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Chapter 9 Managing Flow Variability
Managing Business Process Flows:
1
Managing Flow Variability: Process Control
and Capability
Chapter 9 Managing Flow Variability
Managing Flow Variability
2
 9.1 Performance Variability
 9.2 Analysis of Variability
 9.3 Process Control
 9.4 Process Capability
 9.5 Process Capability Improvement
 9.6 Product and Process Design
Chapter 9 Managing Flow Variability
Managing Business Process Flows:
3
Great year…….
Great Products!
Service!
Reputation!
Congratulations!!
Good Job everyone!
Sorry to burst
the bubble... But
we are not doing well.
I heard customers are
not satisfied with our
products and services
Hhhmmm… we need
hard data.
We need to identify,
correct and prevent
future problems!
You’re
Fired
Yikes…mor
e work
Chapter 9 Managing Flow Variability
Managing Business Process Flows:
4
All Products & Services VARY in Terms Of
Cost
Quality
Availability
Flow
Times
Variability often leads to Customer Dissatisfaction
Chapter covers some geographical/statistical
methods for measuring, analyzing, controlling &
reducing variability in product & process
performance to improve customer satisfaction
Chapter 9 Managing Flow Variability
§ 9.1 Performance Variability
5
 All measures of product & process performance (external & internal) display
Variability.
 External Measurements - customer satisfaction, relative product
rankings, customer complaints (vary from one market survey to the next)
 Possible sources: supplier delivery delays or changing tastes
 Internally - flow units in all business processes vary with respect to
cost, quality & flow times
 Possible sources: untrained workers or imprecise equipment
Example 1 ~ No two cars rolling off an assembly line are identical. Even under
identical circumstances, the time & cost required to produce the same
product could be quite different.
Example 2 ~ Cost of operating a department within a company can vary from
one quarter to the next.
Chapter 9 Managing Flow Variability
§ 9.1 Performance Variability
6
 Variability refers to a discrepancy between the actual and
the expected performance.
 Can be due to gap between the following:
 What customer wants and what product is designed for
 What product design calls for and what process for making it is capable of producing
 What process is capable of producing and what it actually produces
 How the produced product is expected to perform and how it actually performs
 How the product actually performs and how the customer perceives it
 This often leads to:
 higher costs, longer flow times, lower quality &
DISSATISFIED CUSTOMERS
Chapter 9 Managing Flow Variability
§ 9.1 Performance Variability
7
 Processes with greater performance variability are generally judged
LESS satisfactory than those with consistent, predictable
performance.
 Variability in product & process performance, not just its average,
Matters to consumers!
 Customers perceive any variation in their product or service from
what they expected as a LOSS IN VALUE.
 In general, a product is classified as defective if its cost, quality,
availability or flow time differ significantly from their expected values,
leading to dissatisfied customers.
Chapter 9 Managing Flow Variability
Quality Management Terms
8
BOOK COVERS A FEW QUALITY MANAGEMENT TERMS:
 Quality of Design: how well product specifications aim to meet customer
requirements (what we promise consumers ~ in terms of what the product can do)
 Quality Function Deployment (QFD): conceptual framework for translating
customers’ functional requirements (such as ease of operation of a door or its
durability) into concrete design specifications (such as the door weight should be
between 75 and 85 kg.)
 Quality of conformance: how closely the actual product conforms to the chosen
design specifications (how well we keep our promise in terms of how it actually
performs)
 Measures: fraction of output that meets specifications, # defects per car,
percentage of flights delayed for more than 15 minutes OR the number of
reservation errors made in a specific period of time.
Chapter 9 Managing Flow Variability
§ 9.2 Analysis of Variability
9


To analyze and improve variability there are diagnostic tools to help us:

