1. NATIONAL PRODUCTIVITY COUNCIL WELCOMES YOU TO A PRESENTATION ON
CONTROL CHARTS
By B.Girish
Dy. Director

2. Three SQC Categories Traditional descriptive statistics
e.g. the mean, standard deviation, and range
Acceptance sampling used to randomly inspect a batch of goods to determine acceptance/rejection
Does not help to catch in-process problems
Statistical process control (SPC)
Involves inspecting the output from a process
Quality characteristics are measured and charted
Helpful in identifying in-process variations

3. Statistical Process Control (SPC)
A methodology for monitoring a process to identify special causes of variation and signal the need to take corrective action when appropriate
SPC relies on control charts

4. SPC Implementation Requirements
Top management commitment
Project champion
Initial workable project
Employee education and training
Accurate measurement system

5. Traditional Statistical Tools
The Mean- measure of central tendency
The Range- difference between largest/smallest observations in a set of data
Standard Deviation measures the amount of data dispersion around mean

6. Distribution of Data
Normal distributions
Skewed distribution

7. Sources of Variation Common causes of variation
Random causes that we cannot identify
Unavoidable
e.g. slight differences in process variables like diameter, weight, service time, temperature
Assignable causes of variation
Causes can be identified and eliminated
e.g. poor employee training, worn tool, machine needing repair

8. Common Causes
Special Causes

9. Histograms do not take into account changes over time.
Control charts can tell us when a process changes

10. Introduction to Control Charts
Important uses of the control chart
Most processes do not operate in a state of statistical control
Consequently, the routine and attentive use of control charts will identify assignable causes. If these causes can be eliminated from the process, variability will be reduced and the process will be improved
The control chart only detects assignable causes. Management, operator, and engineering action will be necessary to eliminate the assignable causes.

11. Introduction to Control Charts
Monitor Variation in Data
Exhibit trend - make correction before process is out of control
A Process - A Repeatable Series of Steps Leading to a Specific Goal

12. Introduction to Control Charts
(continued)
Show When Changes in Data are Due to:
Special or assignable causes
Fluctuations not inherent to a process
Represent problems to be corrected
Data outside control limits or trend
Chance or common causes
Inherent random variations
Consist of numerous small causes of random variability

13. Introduction to Control Charts
Graph of sample data plotted over time
Special Cause Variation
Process Average 
UCL
Mean
LCL
Common Cause Variation

14. Commonly Used Control Charts
Variables data
x-bar and R-charts
x-bar and s-charts
Charts for individuals (x-charts)
Attribute data
For “defectives” (p-chart, np-chart)
For “defects” (c-chart, u-chart)

15. Introduction to Control Charts
Popularity of control charts
1) Control charts are a proven technique for improving productivity.
2) Control charts are effective in defect prevention.
3) Control charts prevent unnecessary process adjustment.
4) Control charts provide diagnostic information.
5) Control charts provide information about process capability.

16. Control Chart Selection
Quality Characteristic
variable
attribute
defective
defect no
n>1?
x and MR
constant
sampling
unit?
yes
constant
sample
size?
yes
p or np no
n>=10 or
computer?
x and R
yes no no
yes
p-chart with
variable sample
size
c u
x and s

17. SPC Methods-Control Charts
Control Charts show sample data plotted on a graph with CL, UCL, and LCL
Control chart for variables are used to monitor characteristics that can be measured, e.g. length, weight, diameter, time
Control charts for attributes are used to monitor characteristics that have discrete values and can be counted, e.g. % defective, number of flaws in a shirt, number of broken eggs in a box

18. Control Charts for Attributes –P-Charts & C-Charts
Use P-Charts for quality characteristics that are discrete and involve yes/no or good/bad decisions
Number of leaking caulking tubes in a box of 48
Number of broken eggs in a carton
Use C-Charts for discrete defects when there can be more than one defect per unit
Number of flaws or stains in a carpet sample cut from a production run
Number of complaints per customer at a hotel

19. Control Chart Design Issues
Basis for sampling
Sample size
Frequency of sampling
Location of control limits

21. Developing Control Charts
Prepare
Choose measurement
Determine how to collect data, sample size, and frequency of sampling
Set up an initial control chart
Collect Data
Record data
Calculate appropriate statistics
Plot statistics on chart

22. Pre-Control nominal value Green Zone Yellow Zones Red Zone LTL UTL
Good for machining, but only when Cp is 1.14
Initiate mfg run:
5 consecutive must fall in green zone, if not reevaluate setup.
Sample a part. If green continue. If yellow sample another. If second is green continue, and if not look for special cause. If any part is red look for special cause.
Sample rate is time between out of control divided by 6.

