Spc(small)

S TATISTICAL PROCESS CONTROL CUSTOMER & COMPETITIVE INTELLIGENCE FOR PRODUCT, PROCESS, SYSTEMS & ENTERPRISE EXCELLENCE

Data Driven Decision Making  “In God we trust. ... all others must bring data.” --- The Statistician’s Creed  SPC is one method that assists in enabling “data-driven decision making”  SPC is a key quantitative aid to quality improvement efforts

Statistical Process Control  Statistical Process Control (SPC) can be thought of as the application of statistical methods for the purposes of quality control and improvement  Quality Improvement is perhaps foremost among all areas in business for application of statistical methods

The Aim of S.P.C. - Detection Strategy Detection: • This focuses on identification of problems after production, by 100% inspection or through customer complaints Detection Drawbacks: • Production is already made • Customer dissatisfaction • Inflated costs - rework; inspection • Repetitive problems • Neglected improvements

Aim of S.P.C. - Prevention Strategy Prevention: • This focuses on in-process production and identification of problems through analysis of process capability • It is a future-orientated strategy Prevention Benefits: • Improved design and process capability • Improved manufacturing quality • Improved organisation • Continuous Improvement

SPC Techniques • Graphs and charts have to be chosen for their simplicity, usefulness and visibility • • • • • • •

Pareto Diagram Process Flow Diagram Cause-and-Effect Diagram Check Sheets Histogram Scatter Diagram Control Charts

Techniques For Improvement. Inputs

Scatter Diagrams

Outputs

Input-Output analysis Flow Charts Cause-Effect Diagrams

Pareto Analysis

x x x x x x x x

Why - why analysis Why? Why? Why?

Pareto Diagram • Graph that ranks data classifications in descending order from left to right – Problems, causes, complaints, field failures, NC etc

• Used to identify the most important problems and measurement of progress – Resources are then directed to take necessary corrective action

• ‘Vital Few’ are placed on the left and ‘Useful Many’ on the right – Some of ‘Useful Many’ are grouped together and placed on the far right side of graph

• Few customers account for the majority of sales

80% 80%of of the the problems problems may may be be attributed attributed to to 20% 20%of of the the causes. causes.

Number of defects

Pareto Analysis

Off Smeared Missing Loose Other centre print label

Pareto Diagram • Pareto diagram is constructed in five steps – Determine the method of classifying the data: by problem, cause, NC etc – Decide of dollars (best), frequency, or both are to be used to rank the characteristics – Collect data for an appropriate time interval or use historical data – Summarize the data & rank order categories from largest to smallest – Construct the diagram and find the ‘Vital Few’

Process Flow Diagram • These show the flow of products or services as it moves through the various processing operations • Makes it easy to visualize the entire system identify potential trouble spots, & locate control activities – Enables to know ‘WHO IS THE NEXT CUSTOMER’

• It subsequently leads to improvements by reducing, combining, or eliminating steps • The symbols are also used to provide additional information about processes & decision making

Process Flow Diagram

Cause-and-Effect Diagram (C& E) • Composed of lines & symbols designed to represent a relationship b/w an effect & its causes – Also called a ‘Fishbone’ or ‘Ishikawa’ diagram – Causes are listed on left and Effect on right side

• Used to investigate a ‘Bad/Good Effect’ and to take action to correct/learn the causes • Causes are broken down into major & then into numerous minor causes • Most likely causes are then selected by the team • Solutions for these causes are proposed and evaluated before implementation

Cause-and-Effect Diagram Methods Cause

Environment

Materials Cause Cause

Cause

Cause

Cause Cause

People

Cause

Cause

Cause Cause

Cause

Equipment

Effect

Cause-and-Effect Diagram (C& E) • Tips for making a C & E Diagram; – Participation is required from each member – Quantity rather than quality is imp for creative solution – Focus on solving the problem rather than discussing how it began. Criticism of any idea is not allowed – Let the idea to incubate for some time;at least overnight

• Benefits – Analyze actual conditions for quality improvements, efficient use of resources & reduced costs – Eliminate conditions causing NCs & complaints – Standardize existing & proposed operations – Educate & train personnel in decision-making and corrective-action activities

Check Sheets • Meant to ensure that data are collected carefully & accurately by operating personnel – So that they are analyzed quickly & carefully