Monitor the actual process performance over time

Analyze variability in the process

Uncover root causes

Eliminate those causes

Prevent them from recurring in the future
Again we will use MBPF Inc. as an example and look at how their
customers perceive the experience of doing business with the company &
how it can be improved.
–
Need to present raw data in a way to make sense of the numbers,
track change over time, or identify key characteristics of the data set.
Chapter 9 Managing Flow Variability
§ 9.2.1 Check Sheets
10
 A check sheet is simply a tally of the types and
frequency of problems with a product or a service
experienced by customers.
Chapter 9 Managing Flow Variability
Example 9.1
11
Type of Complaint
Number of Complaints
Cost
IIII IIII
Response Time
IIII
Customization
IIII
Service Quality
IIII IIII IIII
Door Quality
IIII IIII IIII IIII IIII
Chapter 9 Managing Flow Variability
Check Sheets
12
Pros
 Easy to collect data
Cons
 Not very enlightening
 No numerical characteristics
Chapter 9 Managing Flow Variability
§ 9.2.2 Pareto Charts
13
 A Pareto chart is simply a bar chart that plots
frequencies of occurrences of problem types in
decreasing order.
 The 80-20 Pareto principle states that 20% of problem
types account for 80% of all occurrences.
Chapter 9 Managing Flow Variability
Example 9.2
14
25
20
15
10
5
0
Door Quality
Service Quality
Cost
Response Time
Customization
Chapter 9 Managing Flow Variability
Pareto Charts
15
Pros
 Ranks problems
 Shows relative size of quantities
Cons
 No numerical characteristics
 Only categorizes data
 No comparison process information
Chapter 9 Managing Flow Variability
§ 9.2.3 Histograms
16
 A histogram is a bar plot that displays the frequency
distribution of an observed performance characteristic.
Chapter 9 Managing Flow Variability
Example 9.3
17
14
Frequency
12
10
8
6
4
2
0
72
74
76
78
80
82
84
Weight (kg)
86
88
90
92
Chapter 9 Managing Flow Variability
Histograms
18
Pros
 Visualizes data distribution
 Shows relative size of quantities
Cons
 No numerical characteristics
 Dependant on category size
 No focus on change over time
Chapter 9 Managing Flow Variability
Table 9.1
19
Day
Time
1
2
3
4
5
6
7
8
9
10
9:00 AM
81
82
80
74
75
81
83
86
88
82
11:00 AM
73
87
83
81
86
86
82
83
79
84
1:00 PM
85
88
76
91
82
83
76
82
86
89
3:00 PM
90
78
84
75
84
88
77
79
84
84
5:00 PM
80
84
82
83
75
81
78
85
85
80
Day
Time
11
12
13
14
15
16
17
18
19
20
9:00 AM
86
86
88
72
84
76
74
85
82
89
11:00 AM
84
83
79
86
85
82
86
85
84
80
1:00 PM
81
78
83
80
81
83
83
82
83
90
3:00 PM
81
80
83
79
88
84
89
77
92
83
5:00 PM
87
83
82
87
81
79
83
77
84
77
Chapter 9 Managing Flow Variability
Raw Data
20
Pros
 Actual information
 Specific numbers
Cons
 Not intuitive
 Does not help with understanding of relationships
Chapter 9 Managing Flow Variability
§ 9.2.4 Run Charts
21
 A run chart is a plot of some measure of process
performance monitored over time
 Advantage is that it is dynamic
Chapter 9 Managing Flow Variability
Example 9.4
22
95
90
85
80
75
70
1
5
9
13
17
21
25
29
33
37
41
45
49
53
57
61
65
69
73
77
81
85
89
93
97
Chapter 9 Managing Flow Variability
Run Charts
23
Pros
 Shows data in chronological order
 Displays relative change over time (trends, seasonality)
Cons
 Erratic graph
 No numerical characteristics
Chapter 9 Managing Flow Variability
§ 9.2.5 Multi-Vari Charts
24
 A multi-vari chart is a plot of high-average-low values of
performance measurement sampled over time.
Chapter 9 Managing Flow Variability
Example 9.5
25
95
90
85
High
Low
Average
80
75
70
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
Chapter 9 Managing Flow Variability
Table 9.2
26
Day
1
2
3
4
5
6
7
8
9
10
High
90
88
84
91
86
88
83
86
88
89
Low
73
78
76
74
75
81
76
79
79
80
81.8
83.8
81.0
80.8
80.4
83.8
79.2
83.0
84.4
83.8
Average
Day
11
12
13
14
15
16
17
18
19
20
High
87
86
88
87
88
84
89
85
92
90
Low
81
78
79
72
81
76
74
77
82
77
83.8
82.0
83.0
80.8
83.8
80.8
83.0
81.2
85.0
83.8
Average
Chapter 9 Managing Flow Variability
Multi-Vari Charts
27
Pros
 Shows numerical range and average
 Displays relative change over time
Cons
 Erratic graph
 No numerical characteristics
 Lacks distribution information
 Does not provide guidance for taking actions
Chapter 9 Managing Flow Variability
§ 9.3 Process Control
28
 Goal  Actual Performance vs. Planned Performance
 Involves 
 Tracking Deviations
 Taking Corrective Actions
 Principle of feedback control of dynamical systems
Chapter 9 Managing Flow Variability
Plan-Do-Check-Act (PDCA)
29
 Process planning and process control are similar to the Plan-DoCheck-Act (PDCA) cycle.
 PDCA cycle…
 “involves planning the process, operating it, inspecting its
output, and adjusting it in light of the observation.”
 Performed continuously to monitor and improve the process
performance
 Main Problems
 When to Act ….
 Variances beyond control …
Chapter 9 Managing Flow Variability
Process Control
30

