process

45

Different Levels of C

_p

The C

index reflects the

potential of the process if

the mean were perfectly

centered between the

specification limits.

For a Six Sigma Process,

C_p = 2

The larger the C_p index, the better!

− = 6 LSL USL C p

σ

C

= 1

C

> 1

C

< 1

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 – C

_pk









−

−

=

σ

LSL

x

or

σ

x

USL

Min

C

3

47

Process Capability Ratio – C

_pk

(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 C_pk 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 C_pk

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

with P_pk

• “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

48

Actual Process Performance (C

_pk

)

Unlike the C_p index, the C_pk index takes into account off-centering of the

process. The larger the C_pk index, the better.

6σ LSL USL 6σ LSL USL

C

= 1

C

= 1

C

= 1

C

< 1

49

Calculating C

_p

, C

_pk

and P

_p

, P

_pk

How did Minitab calculate these values?

602 601 600 599 598 USL LSL PPM Total PPM > USL PPM < LSL PPM Total PPM > USL PPM < LSL PPM Total PPM > USL PPM < LSL Ppk PPL PPU Pp Cpm Cpk CPL CPU Cp StDev (Overall) StDev (Within) Sample N Mean LSL Target USL 6367.35 39.19 6328.16 3631.57 10.51 3621.06 10000.00 0.00 10000.00 0.83 0.83 1.32 1.07 * 0.90 0.90 1.42 1.16 0.620865 0.576429 100 599.548 598.000 * 602.000

Exp. "Overall" Performance Exp. "Within" Performance

Observed Performance Overall Capability

Potential (Within) Capability Process Data

Within Overall

Cp and Cpk values are calculated based on estimated

StDev(Within).

The minimum of C_PU (capability with respect to USL) and

C_PL (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.”

50

C

_p

, C

_pk

vs. P

_p

, P

_pk

How did Minitab calculate these values?

602 601 600 599 598 USL LSL PPM Total PPM > USL PPM < LSL PPM Total PPM > USL PPM < LSL PPM Total PPM > USL PPM < LSL Ppk PPL PPU Pp Cpm Cpk CPL CPU Cp StDev (Overall) StDev (Within) Sample N Mean LSL Target USL 6367.35 39.19 6328.16 3631.57 10.51 3621.06 10000.00 0.00 10000.00 0.83 0.83 1.32 1.07 * 0.90 0.90 1.42 1.16 0.620865 0.576429 100 599.548 598.000 * 602.000

Exp. "Overall" Performance Exp. "Within" Performance

Observed Performance Overall Capability

Potential (Within) Capability Process Data

Within Overall

Pp and Ppk values are calculated based on estimated

StDev(Overall).

The minimum of P_pu (capability with respect to USL) and

P_pl (capability with respect to LSL) is the Ppk.

Pp and Ppk values are considered to be “longer term.”

•Process Capability Analysis for Supp1

If the Cp and Pp values are significantly different this is an

Slide 51

PART 3:

Slide 52

Process Should be Stable before Checking Capability

A

Stable Process

NOT a Stable Process

UCL

LCL

UCL

Slide 53

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 d LSL 2σ -2σ -1σ Individuals Distribution Percent out of Spec

Slide 54

Cp

Compares the Specification Range to

the Width of the Process, (±3

σ each

side of the mean):

C

_p

= USL-LSL

6S

LSL

Cp = 1.5

Cp = 2

Cp Does Not Consider Centering

Cp = 1 Cp = 0.5

Slide 55

Cp = 1

Allows a ±1.5

σ operating window, worse case

is 6.7% defective.

Slide 56

Cp = 1.5

Allows a ±1.5

σ operating window, worse case

is 1350 defects per million.

LSL ±1.5σ 1350 Defects/Million -4.5σ 4.5σ 4.5 – Sigma Process USL

Slide 57

Cp = 2.0

Allows a ±1.5

σ operating window, worse case

is 3.4 defects per million.

•LSL ±1.5σ _•USL

3.4

Defects/Million

-6σ 6σ

Slide 58

What has Changed?

6 – Sigma Process LSL ±1.5σ _USL -6σ 6σ LSL USL ±1.5σ -4.5σ 4.5σ 4.5 – Sigma Process LSL USL ±1.5σ -3σ 3σ • 3 – Sigma Process

Slide 59

Operating Windows

• Don’t forget to include them in your

process design.

• Stable process can hold a ±1.5

σ operating

window.

• Automated processes may be able to hold

a ±1.0

σ operating window.

• If a process is not stable, a ±1.5

σ window

may not be enough room for the average.

Why?

UCL, LCL = X ± 3σ/√n

When, n = 5

then,

Slide 60

Cp Does Not Consider Centering

LSL USL

C_p = 2

Slide 61

Determine Cpk

LSL

X

Cpk =

Distance from X to the nearest Spec 3S

3S Average - LSL

Slide 62

C

_pk

= 1

USL

LSL

Slide 63

C

_pk

= 2

USL

LSL

Slide 64

C

_pk

When C

_p

= 2

Fix the variability, then move the average

When the process is perfectly centered,

C

= C

.

