Managing VariabilityProcess Control and Process

Capability

Sangeeta Shah Bharadwaj

Managing Process Variation

• Which sub-process do you want to Control?

• What do you want to control? – Measures and metrics?

• Will it Impact the output/outcome?

Control Charts

• Detect if something is wrong with process• Establish what the process is inherently

capable of achieving• Help diagnose the cause of abnormal behavior

of process• Monitor and control process• When not to take any corrective action.

Analyze Process Variability

• Collect the data• Related to some KPI• Collect samples over time period• Calculate X bar and standard deviation• Draw X Bar control charts

X-bar and R Chart

• X-bar chart monitors the process mean by using the means of small samples taken frequently

• R chart monitors the process variation by using the sample ranges as the measure of variability– Range = Maximum value – Minimum value

Example of Notation

HourService Time

(minutes)Sample Mean,

Sample Range, R

T1 T2 T3

10:00 AM 5 12 4 21/3 = 7 12 – 4 = 8

12 Noon 6 8 10 24/3 = 8 10 – 6 = 4

3:00 PM 9 4 2 15/3 = 5 9 – 2 = 7

= 20/3 = 6.7 =19/3 =6.3

X

X R

X bar Chart

• X bar chart is used to monitor the variation of the subgroup averages that are calculated from individual sampled data

Control Charts

X bar Control Charts

Underlying Distributions

X

Samplingdistribution of Distribution of

X

X

Control Limits for X-bar Chart• Since we are plotting sample means on the X-bar chart, the control limits are based on the distribution of the sample means.

• The control limits are therefore

nXUCL

3

nXLCL

3

Control Limits for X-bar Chart

UCLLCL

Xn

X

3n

X

3

Distribution of X

nXUCL

nXLCL

ˆ3

ˆ3

RAXUCL

RAXLCL

2

2

Control Limits for X-bar Chart and Relation with Range

Control Limits for X-bar Chart

RAn

2

ˆ3

A2 is a factor that depends on the n, the sample size,

and will be given in a table.

Example of X-bar Chart

· A company that makes soft drinks wants to monitor the sugar content of its drinks.

· The sugar content (X) is normally distributed, but the means and variances are unknown.

· The target sugar level for one of its drinks is 15 grams.

· The lower spec limit is 10 grams.· The upper spec limit is 20 grams.

Example of X-bar Chart

• The company wants to know how much sugar on average is being put into this soft drink and how much variability there is in the sugar content in each bottle.

• The company also wants to know if the mean sugar content is on target.

• Lastly, the company wants to know the percentage of drinks that are too sweet and the percentage that are not sweet enough. (Next section)

Example of X-bar Chart• To obtain this information, the company

decides to sample 3 bottles of the soft drink at 3 different time each day:– 10 A.M, – 1:00 P.M. and – 4:00 P.M.

• The company will use this data to construct an X-bar and R chart. (In practice, you need 25-30 samples to construct the control limits.)

• For the past two days, the following data were collected:

Example of X-bar Chart

Day Hour X1 X2 X3

1 10 am 17 13 6

1 pm 15 12 24

4 pm 12 21 15

2 10 am 13 12 17

1 pm 18 21 15

4 pm 10 18 17

What is n?

What is the k?

What is the next step?

Example of X-bar ChartDay Hour X1 X2 X3 R1 10 am 17 13 6 36/3 =12 11

1 pm 15 12 24 51/3 =17 12

4 pm 12 21 15 48/3 =16 9

2 10 am 13 12 17 42/3 =14 5

1 pm 18 21 15 54/3 =18 6

4 pm 10 18 17 45/3 =15 8

= 92/6= 15.33

= 51/6= 8.5

X R

X

X-bar Chart Control Limits

RAXUCL

RAXLCL

2

2

Table A: X-bar Chart Factor, A2

n A2

2 1.88

3 1.02

4 0.73

5 0.58

02.1

3

notesin A Table From

5.8

33.15

2

A

n

R

X

X-bar Chart Control Limits

0.24

)5.8(02.133.15

66.6

)5.8(02.133.15

2

2

RAXUCL

RAXLCL

X-bar Chart Control Limits

X-bar Chart for Sugar Content

0.00

5.00

10.00

15.00

20.00

25.00

30.00

10 1 4 10 1 4

Hour Hour

1 2

Day

Interpreting Control Charts

• By points that fall above the UCL and below LCL

• By Points that are not randomly distributed

Interpreting Control Charts

• Run violations: seven or more consecutive points are on one side of the center line

• Trend Violation: Upward or downward movement of five or more consecutive points

• Points not randomly distributed: e.g. non random patterns such as cycles

• Hugging• Oscillatory• Avoidance of 1 sigma area

Statistical Control• Controlled Variation is attributed to chance

and is characterized by stable and consistent pattern of normal variation over time

• Uncontrolled variation changes over time and can be attributed to an assignable cause

Statistical Control• State of randomness

– Variation is due to chance alone and nothing external is disturbing the stability of the process

• Recurring cycles – may reflect wear and fatigue

• Lack of variability– Control limits very relaxed

• Trends can be addressed– Find reasons

Interpretation of X-bar Chart

· The X-bar chart is in control because ????· This means that the only source of variation

among the sample mean is due to random causes.