Two types of variability
1. Normal variability
2. Abnormal variability
–
Statistically predictable
–
Unpredictable
–
Structural variability and
–
Disturbs state of statistical
stochastic variability
–
–
Variations due to random
equilibrium of the process
–
causes only (worker
removed (worker can
cannot control)
control)
PROCESS IS IN
–
CONTROL
–
Identifiable and can be
Process design
improvement
Abnormal - due to
assignable causes
–
PROCESS IS OUT OF
CONTROL
Chapter 9 Managing Flow Variability
Process Control
31


The short run goal is:

Estimate normal stochastic variability.

Accept it as an inevitable and avoid tampering

Detect presence of abnormal variability

Identify and eliminate its sources
The long run goal is to reduce normal variability by improving
process.
When is observed
variability normal
and abnormal???
Chapter 9 Managing Flow Variability
§ 9.3.3 Control Limit Policy
32
 Control Limit Policy
 Control band
 Range within variation in performance  normal
 Due to causes that cannot be identified or eliminated in short run
 Leave alone and do not tamper
 Variability outside this range is abnormal
 Due to assignable causes
 Investigate and correct
 Applications
 Inventory, Process Flow
 Cash management
 Stock trading
Chapter 9 Managing Flow Variability
9.3.4 Control Charts … Continued
33
Process Control Chart:
  - expected
value of the
performance
 UCL and LCL
 Standard
Deviation 
 Assign z
LCL =  - z
UCL =  + z
The smaller the value of “z”, the tighter the control
Chapter 9 Managing Flow Variability
9.3.4 Control Charts … Continued
34
 Within the control band  Performance variability is normal
 Outside the control band Process is “out of control”
 Data Misinterpretation
Type I error, : Process is “in control”, but data outside
the Control Band
Type II error, : Process is “out of control”, but data inside
the Control Band
Chapter 9 Managing Flow Variability
9.3.4 Control Charts … Continued
35
Optimal Degree of Control
Acceptable
Frequency
“z” too small 
unnecessary
investigation;
additional cost
“z” to large 
accept more
variations, less
costly
In practice, a value of z = 3 is used
99.73% of all measurements will fall within the “normal” range
Chapter 9 Managing Flow Variability
9.3.4 Control Charts … Continued
36
 Average and Variation Control Charts
-
To calculate:
Calculate the average value,
A1, A2….AN
Calculate the variance of each sample, V1, V2….VN
A = /n
(n = sample size)
LCL =  - z/n
and
UCL =  + z/n
Take it one step further:
Estimate  by the overall average of all the sample averages, A
A = (A1+ A2+…+AN) / N
(N = # of samples)
Also estimate  by the standard deviation of all N x n observations, S
Chapter 9 Managing Flow Variability
9.3.4 Control Charts … Continued
37
New, Improved equations for UCL and LCL are:
LCL = A - zs/n
and
UCL = A + zs/n
Average and
Variation
Control Charts
CalculateV -- the average variance of the sample variances
V = (V1+ V2+…+VN) / N
Sample
Variances
(N = # of samples)
Also calculate SV -- the standard deviation of the variances
LCL = V - z sV and
UCL = V + z sV
If fall within this range  Process Variability is stable
If not within this range  Investigate cause of abnormal variations
Variance
Control
Limits
Chapter 9 Managing Flow Variability
9.3.4 Control Charts … Continued
38
 Average and Variation Control Charts
Garage Door Example revisited…
Ex: A1 = (81 + 73 + 85 + 90 + 80) / 5 = 81.8 kg
Ex: V1 = (90 - 73) = 17 kg
Chapter 9 Managing Flow Variability
9.3.4 Control Charts … Continued
39
 Average and Variation Control Charts
Average Weights of Garage Door Samples:
A = 82.5 kg
V = 10.1 kg
Std. Dev. of Door Weights:
Std. Dev. of Sample Variances:
s = 4.2 kg
sV = 3.5 kg
Chapter 9 Managing Flow Variability
9.3.4 Control Charts … Continued
40
 Average and Variation Control Charts
Let z = 3
Sample Averages
UCL = A + zs/n = 82.5 + 3 (4.2) / 5 = 88.13
LCL = A - zs/n = 82.5 – 3 (4.2) / 5 = 76.87
Average Weight Control Chart
90
Average Wt. (Kg)
88
UCL = 88.13
86
84
82
`
80
78
LCL = 76.87
Process is
Stable!
76
74
1
2
3
4
5
6
7
8
9
10
11
Days
12
13
14
15
16
17
18
19
20
Chapter 9 Managing Flow Variability
9.3.4 Control Charts … Continued
41
 Average and Variation Control Charts
Let z = 3
Sample Variances
UCL = V + z sV = 10.1 + 3 (3.5) = 20.6
LCL = V - zs sV = 10.1 – 3 (3.5) = - 0.4
Variance (range) of Wt.
(Kg)
Variance Control Chart
25
UCL = 20.6
20
15
10
5
LCL = 0
0
1
2
3
4
5
6
7
8
9
10 11
Days
12 13 14
15 16 17
18 19 20
Chapter 9 Managing Flow Variability
9.3.4 Control Charts … Continued
42
 Extensions
Continuous Variables - Garage Door Weights,
Processing Costs, Customer Waiting Time
Use Normal distribution
Discrete Variables - Number of Customer Complaints,
Whether a Flow Unit is Defective, Number of Defects
per Flow Unit Produced
Use Binomial or Poisson distribution
Control Limit formula differs, but basic principles is same.
Chapter 9 Managing Flow Variability
9.3.5 Cause-Effect Diagrams
43
 Cause-Effect Diagrams
Sample
Plot
Abnormal
Observations
Control Charts
Variability !!
Now what?!!
Brainstorm Session!!
Answer 5 “WHY” Questions !
Chapter 9 Managing Flow Variability
9.3.5 Cause-Effect Diagrams … Continued
44
 Why…? Why…? Why…?
Our famous “Garage Door” Example:
1. Why are these doors so heavy?
Because the Sheet Metal was too ‘thick’.
2. Why was the sheet metal too thick?
Because the rollers at the steel mill were
set incorrectly.
3. Why were the rollers set
Because the supplier is not able to meet
incorrectly?
our specifications.
4. Why did we select this supplier?
Because our Project Supervisor was too
busy getting the product out – didn’t have
time to research other vendors.
5. Why did he get himself in this
Because he gets paid by meeting the
situation?
production quotas.
Chapter 9 Managing Flow Variability
9.3.5 Cause-Effect Diagrams … Continued
45
 Fishbone Diagram
Chapter 9 Managing Flow Variability
9.3.6 Scatter Plots
46
 The Thickness of the Sheet Metals
Change Settings on Rollers
Measure the Weight of the Garage Doors
Determine Relationship between the two
Roller Settings & Garage Door Weights
Plot the results
on a graph:
Scatter
Plot
Door Weight (Kg)
20
15
10
5
0
0
1
2
3
4
5
6
7
8
9
Roller Setting (m m )
10 11 12 13
Chapter 9 Managing Flow Variability
9.3 Section Summary
47
 Process Control involves
– Dynamic Monitoring
– Ensure variability in performance is due to normal random
causes only
– Detect abnormal variability and eliminate root causes
Chapter 9 Managing Flow Variability
9.4 Process Capability
48
 Ease of external product measures (door operations and durability) and
internal measures (door weight)
 Product specification limits vs. process control limits
 Individual units, NOT sample averages - must meet customer specifications.
 Once process is in control, then the estimates of μ (82.5kg) and σ (4.2k) are
reliable. Hence we can estimate the process capabilities.
 Process capabilities - the ability of the process to meet customer
specifications
 Three measures of process capabilities:
 9.4.1 Fraction of Output within Specifications
 9.4.2 Process Capability Ratios (Cpk and Cp)
 9.4.3 Six-Sigma Capability
Chapter 9 Managing Flow Variability
9.4.1 Fraction of Output within Specifications
49
 To compute for fraction of process that meets customer specs:

Actual observation (see Histogram, Fig 9.3)

Using theoretical probability distribution
Ex. 9.7:

US: 85kg; LS: 75 kg (the range of performance variation that customer
is willing to accept)
See figure 9.3 Histogram: In an observation of 100 samples, the process
is 74% capable of meeting customer requirements, and 26%
defectives!!!
OR:
 Let W (door weight): normal random variable with mean = 82.5 kg and
standard deviation at 4.2 kg,
Then the proportion of door falling within the specified limits is:
Prob (75 ≤ W ≤ 85) = Prob (W ≤ 85) - Prob (W ≤ 75)
Chapter 9 Managing Flow Variability
9.4.1 Fraction of Output within Specifications cont…
50
 Let Z = standard normal variable with μ = 0 and σ = 1, we can use the
standard normal table in Appendix II to compute:
AT US:
Prob (W≤ 85) in terms of:
Z = (W-μ)/ σ
As Prob [Z≤ (85-82.5)/4.2] = Prob (Z≤.5952) = .724 (see Appendix II)
(In Excel: Prob (W ≤ 85) = NORMDIST (85,82.5,4.2,True) = .724158)
AT LS:
Prob (W ≤ 75)
= Prob (Z≤ (75-82.5)/4.2) = Prob (Z ≤ -1.79) = .0367 in Appendix II
(In Excel: Prob (W ≤ 75) = NORMDIST(75,82.5,4.2,true) = .037073)
THEN:
Prob (75≤W≤85)
= .724 - .0367 = .6873
Chapter 9 Managing Flow Variability
9.4.1 Fraction of Output within Specifications cont…
51
SO with normal approximation, the process is capable of producing 69% of
doors within the specifications, or delivering 31% defective doors!!!
Specifications refer to INDIVIDUAL doors, not AVERAGES.
We cannot comfort customer that there is a 31% chance that they’ll get doors
that are either TOO LIGHT or TOO HEAVY!!!
Chapter 9 Managing Flow Variability
9.4.2 Process Capability Ratios (C pk and Cp)
52
 2nd measure of process capability that is easier to compute is the process
capability ratio (Cpk)
 If the mean is 3σ above the LS (or below the US), there is very little chance
of a product falling below LS (or above US).
So we use:
 (US- μ)/3σ
(.1984 as calculated later)
 and (μ -LS)/3σ
(.5952 as calculated later)
as measures of how well process output would fall within our specifications.
 The higher the value, the more capable the process is in meeting
specifications.
 OR take the smaller of the two ratios [aka (US- μ)/3σ =.1984] and define a
single measure of process capabilities as:
Cpk = min[(US-μ/)3σ, (μ -LS)/3σ]
(.1984, as calculated later)
Chapter 9 Managing Flow Variability
9.4.2 Process Capability Ratios (C pk and Cp)
53
 Cpk of 1+- represents a capable process
 Not too high (or too low)
 Lower values = only better than expected quality
Ex: processing cost, delivery time delay, or # of error per transaction process
 If the process is properly centered
– Cpk is then either:
(US- μ)/3σ or (μ -LS)/3σ
As both are equal for a centered process.
Chapter 9 Managing Flow Variability
9.4.2 Process Capability Ratios (C pk and Cp) cont…
54
 Therefore, for a correctly centered process, we may simply define the
process capability ratio as:
– Cp = (US-LS)/6σ
(.3968, as calculated later)
Numerator = voice of the customer / denominator = the voice of the
process
 Recall: with normal distribution:
Most process output is 99.73% falls within +-3σ from the μ.
 Consequently, 6σ is sometimes referred to as the natural tolerance of the
process.
Ex: 9.8
Cpk = min[(US- μ)/3σ , (μ -LS)/3σ ]
= min {(85-82.5)/(3)(4.2)], (82.5-75)/(3)(4.2)]}
= min {.1984, .5952}
=.1984
Chapter 9 Managing Flow Variability
9.4.2 Process Capability Ratios (C pk and Cp)
