ISPE-Statistical Method

Statistical Method Jakarta, 29-30 March,2016 Speaker: Heru Purnomo

1

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 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) Target Lower Spec Limit

Upper Spec Limit

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 • Vial fill volume • Potency, Assay

Lower Spec Limit

Upper Spec Limit

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 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

0.9 ml

1.4 ml

Displaying Variation Histogram of Removal Force of the cap cover of Sterile Injection 6

Number Measured

5 4 3 2 1 0

21.6

22.4 23.2 Cap Removal Force in PSI

24.0

The Bell-Shaped Curve Normal Curve

21.6

22.4

23.2

24.0

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

• Total Area = 1

-3

-2

-1

1

2

Standard Deviations from the Mean

3

A STABLE PROCESS Total Variation

Slide 20

AN UNSTABLE PROCESS • Total Variation

Slide 21

A CAPABLE PROCESS CAPABLE

Spec Limits

NOT CAPABLE

Slide 22

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

Slide 23

WHY REDUCE VARIATION?

Slide 24

Reducing Variation Reduces Defects Upper Spec Limit

Lower Spec Limit

GOOD PRODUCT

•Defective Product

Slide 25

Lower Spec Limit

Upper Spec Limit

GOOD PRODUCT

•No Defective Product

Reducing Variation Widens Operating Windows Lower Spec Limit

Upper Spec Limit

Initial Operating Window

Slide 26

Lower Spec Limit

Upper Spec Limit

Wider Operating Window

Reducing Variation Improves Customer Value Lower Spec Limit

$20

L O S S

$10

Bad Product

Target

Upper Spec Limit

GOOD PRODUCT

Bad Product

$0 $20

L O S S

Target Upper Spec Limit

$10 Loss equals value

$0

Slide 27

Lower Spec Limit

•Taguc hi’s Loss

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.

Slide 28

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

Slide 29

Benefits of SPC • • • • •

Fewer Defects Wider Operating Windows Higher Customer Value Better Management Maximize Process Capability

Slide 30

PART 2:

Capability Studies

Slide 31

Variation Reduction Tools • There are many tools that help to achieve stable and capable processes:          Slide 32

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 improvement Pre-Capability Study

Variation Reduction Tool

Post Capability Study Slide 33

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)

Slide 34

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

35

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” measures R  The estimated StDev (Within) is average of d 2 for each subgroup • Pp and Ppk are considered “long-term” measures  The estimated StDev (Overall) is calculated using the standard deviation (n-1) for all the data set points 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. 36

Process Capability Ratio – Cp (Cont.) Allowed variation (spec .) Cp = Normal variation of the process

•or

Cp =

USL - LSL Where σ is “within” rather than pooled

99.73% of values

+3σ

-3σ

Process Width LSL 37

T

6σ

USL

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

38

Is the process Stable? Control Chart for Average and Range UCL=53.043

Individual Value

53.0 52.5

_ X=51.994

52.0 51.5 51.0

LCL=50.945 1

3

5

7

9

11

13

15

17

19

21

Observation UCL=1.289

Moving Range

1.2 0.9 0.6

__ MR=0.394

0.3 0.0

LCL=0 1

3

5

7

9

11

13

15

17

19

21

Observation

Slide 39

Is the process Capable? Histogram of H1 20

• LS L

• US L

Frequency

15

10

5

0

50

51

52

H1

53

54

Potential Capability

Cp = 1.55

Actual Capability

Cpk = 1.23

55

Slide 40

Calculating the Grand Average • If Χ1,Χ2,… ,Χ20 are the subgroup averages, the grand average is: X = Χ1+Χ2+… +Χ20 20 Grand Average

m Ti

Slide 41

e

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.

Slide 42

Between and Within Subgroup Variation Total Variation

Between Subgroup Variation

Within Subgroup Variation

Other names for within subgroup variation: • • • •

Noise Unexplained Inherent Error

Slide 43

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 process is greater than the specification limits. 44

Different Levels of Cp LSL

USL

Cp = 1

Cp > 1

The Cp index reflects the potential of the process if the mean were perfectly centered between the specification limits. The larger the Cp index, the better! Cp =

Cp < 1

45

USL − LSL 6σ

For a Six Sigma Process, Cp = 2

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

C pk

x − LSL  USL − x = Min  or  3 3 σ σ  

•Where σ is “within” rather than pooled

Calculate both values and report the smaller number. Notice how this equation is similar to the Z-statistic.

46

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 =

with Ppk

Σ (xi -x) 2

[ “longer” term] (calculated from (n-1) data points) – use

n-1

• “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

47

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.