· The process mean is therefore stable and predictable and, consequently, we can estimate it.

Interpretation of X-bar Chart

· Our best estimate of the mean is the center line on the control chart, which is the overall mean (X-double bar) of 15.33 grams.

· If the process remains in control, the company can predict that all bottles of this soft drink produced in the future will have a sugar content of, on average, 15.33 grams.

Interpretation of X-bar Chart • This prediction, however, indicates that there

is a problem with the location of the mean. • The process mean is off target by 0.33 grams

(15.33 -15.00).• The process mean, although stable and

predictable, is at the wrong level and should be corrected to the target.

Interpretation of X-bar Chart• Since the process mean is in control, there

are no special causes of variation that may be responsible for the mean being off target.

• Since the operators are responsible for correcting problems due to special causes and management is responsible for correcting problems due to random causes of variation, management action is required to fix this problem.

Range Chart

Range chart looks at the range in a subgroup

R Chart• Monitors the process variability (the variability

of X)• Tells us when the process variability has

changed or is about to change. • R chart must be in control before we can use

the X-bar chart.

R Chart

• Rules for detecting changes in variance:– If at least one sample range falls above the

upper control limit, or there is an upward trend within the control limits, process variability has increased.

– If at least one sample range falls on or below the lower control limit, or there is a downward trend within the control limits, process variability has decreased.

RDUCL

RDLCL

4

3

R Chart Control Limits

n D3 D4

2 0 3.273 0 2.574 0 2.285 0 2.11

Table B: Factors for R Chart

85.21

)5.8(57.2

0

)5.8(0

UCL

LCL

R Chart Control Limits

57.2

0

3

4

3

D

D

n

R Chart for Weight

05

1015

2025

10 1 4 10 1 4

Hour Hour

1 2

Day

R

LCL

UCL

R-bar

Interpretation of R Chart• Since all of the sample ranges fall within the

control limits, the R chart is in control.• The standard deviation is stable and

predictable and can be• This does not necessarily mean that the

amount of variation in the process is acceptable.

Interpretation of R Chart

• Continuous improvement means the company should continuously reduce the variance.

• Since the process variation is in control, management action is required to reduce the variation.

X-bar Chart

UCL

LCL

Expected Pattern in a Stable Process

Time

Expected pattern is a normal distribution

Is a Stable Process a Good Process?

• “In control” indicates that the process mean is stable and hence predictable.

• A stable process, however, is not necessary a “good” (defect free) process.

• The process mean, although stable, may be far off target, resulting in the production of defective product.

• In this case, we have, as Deming puts it, “A stable process for the production of defective product.”

Control Charts

• Is the process unstable? Problem Solving tools– -by pointing out where improvement is needed– Take corrective action.

• Is the process stable? Decision making tool– What is the process capability?– Whether to improve it further and or leave it as it

is

Responsibility for Corrective Action

Special Causes(Process out of

control)

Random Variation(Process in Control)

Operators (workers)

Management

Benefits of Control Charts• Control charts prevent unnecessary

adjustments.– If process is in control, do not adjust it.– Adjustments will increase the variance. – Management action is required to improve

process.– Adjustments should be made only when

special causes occur.

Benefits of Control Charts

• Control charts assign responsibility for corrective action.

• Control charts are the only statistical valid way to estimate the mean and variance of a process or product.

• Control charts make it possible to predict future performance of a process and thereby take early corrective action.

Analyze the reason for variation

Root Cause Analysis

• ??

• 4Ms: Methods, Manpower, Materials and Machinery

• 4Ps: Policies, Procedures, People , Plant• Environment, workflow.

Data Entry Clerk Materials

Data entry Variation

Environment Machine

Incorrect forms or materials

Running out of materials

Outdated materials

Fatigue Inadequate training

AttitudeNot familiar with work place

TemperatureWaiting line not managed well

Power outageDisruptions due to meetings or other chores

downtimeNot User friendly

Slow response time (Network)

Too many steps in the procedure

Fishbone Diagram for Analyzing Customer Dissatisfaction

Reasons for variability

• Inadequate training• Machine downtime• Slow response time• Incorrect forms • Etc

Pareto Chart

• Allows you to focus on significant problems• 80-20 rule (80 percent problems come from 20%

causes)

• Need a measurement of ranking?– Cost, Frequency, percentage

• Determine time frame• Collect data• Plot in descending order

Pareto Diagram of Causes of Customer Dissatisfaction

Causes0

10

20

30

40

50

60

50

30

10

7

3

Inadequate Training

Machine Downtime

Slow response time

Incorrect forms

Others