• Each check sheet is individualized for each situation & designed by the project team • Check sheets may also be designed to show location • It should be user friendly and may also include information on time and location, whenever possible

Check Sheet Billing Errors Wrong Account Wrong Amount

A/R Errors Wrong Account Wrong Amount

Monday

Histogram • Basic statistical method that describes variation in the process (like a snapshot of a process) • It gives sufficient info about a quality problem to provide a basis for quick decision making • It can determine the process capability, compare with the specs, suggest the shape of population & indicate discrepancies in the data, such as gaps – Graphically estimates the process capability & relationship to the specifications & target

• The data is usually so voluminous that it is more confusing then useful

Histogram • Some means are thus essential to summarize the data to show; – What value the data tend to cluster about – How the data are dispersed or spread out

• Two techniques are needed to accomplish this summarization of data- graphical & analytical • Graphical technique is a picture of frequency distribution – Summarization of how the data points occur within each subdivision of observed values or groups of observed values

• Analytical techniques summarize data by computing a measure of the central tendency (avg, median & mode)

Data Interpretation Consider these 50 measurements Bore Diameter 36.32 ±0.05mm (36.27 - 36.37mm) 1 2 3 4 5 6 7 8 9 10

36.36 36.34 36.34 36.33 36.35 36.33 36.33 36.34 36.35 36.35

11 12 13 14 15 16 17 18 19 20

36.37 36.35 36.32 36.35 36.34 36.34 36.35 36.33 36.32 36.35

21 22 23 24 25 26 27 28 29 30

36.34 36.37 36.34 36.35 36.34 36.35 36.36 36.33 36.36 36.38

31 32 33 34 35 36 37 38 39 40

36.35 36.35 36.36 36.37 36.34 36.36 36.38 36.34 36.35 36.35

41 42 43 44 45 46 47 48 49 50

36.36 36.37 36.37 36.35 36.37 36.36 36.35 36.34 36.35 36.34

Data Interpretation • As a set of numbers it is difficult to see any pattern • Within the table, numbers 30 and 37 were outside the tolerance – but were they easy to spot? • A way of obtaining a pattern is to group the measurements according to size

Data Interpretation – Tally Chart 36.39 36.38 36.37 36.36 36.35 36.34 36.33 36.32 36.31 36.30 36.29 36.28

• The tally chart groups the measurements together by size as shown • The two parts that were out of tolerance are now easier to detect (36.38mm)

Tally Chart - Frequency 36.39 36.38 36.37 36.36 36.35 36.34 36.33 36.32 36.31 36.30 36.29 36.28

2 6 7 16 12 5 2

• The tally chart shows patterns and we can obtain the RANGE 36.32mm to 36.38mm • The most FREQUENTLY OCCURRING size is 36.35mm

Tally Chart - Information • The tally chart gives us further info: – Number of bores at each size; – Number of bores at the most common size; – The number of bores above and below the most common size (36.35mm) – Number above 36.35mm is 7+6+2=15 – Number below 36.35mm is 12+5+2=19

Histogram We can redraw the frequency chart as a bar chart known as a histogram: 16 14 12 10 8 6 4 2 0

36.31

36.32

36.33

36.34

36.35

36.36

36.37

36.38

36.39

Smoothed Frequency If we draw a smooth curve through the top of each box we get a bell-shaped pattern: 16 14 12 10 8 6 4 2 0

36.31

36.32

36.33

36.34

36.35

36.36

36.37

36.38

36.39

Distribution • The bell-shaped pattern is fairly typical of most industrial processes • There is a central value at the highest point of the curve and the pattern of results spread out equally on both sides of the central value • The further we move from the central value, the fewer values we will find • This bell-shaped pattern is known as the ‘NORMAL DISTRIBUTION’ – Expected where the process is running in a stable condition

Scatter Diagram • The simplest way to determine if the cause-andeffect relationship exist b/w two variables • Few steps to construct a scatter diagram are; – Data are collected as ordered pairs (x,y) – The sample numbers are plotted and scatter diagram is complete – After constructing the scatter diagram, correlation b/w the two variables can be evaluated • • • •

If ‘Y’ increases with ‘X’, it has a positive correlation If ‘Y’ decreases with ‘X’, it has a negative correlation If ‘Y’ does not change with ‘X’, it has no correlation Curvilinear correlation may exist

Process Variation Process Variability Variations due to:

Natural Causes: • Environment variation • Material variation • Equipment variation • Operator performance

Must be monitored

Assignable Causes: • Machine is breaking • Untrained operative • Machine movement • Process has changed

Early and visible warning required

Control Charts: Recognizing Sources of Variation • Why Use a Control Chart? – To monitor, control, and improve process performance over time by studying variation and its source

• What Does a Control Chart Do? – Focuses attention on detecting & monitoring process variation over time; – Distinguishes special from common causes of variation, as a guide to local or management action; – Serves as a tool for ongoing control of a process; – Helps improve a process to perform consistently and predictably for higher quality, lower cost, and higher effective capacity; – Provides a common language for discussing process performance

Diameter

Run Chart 0 .5 8 0 .5 6 0 .5 4 0 .5 2 0 .5 0 .4 8 0 .4 6 0 .4 4 1

2

3

4

5

6

7

8

9

T im e ( H o u rs )

Time (Hours)

10

11

12

Control Chart 1020

UCL

1010 1000 990

LCL

980 970 0

1

2

3

4

5

6

7

8

9 10 11 12 13 14 15

Control Chart Construction • Select the process to be charted • Determine sampling method and plan; – How large a sample needs to be selected? Balance the time and cost to collect a sample with the amount of info you will gather – As much as possible, obtain the samples under the same technical conditions: the same machine, operator, lot, and so on – Frequency of sampling will depend on whether you are able to discern patterns in the data. Consider hourly, daily, shifts, monthly, annually, lots, and so on. Once the process is “in control”, you might consider reducing the frequency with which you sample – Generally, collect 20-25 groups of samples before calculating the statistics and control limits – Consider using historical data to establish a performance baseline

Control Chart Construction • Initiate data collection: – Run the process untouched, and gather sampled data – Record data on an appropriate Control Chart sheet or other graph paper. Include any unusual events that occur • Calculate the appropriate statistics and control limits: – Use the appropriate formulas • Construct the control chart(s) and plot the data

Tracking Improvements UCL

UCL

LCL LCL

Process centered Process not centered and stable and not stable

UCL

LCL Additional improvements made to the process

Control Charts: Control Limits UCL A

*

**

C

*

*C B A

U2SWL

*

B

* * * *

*

*

*

* *

U1SL CL L1SL L2SWL LCL

Control Chart Interpretation • Center line (CL) positioned at the estimated mean • Upper and lower one standard deviation lines (U1SL and L1SL) positioned one standard deviation above and below the mean. • Upper and lower two standard deviation warning lines (U2SWL and L2SWL) positioned at two standard deviations above and below the mean. • Upper and lower control lines (UCL and LCL) positioned at three standard deviations above and below the mean.

Control Charts for the

Process Mean and  Dispersion            ‘X bar’ Chart  Typically used to monitor process centrality (or location)  Limits depend on the measure used to monitor process dispersion

‘S’ or ‘Standard Deviation’ Chart:  Used to monitor process dispersion when n > 10  Used where more sensitivity is desired  When data are collected automatically

‘R’ or ‘Range’ Chart:  Also used to monitor process dispersion when only one observation is possible at a time and data are normal  Equations are based upon moving range of two

Sample Summary Information • m = 20 to 40 initial samples of n observations each • Xi = mean of ith sample • Si = standard deviation of ith sample • Ri = range of ith sample R = (R1 + R2 + ... +Rm)/m S = (S1 + S2 + ... + Sm)/m σ = R/d2 where d2 depends only on n

Coordinates for the X­bar Control Chart • CL= X, • UCL= X+ A2R, • UCL= X- A2R • U2SWL= X+ 2A2R/3 • L2SWL= X- 2A2R/3 • U1SL= X+ A2R/3 • L1SL= X- A2R/3 A2 is a constant that depends only on n

Coordinates for an R Control Chart • CL= R • UCL= D4R • LCL= D3R • U2SWL= R+ 2(D4-1)R/3 • L2SWL= R- 2(D4-1)R/3 • U1SL= R+ (D4-1)R/3 • L1SL= R- (D4-1)R/3 • where D3 and D4 depend only on n

   Championship Card Company

Championship

Championship Card Company Championship Card Company (CCC) produces collectible sports cards of college and professional athletes. CCCs card-front design uses a picture of the athlete, bordered all-the-way-around with one-eighth inch gold foil. However, the process used to center an athlete’s picture does not function perfectly. Five cards are randomly selected from each 1000 cards produced and measured to determine the degree of off-centeredness of each card’s picture. The measurement taken represents percentage of total margin (.25”) that is on the left edge of a card. Data from 30 consecutive samples is included and summarized on the following slides.