LSL

USL

6σ

48

LSL

USL

6σ

Cp = 1

Cp = 1

Cpk = 1

Cpk < 1

Calculating Cp, Cpk and Pp, Ppk How did Minitab calculate these values? LSL

•Process Capability Analysis for Supp1

USL

Process Data USL

602.000

Target LSL

* 598.000

Mean

599.548

Sample N StDev (Within)

100 0.576429

StDev (Overall)

0.620865

Potential (Within) Capability Cp

1.16

CPU CPL

1.42 0.90

Cpk

0.90

Cpm

* Overall Capability

Pp

1.07

PPU

1.32

PPL Ppk

0.83 0.83

49

Within Overall

Cp and Cpk values are calculated based on estimated StDev(Within). The minimum of CPU (capability with respect to USL) and CPL to LSL) 598 (capability 599 with respect 600 601 is the Cpk 602. capability index, IfObserved a target is entered, then Cpm, Taguchi’s Performance Exp. "Within" Performance Exp. "Overall" Performance PPM LSL 10000.00 PPM < LSL 3621.06 PPM < LSL 6328.16 is USL 0.00 PPM > USL 10.51 PPM > USL 39.19 PPM Total 10000.00 PPM Total 3631.57 PPM Total 6367.35 Cp and Cpk values are considered to be “short term.”

Cp, Cpk vs. Pp, Ppk How did Minitab calculate these values? If the Cp and Pp values are significantly different this is an •Process Capability Analysis for Supp1 LSL USL indication of an out of control process.

Process Data USL

602.000

Target LSL

* 598.000

Mean

599.548

Sample N StDev (Within)

100 0.576429

StDev (Overall)

0.620865

Within Overall

Potential (Within) Capability Cp

1.16

CPU CPL

1.42 0.90

Cpk

0.90

Cpm

* Overall Capability

Pp

1.07

PPU

1.32

PPL Ppk

0.83 0.83

50

Pp and Ppk values are calculated based on estimated StDev(Overall). 598 599 600 601 602 The minimum of Ppu respect to USL) and Observed Performance Exp. (capability "Within" Performance with Exp. "Overall" Performance PPM < LSL 10000.00 PPM < LSL 3621.06 PPM < LSL 6328.16 P (capability with respect to LSL) is the P . pk pl PPM > USL 0.00 PPM > USL 10.51 PPM > USL 39.19 PPM Total 10000.00 PPM Total 3631.57 PPM Total 6367.35 Pp and Ppk values are considered to be “longer term.”

PART 3:

Cp, Cpk and Six Sigma

Slide 51

Process Should be Stable before Checking Capability UCL

LCL

NOT a Stable Process UCL

LCL

A Stable Process Slide 52

Stable Process are Predictable! LSL d Individuals Distribution Percent out of Spec

-3σ -2σ -1σ 0

Slide 53

1σ 2σ 3σ

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%

Cp Compares the Specification Range to the Width of the Process, (±3σ each side of the mean): Cp = USL-LSL 6S USL Cp = 0.5

Cp = 1

Cp = 1.5

Cp Does Not Consider Centering

Slide 54

Cp = 2

LSL

Cp = 1 ±1.5σ

LSL

USL

6.75% Defective

• -3σ

• 3σ

• 3 – Sigma Process

Allows a ±1.5σ operating window, worse case is 6.7% defective. Slide 55

Cp = 1.5 ±1.5σ

LSL

USL

1350 Defects/Million

-4.5σ

4.5σ 4.5 – Sigma Process

Allows a ±1.5σ operating window, worse case is 1350 defects per million. Slide 56

Cp = 2.0 •LSL

±1.5σ

•USL

3.4 Defects/Million

-6σ

6σ 6 – Sigma Process

Allows a ±1.5σ operating window, worse case is 3.4 defects per million. Slide 57

What has Changed? ±1.5σ

LSL

USL

• 3 – Sigma Process

-3σ

3σ ±1.5σ

LSL

USL

4.5 – Sigma Process

-4.5σ

4.5σ LSL

±1.5σ

USL

6 – Sigma Process

-6σ

Slide 58

6σ

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 = 5 then, ±3σ/√n = ±3σ/√5 = ±1.34σ Slide 59

Cp Does Not Consider Centering Cp = 2 LSL

-6σ

Slide 60

USL

6σ

Determine Cpk Distance from X to the nearest Spec

Cpk =

3S X LSL

3S Average - LSL

Slide 61

Cpk = 1 USL

Cp = 1

LSL

Slide 62

Cpk = 2 USL

• Cp = 2

LSL

Slide 63

Cpk When Cp = 2 USL • Cpk = 1/2 Cpk = 1 • Cpk = 1.5

• Cpk = 2.0

• Cpk = 1.5 Cpk = 1 Cpk = 1/2

LSL Fix the variability, then move the average

When the process is perfectly centered, Cpk = Cp. Slide 64

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%

Slide 65

PART 4:

Use of Capability Studies

Slide 66

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.