Slide 65

Interpreting Cpk

Table below gives the corresponding defect level of

various Cpk’s with Cp = 2.0:

Slide 66

PART 4:

Slide 67

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.

Slide 68

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.

Slide 69

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

.

Slide 70

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.

Slide 71

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.

Slide 72

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.

Slide 73

PART 5:

Slide 74

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. d

, A

, D

, 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”

Slide 75

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.

Slide 76

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.

Slide 77

Rational Sub grouping

Some 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.

Slide 78

PART 6:

79

Control Charts

Control 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

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 change

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

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

20 18 16 14 12 10 8 6 4 2 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

87

• 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

Attribute Data (Cont.)

88

• 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

89

Control Chart Selection Tree

TYPE OF DATA •Poisson Distribution Count or Classification (Attribute Data) Count Defects or Nonconformance Fixed Opportunity C Chart Variable Opportunity U Chart Classification Defectives or Nonconforming Units Fixed Opportunity NP Chart Variable Opportunity P Chart Subgroup Size of 1 I-mR Subgroup Size < 9 X-bar R Subgroup Size > 9 X-bar S Measurement (Variable Data)

•Binomial DistributionBinomial Distribution •Normal DistributionNormal Distribution

90

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

91

Calculations for Individuals Charts

2. Take a sample at each specified interval of time

3. 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 chart

6. If the Range chart is not in control, take appropriate action

7. If the Range chart is in control, calculate limits for individuals chart 8. If the Individuals chart is not in control, take appropriate action

92

Why Use Subgroups?

It allows us to examine both within

sample variation and between sample

93

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 each subgroup

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

• X-bar control limits based on +/- 3 sigma from the process mean are calculated using the Range chart

• R Chart

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

94

Calculations for X-Bar & R Charts

1. Determine an appropriate subgroup size and sampling plan

2. Sample: (Take a set of readings at each specified interval of time) 3. Calculate the average and range for each subgroup

4. Plot the data. (Both the averages and the ranges)

5. After ‘30' or more sets of measurements, calculate control limits for the range chart

6. 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 chart 8. If the X-bar chart is not in control, take appropriate action

95

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

96

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

97

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)

Slide 98

PART 7:

Slide 99

Uses of Control Charts

• Evaluation

• Improvement

Slide 100

Uses of Control Charts

• Evaluation: Determine if the process is both stable

and capable, as part of a capability study.

• Improvement

Slide 101

Uses of Control Charts

• Evaluation

• Improvement: Identify changes to the process so

that the causes may be investigated and

eliminated.

Slide 102

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

Slide 103

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.

Slide 104

Statistical Step to Establish Control Limit

1. 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

105

Rule 1 The data outside of control limit: One point of outside the control limit 20 18 16 14 12 10 8 6 4 2 56 55 54 53 52 51 Index UCL=53.043 LCL=50.945 Avg=51.99

Real Time Evaluation

106

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

27 24 21 18 15 12 9 6 3 53.0 52.5 52.0 51.5 51.0 Index UCL=53.043 Avg=51.99 LCL=50.945

Real Time Evaluation

107

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

24 21 18 15 12 9 6 3 53.0 52.5 52.0 51.5 51.0 Index UCL=53.043 Avg=51.99 LCL=50.945

Slide 108

PART 8:

Opening a new project in Minitab

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 / time

T : text (alphanumeric)

If no letter appears, the data are numeric

Example 1

Problem

Supervisor 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

Example 1

Tools

• Dotplot

• Time Series Plot • Graphical Summary

• Display Descriptive Statistics • Layout Tools

Open Project

1. Choose File > Open project 2. Choose ISPE_Example 1.MPJ. 3. Click open.

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

Interpreting your result

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

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]

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

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

Graphical Summary

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

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

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.

Problem

The 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

Tools

I-MR

126

I-MR

• Open ISPE_Example 2.MPJ

• Choose Stat > Control Charts > Variable Charts for Individuals > I-MR

• Complete the dialog box as shown below

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

129 Individual chart shows that the process is clearly not in

statistical control also process operated consistently above the mean.

130

Next Step

Problem

With previous data analyse normality and capability process

Tools

Probability

Capability Six Pack

131

Probability Plot

• Open ISPE_Example 2.MPJ

• Choose Grap > Probability Plot > Single

• Complete the dialog box as shown below

• Complete dialog as shown below

Normality Check

• Check normality data (P>0.05)

133 1200 1190 1180 1170 1160 1150 1140 1130 99.9 99 95 90 80 70 60 50 40 30 20 10 5 1 0.1 Mean 1164 StDev 8.576 N 60 AD 0.293 P-Value 0.591 Fill Weight Pe rc en t

Probability Plot of Fill Weight

Normal - 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

Capability Analysis

• Cp/Cpk > 1.33

Overall Capability

PPM < LSL 0.00 0.00 0.00

PPM > USL 0.00 10.81 6.39

PPM Total 0.00 10.81 6.39

Observed Expected Overall Expected WithinPerformance

LSL USL

Overall Within 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