Championship Card Company Sample X-bar R 1 55.6 22 2 61.0 23 3 45.2 20 4 46.2 11 5 46.8 18 6 7 8 9 10

49.8 46.8 44.2 50.8 48.4

23 18 20 32 16

Sample X-bar R 11 51.2 15 12 49.4 14 13 44.0 32 14 51.6 14 15 53.2 12 16 17 18 19 20

52.4 50.6 56.0 50.2 44.0

23 8 18 19 23

Sample 21 22 23 24 25

X-bar 50.0 47.0 50.6 48.8 44.6

R 11 14 15 16 22

26 27 28 29 30

46.8 49.2 45.6 57.6 51.4

16 8 19 40 17

Championship Card Company Summary Information n=5

A3 = 1.427

X = 49.63

B3 = NA

S = 7.42

B4 = 2.089

R = 18.63 d2 = 2.326 A2 = 0.577

D3 = NA D4 = 2.115 σ = R/d2 = 8.01

Championship Card Company X­bar and R Control Chart Limits UCL U2SWL U1SL CL L1SL L2SWL LCL

X based on R

R

60.38 56.80 53.22 49.63 46.05 42.47 38.89

39.40 32.48 25.55 18.63 11.71 4.79 ------

Championship Card Company X Bar Chart for Sports Cards CenteringValues Limits Based on R 1 60

3.0S L=60.38

n a e M e l p 50 m a S

2.0S L=56.80 1.0SL=53.22 X=49.63 -1.0SL=46.05 -2.0S L=42.47

40

-3.0S L=38.89 0

10

20

SampleNumber

30

Samples of 5 fromeach 1000 Cards Printed

Championship Card Company R Chart for Sports Card Centering 40

3.0S L=39.40

e g 30 n a R e l p 20 m a S

2.0S L=32.48 1.0SL=25.55 R=18.63 -1.0SL=11.71

10

-2.0S L=4.791 0

-3.0S L=0.000 0

10

20

SampleNumber

30

Samples of 5 Cards fromeach 1000 Produced

Championship Card Company X­bar & R Chart Interpretation • Application of all eight to the X-bar chart indicated a violation of one point plotting above the UCL at sample 2. Apparently, a successful process adjustment was made, as suggested by examination of the remainder of the chart. • Application of one through four to the R chart indicated a violation at sample 29. Measures would be investigated to reduce process variation at that point. The violation was a “close call” and was out of character with the remainder of the data. • Now we will be able to apply PDCA to the process for the purpose of achieving lasting process improvements.

Common Questions for Investigating an Out­of­Control Process • Are there differences in the measurement accuracy of instruments / methods used? • Is the process affected by predictable conditions such as tool wear? • Has there been a change in the source for input to the process such as a new supplier or information? • Are there differences in the methods used by different personnel? • Were any untrained personnel involved in the process at the time? • Is the process affected by employee fatigue? • Is the process affected by the environment, e.g. temperature/humidity? • Has there been a significant change in the environment?

Common Questions for Investigating an Out-of-Control Process

• Is the process frequently adjusted? • Did the samples come from different parts of the process? Shifts? Individuals? • Has there been a change in policies or procedures such as maintenance procedures? • Are employees afraid to report “bad news”

P-Chart • It is used to report the performance of group or quality of produced item • It is used to control; – One quality Characteristic or; – Group of Quality Characteristic of the same type or same part or; – To control the entire product

• A hierarchy of utilization exists so that data collected for one chart can also be used on a more all-inclusive chart

P Chart Control Lines &  Limits The coordinates for the seven lines on the P chart are positioned at: CL = U1SL = U2SWL = UCL =

p p + Sp p + 2Sp p + 3Sp

L1SL = p - Sp L2SWL = p - 2Sp LCL = p - 3Sp

South of the Borders, Inc. Custom Wallpapers & Borders

Free Estimates (013) 555-9944

   South of the Borders, Inc. South of the Borders, Inc. is a custom wallpapers and borders manufacturer. While their products vary in visual design, the manufacturing process for each of the products is similar. Each day a sample of 100 rolls of wallpaper border is sampled and the number of defective rolls in the sample is noted. The number of defective rolls in samples from 25 consecutive production days follows. Determine all coordinates; construct & interpret the p chart.