23. Control Limits UCL = Process Average + 3 Standard Deviations
LCL = Process Average - 3 Standard Deviations X
UCL
+ 3
Process Average
- 3
LCL
TIME

24. Next Steps Determine trial control limits
Center line (process average)
Compute UCL, LCL
Analyze and interpret results
Determine if in control
Eliminate out-of-control points
Recompute control limits as necessary

25. Setting Control Limits
Control limits balance
risks like Type I error
Percentage of values under normal curve

28. Comparing Control Chart PatternsX X X
Common Cause Variation: No Points Outside Control Limits
Special Cause Variation: 2 Points Outside Control Limits
Downward Pattern: No Points Outside Control Limits but Trend Exists

29. Typical Out-of-Control Patterns
Point outside control limits
Sudden shift in process average
Cycles
Trends
Hugging the center line
Hugging the control limits
Instability

30. Control Charts for Variables
Use x-bar and R-bar charts together
Used to monitor different variables
X-bar & R-bar Charts reveal different problems
In statistical control on one chart, out of control on the other chart? OK?

31. Processes In Control

32. Process Out of Control

33. Shift in Process Average

34. Identifying Potential Shifts

35. Cycles

36. Trend

37. PROCESS STREAMS
UCL
Mixtures
Sudden stability
Center
line
LCL

38. Interpreting Control Charts
Process In
Control
Out of
Run
Chart points do
not form a parti-
cular pattern and
lie within the
upper and lower
chart limits
Chart points
form a particular
pattern OR one
or more points
lie beyond the
uppor or lower
Chart points are
on one side of the
center line. The
number of points
in a run is called
the “length of the
run”
UCL 10
x 19
lcl 30
The process is stable, not
changing. Doesn’t
necesarily mean to leave
the process alone. May
be opportunities to improve
the process and enjoy
substantial benefits
Alerts us that the process
is changing. Doesn’t mean
you need to take a
corrective action. May be
relate to a change you have
made. Be sureto identify
the reason\(s) before taking
any constructive actions(w)
Suggest the process has
undergone a permanent
change (positive or
negative) and is now
becoming stable. Often
requires tha t you
recompute the control
lines for future interpre-
tation efforts.
Description
Example # 1
Example # 2
Interpretation

39. Interpreting Control Charts
Trend
Cycle
Hugging
A continued rise
or fall in a series
of points (7 or
more consecutive
points direction)
Chart ponts show
the same pattern
changes (e.g.rise
or fall) over equal
periods of time
Chart points are
close to the center
line or to a
control limit line
(2 out of 3, 3 out of
4, or 4 out of 10.)
UCL 10
x 19
lcl 30
CL 10
Description
Example # 1
Example # 2
Interpretation 1 2 3 4 5 6 7
1/2
Often seen after some change
has been made. Helps tell
you if the change(s) had a
positive or negative effect.
may also be part of a
learning curve associated
with some form of training
often relates to factors that
influence the process in a
predictable manner. Factors
occur over a set time period
and a positive/negative effect
Helps determine future work
load and staffing levels
Suggests a different type of
data has been mixed into the
sub-group being sampled.
Often need to change the
sub-group, reassemble the
data, redraw the control
chart

40. When to Take Corrective Action
Corrective Action Should Be Taken When Observing Points Outside the Control Limits or when a Trend Has Been Detected
Eight consecutive points above the center line (or eight below)
Eight consecutive points that are increasing (decreasing)

41. Out-of-Control Processes
If the Control Chart Indicates an Out-of-Control Condition (a Point Outside the Control Limits or Exhibiting Trend)
Contains both common causes of variation and assignable causes of variation
The assignable causes of variation must be identified
If detrimental to quality, assignable causes of variation must be removed
If increases quality, assignable causes must be incorporated into the process design

42. In-Control Process
If the Control Chart is Not Indicating Any Out-of-Control Condition, then
Only common causes of variation exist
It is sometimes said to be in a state of statistical control
If the common-cause variation is small, then control chart can be used to monitor the process
If the common-cause variation is too large, the process needs to be altered

43. Types of Error First Type: Second Type:
Belief that observed value represents special cause when, in fact, it is due to common cause
Second Type:
Treating special cause variation as if it is common cause variation

44. Remember
Control does not mean that the product or service will meet the needs. It only means that the process is consistent (may be consistently bad).
Capability of meeting the specification.

45. How to use the results
By eliminating the special causes first and then reducing the common causes, quality can be improved.

46. Final Steps Use as a problem-solving tool Compute process capability
Continue to collect and plot data
Take corrective action when necessary
Compute process capability

47. Process Capability Product Specifications
Preset product or service dimensions, tolerances
e.g. bottle fill might be 16 oz. ±.2 oz. (15.8oz.-16.2oz.)
Based on how product is to be used or what the customer expects
Process Capability – Cp and Cpk
Assessing capability involves evaluating process variability relative to preset product or service specifications
Cp assumes that the process is centered in the specification range
Cpk helps to address a possible lack of centering of the process

48. Relationship between Process Variability and Specification Width
Three possible ranges for Cp
Cp = 1, as in Fig. (a), process
variability just meets specifications
Cp ≤ 1, as in Fig. (b), process not capable of producing within specifications
Cp ≥ 1, as in Fig. (c), process
exceeds minimal specifications
One shortcoming, Cp assumes that the process is centered on the specification range
Cp=Cpk when process is centered