55
 If the process is correctly centered at μ = 80kg (between 75 and 85kg),
we compute the process capability ratio as
Cp = (US-LS)/6σ
= (85-75)/[(6)(4.2)]
= .3968
 NOTE: Cpk = .1984 (or Cp = .3968) does not mean that the process is
capable of meeting customer requirements by 19.84% (or 39.68%), of the
time. It’s about 69%.
 Defects are counted in parts per million (ppm) or ppb, and the process is
assumed to be properly centered. IN THIS CASE, If we want no more than
100 defects per million (.01% defectives), we SHOULD HAVE the
probability distribution of door weighs so closely concentrated around the
mean that the standard deviation is 1.282 kg, or Cp=1.3 (see Table 9.4)
Test: σ = (85-75)/(6)(1.282)] = 1.300kg
Chapter 9 Managing Flow Variability
Table 9.4
56
Table 9.4 Relationship Between Process Capability Ratio and Proportion Defective
Defects (ppm)
10000
1000
100
10
1
2 ppb
Cp
0.86
1
1.3
1.47
1.63
2
Chapter 9 Managing Flow Variability
9.4.3 Six-Sigma Capability
57
 Sigma measure
S = min[(US- μ /σ), (μ -LS)/σ]
(= min(.5152,1.7857) = .5152 to be calculated later)
 S-Sigma process
If process is correctly centered at the middle of the specifications,
S = [(US-LS)/2σ]
Ex: 9.9
Currently the sigma capability of door making process is
S=min[(85-82.5)/(4.2), (82.5-75)/4.2] = .5952
By centering the process correctly, its sigma capability increases to
S=min(85-75)/[(2)(4.2)] = 1.19
THUS, with a 3σ that is correctly centered, the US and LS are 3σ away from
the mean, which corresponds to Cp=1, and 99.73% of the output will meet
the specifications.
Chapter 9 Managing Flow Variability
9.4.3 Six-Sigma Capability cont…
58
 Correctly centered six-sigma process has a standard deviation so small that
the US and LS limits are 6σ from the mean each.
 Extraordinary high degree of precision.
Corresponds to Cp=2 or 2 defective units per billion produced!!! (see Table
9.5)
 In order for door making process to be a six-sigma process, its standard
deviation must be:
σ = (85-75)/(2)(6)] = .833kg
 Adjusting for Mean Shifts
- +-1.5 standard deviation from the center of specifications.
-
Producing an average of 3.4 defective units per million. (see table 9.5)
Chapter 9 Managing Flow Variability
Table 9.5
59
Table 9.5 Fraction Defective and Sigma Measure
Sigma S
3
4
5
Capability Ratio Cp
1
1.33
1.667
Defects (ppm)
66810
6210
233
6
2
3.4
Chapter 9 Managing Flow Variability
9.4.3 Six-Sigma Capability cont…
60
 Why Six-Sigma?
– See table 9.5
– Improvement in process capabilities from a 3-sigma to 4-sigma = 10-fold
reduction in the fraction defective (66810 to 6210 defects)
– While 4-sigma to 5-sigma = 30-fold improvement (6210 to 232 defects)
– While 5-sigma to 6-sigma = 70-fold improvement (232 to 3.4 defects, per
million!!!).
 Average companies deliver about 4-sigma quality, where best-in-class
companies aim for six-sigma.
Chapter 9 Managing Flow Variability
9.4.3 Six-Sigma Capability cont…
61
 Why High Standards?
 The overall quality of the entire product/process that requires ALL of
them to work satisfactorily will be significantly lower.
Ex:
If product contains 100 parts and each part is 99% reliable, the chance
that the product (all its parts) will work is only (.99)100 = .366, or
36.6%!!!
 Also, costs associated with each defects may be high
 Expectations keep rising
Chapter 9 Managing Flow Variability
9.4.3 Six-Sigma Capability cont…
62
 Safety capability