    South of the Borders, Inc. Day Defective Rolls 1 13 2 4 3 7 4 11 5 8 6 10 7 2 8 9 9 12 10 6 11 4 12 7 13 9

Day 14 15 16 17 18 19 20 21 22 23 24 25

Defective Rolls 8 9 3 5 14 10 11 6 6 9 3 10

South of the Borders, Inc. Total # of items sampled = 2500 Total # of defective items = 196 p = 196/2500 = .0784 Sp = √ .0784(.9216)/100 = .02688

  South of the Borders, Inc. CL =

.0784

UCL =

.0784 +

3(.0269) =

.1590

LCL =

.0784 -

.0807 =

-.0023

U2SWL = .0784 +

2(.0269) =

.1322

L2SWL = .0784 -

.0538 =

.0246

U1SL =

.0784 +

.0269 =

.1053

L1SL =

.0784 -

.0269 =

.0515

P Chart for Defective Wallpaper Rolls 3.0SL=0.1590

n o it ro 0.10 p o r P 0.05 0.15

2.0SL=0.1322 1.0SL=0.1053 P=0.07840 -1.0SL=0.05152 -2.0SL=0.02464

0.00 Subgroup Rolls

-3.0SL=0.000 0

5

10

15

20

25

8

6

9

11

10

Proportion of Defective Rolls Received

South of the Borders, Inc.   P Chart Interpretation • No violations are apparent. This implies that the process is “in a state of statistical control”. • It does not indicate that we are satisfied with the performance of the process. • It does, however, indicate that the process is stable enough in its performance that we may seriously engage in PDCA for the purpose of long-term process improvement.

Process Capability: 1.

Construct the control chart and remove all special causes. NOTE: special causes are “special” only in that they come and go, not because their impact is either “good” or “bad”

2. Estimate the standard deviation. The approach used depends on whether a R or P chart is used to monitor process variability.

^

_

σ = R / d2 Several capability indices are provided on the following slide.

Process Capability Indices: Variables Data ^

^

CP = (Engineering Tolerance)/6σ = (USL – LSL) / 6σ • •

This index is generally used to evaluate machine capability, tolerance to the engineering requirements. Assuming that ‘the process is (approximately) normally distributed and that the process average is centered between the specifications’, • An index value of “1” is considered to represent a “minimally capable” process. HOWEVER … • Allowing for a drift, a min value of 1.33 is ordinarily sought … bigger is better. • A true “Six Sigma” process will have Cp = 2.

Process Capability Indices: Variables Data _ ^ ZU = (USL – X) / σ

_

^

ZL = (X – LSL) / σ

Zmin = Minimum (ZL , ZU) Cpk = Zmin / 3 •

This index DOES take into account how well or how poorly centered a process is. A value of at least +1 is required with a value of at least +1.33 being preferred.

•

Cp and Cpk are closely related. In some sense Cpk represents the current capability of the process whereas Cp represents the potential gain to be had from perfectly centering the

Process Capability: Example Assume that we have conducted a capability analysis using X-bar and R charts with subgroups of size n = 5. Also assume the process is in statistical control with an average of 0.99832 and an average range of 0.02205. A table of d2 values gives d2 = 2.326 (for n = 5). Suppose LSL = 0.9800 and USL = 1.0200

^

_ σ = R / d2 = 0.02205/2.326 = 0.00948 Cp = (1.0200 – 0.9800) / 6(.00948) = 0.703 ZL = (.99832 - .98000)/(.00948) = 1.9 ZU = (1.02000 – .99832)/(.00948) = 2.3 so that Zmin = 1.9 Cpk = Zmin / 3 = 1.9 / 3 = 0.63

Process Capability: Interpretation Cp = 0.703 … since this is less than 1, the process is not regarded as being capable ZL = 1.9 … This should be at least +3 and this value indicates that more percentage of products will be undersized ZU = 2.3 should be at least +3 and this value indicates less percentage of products will be oversized Cpk = 0.63 … since this is only slightly less that the value of Cp the indication is that there is little to be gained by centering and that the need is to reduce process variation