Slide 67

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 68

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 69

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 70

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 71

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 72

PART 5:

Technical Considerations

Slide 73

The Normality Assumption • Common Misconception: “The data has to be normally distributed to be control charted”

• 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*.

Slide 74

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 75

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 76

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 77

PART 6:

Use of Control Charts

Slide 78

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 baseline from which to measure improvements

79

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 Control charts tell you when, not why 80

Why Use a Control Chart? •

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”

81

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 82

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?

83

Two General Kinds of Data • 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.

84

Continuous Data • 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

85

Control Charts for Individual Values Time ordered plot of results (just like time plots) Statistically determined control limits are drawn on the plot. Centerline calculation uses the mean UCL=53.043

53.0

LCL= X + 2.66mR Centerline = X

52.5

52.0

Avg=51.99

UCL= X + 2.66mR

51.5

51.0

LCL=50.945 2

4

6

8

10

Index

12

14

16

18

20

86

Attribute Data • 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 87

Attribute Data (Cont.) • 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 88

Control Chart Selection Tree TYPE OF DATA

Count or Classification (Attribute Data)

Measurement (Variable Data)

Count

Classification

Defects or Nonconformance

Defectives or Nonconforming Units

Fixed Opportunity

Variable Opportunity

Fixed Opportunity

Variable Opportunity

Subgroup Size of 1

Subgroup Size < 9

Subgroup Size > 9

C Chart

U Chart

NP Chart

P Chart

I -m R

X-bar R

X-bar S

PoissonDistribution Distribution •Poisson

89

BinomialDistribution Distribution •Binomial

Normal Distribution •Normal Distribution

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 90

Calculations for Individuals Charts 1. Determine sampling plan 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

91

Why Use Subgroups? It allows us to examine both within sample variation and between sample variation

92

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

93

Calculations for X-Bar & R Charts 1. 2. 3. 4. 5.

Determine an appropriate subgroup size and sampling plan Sample: (Take a set of readings at each specified interval of time) Calculate the average and range for each subgroup Plot the data. (Both the averages and the ranges) 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

94

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

95

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

96

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) 97

PART 7:

Use of Control Charts

Slide 98

Uses of Control Charts • Evaluation

• Improvement

• Maintenance

Slide 99

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

• Improvement

• Maintenance

Slide 100

Uses of Control Charts • Evaluation

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

• Maintenance Slide 101

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

Slide 102

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 103

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.

Slide 104

Real Time Evaluation

Rule 1 The data outside of control limit: One point of outside the control limit 56

55

54

53

UCL=53.043

52

Avg=51.99

51

LCL=50.945 2

4

6

8

10

12

Index

14

16

18

20

105

Real Time Evaluation Rule 2 Trend Shift: 8 consecutive point on same side of center line UCL=53.043

53.0

52.5

52.0

Avg=51.99

51.5

51.0

LCL=50.945 3

6

9

12

15

Index

18

21

24

27

106

Real Time Evaluation Rule 3 Trend drift: 6 consecutive points that trend in the same direction (all increasing or all decreasing) UCL=53.043

53.0

52.5

52.0

Avg=51.99

51.5

51.0

LCL=50.945 3

6

9

12

Index

15

18

21

24

107

PART 8:

Minitab Exercise

Slide 108

Opening a new project in Minitab Menu bar Toolbars Session window Data window Project Manager window (minimized)

109

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

110

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

111

Example 1 Tools • • • • •

Dotplot Time Series Plot Graphical Summary Display Descriptive Statistics Layout Tools

112

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

113

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 114

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.

115

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] 116

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

117

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

118

119

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

120

121

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

122

123

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.

124

125

Example 2 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

127

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

128

Individual chart shows that the process is clearly not in statistical control also process operated consistently above the mean. 129

Next Step Remove mean then replot the I-MR Chart

130

Example 3 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

132

Normality Check • Check normality data (P>0.05) Probability Plot of Fill Weight Normal - 95% CI

99.9

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

99 95

Normal Data P > 0.05

Percent

90 80 70 60 50 40 30 20 10 5 1 0.1

1130

1140

1150

1160

1170

Fill Weight

1180

1190

1200

133

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

134

Capability Analysis • Cp/Cpk > 1.33 Process Capability Report for Fill Weight Process Data LSL 1100 Target * USL 1200 Sample Mean 1163.58 Sample N 60 StDev(Overall) 8.57554 StDev(Within) 8.34686

LSL

USL

Overall Capability Pp 1.94 PPL 2.47 PPU 1.42 Ppk 1.42 Cpm * Potential (Within) Capability Cp 2.00 CPL 2.54 CPU 1.45 Cpk 1.45

1110

PPM < LSL PPM > USL PPM Total

Overall Within

Performance Observed Expected Overall 0.00 0.00 0.00 10.81 0.00 10.81

1125

1140

1155

1170

1185

1200

Expected Within 0.00 6.39 6.39

135

Summary • • • • •

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

136

137