We may also express process capabilities in terms of the desired
margin [(US-LS)-zσ] as safety capability

It represents an allowance planned for variability in supply and/or
demand

Greater process capability means less variability

If process output is closely clustered around its mean, most of the
output will fall within the specifications

Higher capability thus means less chance of producing defectives

Higher capability = robustness
Chapter 9 Managing Flow Variability
9.4.4 Capability and Control
63
 In Ex. 9.7: the production process is not performing well in terms of
MEETING THE CUSTOMER SPECIFICATIONS. Only 69% meets output
specifications!!! (See 9.4.1: Fraction of Output within Specifications)
 Yet in example 9.6, “the process was in control!!!”, or within us & ls limits.
 Being in control and meeting specifications are two different measures of
performance. The former indicates internal stability, the latter indicates the
ability to meet the customers specifications.
 Observation of a process in control ensures that the resulting estimates of
the process mean and standard deviation are reliable so that our
measurement of the process capability is accurate.
 The final step is to improve process capability, so it is satisfactory from the
customers viewpoint as well.
Chapter 9 Managing Flow Variability
9.5 Process Capability Improvement
64
 How do we improve the process capability?
 Shift the process mean
 Reduce the variability
 Both
Chapter 9 Managing Flow Variability
9.5.1 Mean Shift
65
 Examine where the current process mean lies in comparison to the
specification range (i.e. closer to the LS or the US)
 Alter the process to bring the process mean to the center of the specification
range in order to increase the proportion of outputs that fall within
specification
Chapter 9 Managing Flow Variability
Ex 9.10
66
 MBPF garage doors (currently)
 specification range: 75 to 85 kgs
 process mean: 82.5 kgs
 proportion of output falling within specifications: .6873
 The process mean of 82.5 kgs was very close to the US of 85 kgs (i.e. too
thick/heavy)
 To lower the process mean towards the center of the specification range the
supplier could change the thickness setting on their rolling machine.
Chapter 9 Managing Flow Variability
Ex 9.10 Continued
67
 Center of the specification range: (75 + 85)/2 = 80 kgs
 New process mean: 80 kgs
 If the door weight (W) is a normal random variable, then the proportion of
doors falling within specifications is: Prob (75 =< W =< 85)
 Prob (W =< 85) – Prob (W =< 75)
 Z = (weight – process mean)/standard deviation
 Z = (85 – 80)/4.2 = 1.19
 Z = (75 – 80)/4.2 = -1.19
Chapter 9 Managing Flow Variability
Ex 9.10 Continued
68
 [from table A2.1 on page 319]
Z = 1.19
Z = -1.19
.8830
(1 - .8830)
.1170
 Prob (W =< 85) – Prob (W =< 75) =
.8830 - .1170 = .7660
 By shifting the process mean from 82.5 kgs to 80 kgs, the proportion of
garage doors that falls within specifications increases from .6873 to .7660
Chapter 9 Managing Flow Variability
9.5.2 Variability Reduction
69
 Measured by standard deviation
 A higher standard deviation value means higher variability amongst outputs
 Lowering the standard deviation value would ultimately lead to a greater
proportion of output that falls within the specification range
Chapter 9 Managing Flow Variability
9.5.2 Variability Reduction Continued
70
 Possible causes for the variability MBPF experienced are:
 old equipment
 poorly maintained equipment
 improperly trained employees
 Investments to correct these problems would decrease variability however
doing so is usually time consuming and requires a lot of effort
Chapter 9 Managing Flow Variability
Ex 9.11
71
 Assume investments are made to decrease the standard deviation from 4.2
to 2.5 kgs
 The proportion of doors falling within specifications:
85)
 Prob (W =< 85) – Prob (W =< 75)
 Z = (weight – process mean)/standard deviation
 Z = (85 – 80)/2.5 = 2.0
 Z = (75 – 80)/2.5 = -2.0
Prob (75 =< W =<
Chapter 9 Managing Flow Variability
Ex 9.11 Continued
72
 [from table A2.1 on page 319]
Z = 2.0
Z = -2.0
.9772
(1 - .9772)
.0228
 Prob (W =< 85) – Prob (W =< 75) =
.9772 - .0228 = .9544
 By shifting the standard deviation from 4.2 kgs to 2.5 kgs and the process
mean from 82.5 kgs to 80 kgs, the proportion of garage doors that falls within
specifications increases from .6873 to .9544
Chapter 9 Managing Flow Variability
9.5.3 Effect of Process Improvement on Process Control
73
 Changing the process mean or variability requires re-calculating the control
limits
 This is required because changing the process mean or variability will also
change what is considered abnormal variability and when to look for an
assignable cause
Chapter 9 Managing Flow Variability
9.6 Product and Process Design
74
 Reducing the variability from product and process design

simplification

standardization

mistake proofing
Chapter 9 Managing Flow Variability
Simplification
75
 Reduce the number of parts (or stages) in a product (or process)
 less chance of confusion and error
 Use interchangeable parts and a modular design
 simplifies materials handling and inventory control
 Eliminate non-value adding steps
 reduces the opportunity for making mistakes
Chapter 9 Managing Flow Variability
Standardization
76
 Use standard parts and procedures
 reduces operator discretion, ambiguity, and opportunity for making
mistakes
Chapter 9 Managing Flow Variability
Mistake Proofing
77
 Designing a product/process to eliminate the chance of human error
 ex. color coding parts to make assembly easier
 ex. designing parts that need to be connected with perfect symmetry or
with obvious asymmetry to prevent assembly errors
Chapter 9 Managing Flow Variability
9.6.2 Robust Design
78
 Designing the product in a way so its actual performance will not be affected
by variability in the production process or the customer’s operating
environment
 The designer must identify a combination of design parameters that protect
the product from the process related and environment related factors that
determine product performance
Chapter 9 Managing Flow Variability
9.6 Product and Process Design
79
 Summary
 Variability is inevitable. It is a problem when it creates process instability,
lower capability, and customer dissatisfaction.
 The goal of this chapter has been to study how to measure, analyze, and
minimize sources of this variability.
 The point of this it to improve consistency in product process and
performance, which will hopefully lead to…
 Total customer satisfaction, and..
 A better competitive position.