49. Computing the Cp Value at Cocoa Fizz: three bottling machines are being evaluated for possible use at the Fizz plant. The machines must be capable of meeting the design specification of oz. with at least a process capability index of 1.0 (Cp≥1)
The table below shows the information gathered from production runs on each machine. Are they all acceptable?
Solution:
Machine A
Machine B
Cp=
Machine C
Machine σ
USL-LSL 6σ A
.05 .4 .3 B .1 .6 C .2
1.2

50. Computing the Cpk Value at Cocoa Fizz
Design specifications call for a target value of 16.0 ±0.2 OZ.
(USL = 16.2 & LSL = 15.8)
Observed process output has now shifted and has a µ of 15.9 and a
σ of 0.1 oz.
Cpk is less than 1, revealing that the process is not capable

51. Process Capability (2)

52. Capability Versus Control
Capable
Not Capable
In Control Out of Control
IDEAL

53. Excel Template

55. Special Variables Control Charts
x-bar and s charts
x-chart for individuals

60. Charts for Attributes Fraction nonconforming (p-chart)
Fixed sample size
Variable sample size
np-chart for number nonconforming
Charts for defects
c-chart
u-chart

71. p Chart Control Chart for Proportions
Is an attribute chart
Shows Proportion of Nonconforming (Success ) Items
E.g., Count # of nonconforming chairs & divide by total chairs inspected
Chair is either conforming or nonconforming
Used with Equal or Unequal Sample Sizes Over Time
Unequal sizes should not differ by more than ±25% from average sample size

72. p Chart Control Limits Average Proportion of Nonconforming Items
Average Group Size
# Defective Items in Sample i
# of Samples
Size of Sample i

73. p Chart Example
You’re manager of a 500-room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control?

74. p Chart Hotel Data # Not Day # Rooms Ready Proportion

75. p Chart Control Limits Solution

76. p Chart Control Chart Solution
0.15
UCL
0.10
Mean
0.05
LCL
0.00 1 2 3 4 5 6 7
Day
Individual points are distributed around without any pattern. Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of the management.

77. p Chart in PHStat PHStat | Control Charts | p Chart …
Excel Spreadsheet for the Hotel Room Example

78. Understanding Process Variability: Red Bead Example
Four workers (A, B, C, D) spend 3 days to collect beads, at 50 beads per day. The expected number of red beads to be collected per day per worker is 10 or 20%.
Worker Day 1 Day 2 Day 3 All Days
A (18%) 11 (12%) (12%) (17.33%)
B (24%) 12 (24%) 8 (16%) (21.33%)
C (26%) 6 (12%) (24%) (20.67%)
D (14%) 9 (18%) 8 (16%) (16.0%)
Totals

79. Understanding Process Variability: Example Calculations
Average Day 1 Day 2 Day 3 All Days X
p 20.5% 19% 17% % _

80. Understanding Process Variability: Example Control Chart
UCL
.30
.20
.10 _ p
LCL
0 A1 B1 C1 D A2 B2 C2 D2 A3 B3 C3 D3

81. Morals of the Example Variation is an inherent part of any process.
The system is primarily responsible for worker performance.
Only management can change the system.
Some workers will always be above average, and some will be below.

82. The c Chart
Control Chart for Number of Nonconformities (Occurrences) in a Unit (an Area of Opportunity)
Is an attribute chart
Shows Total Number of Nonconforming Items in a Unit
E.g., Count # of defective chairs manufactured per day
Assume that the Size of Each Subgroup Unit Remains Constant

83. c Chart Control Limits Average Number of Occurrences
# of Occurrences in Sample i
# of Samples

84. c Chart: Example
You’re manager of a 500-room hotel. You want to achieve the highest level of service. For 7 days, you collect data on the readiness of 200 rooms. Is the process in control?

85. c Chart: Hotel Data # Not Day # Rooms Ready

86. c Chart: Control Limits Solution

87. c Chart: Control Chart Solution30
UCL 20 10
LCL 1 2 3 4 5 6 7
Day
Individual points are distributed around without any pattern. Any improvement in the process must come from reduction of common-cause variation, which is the responsibility of the management.

88. Variables Control Charts: R Chart
Monitors Variability in Process
Characteristic of interest is measured on numerical scale
Is a variables control chart
Shows Sample Range Over Time
Difference between smallest & largest values in inspection sample
E.g., Amount of time required for luggage to be delivered to hotel room

89. R Chart Control Limits From Table Sample Range at Time i or Subgroup i
# Samples

90. R Chart Example
You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?

91. R Chart and Mean Chart Hotel Data
Sample Sample Day Average Range

92. R Chart Control Limits Solution
From Table (n = 5)

93. R Chart Control Chart Solution
Minutes
UCL 8 6 _ 4 R 2
LCL 1 2 3 4 5 6 7
Day

94. Variables Control Charts: Mean Chart (The Chart)
Shows Sample Means Over Time
Compute mean of inspection sample over time
E.g., Average luggage delivery time in hotel
Monitors Process Average
Must be preceded by examination of the R chart to make sure that the process is in control

95. Mean Chart Computed From Table Sample Mean at Time i
Sample Range at Time i
# Samples

96. Mean Chart Example
You’re manager of a 500-room hotel. You want to analyze the time it takes to deliver luggage to the room. For 7 days, you collect data on 5 deliveries per day. Is the process in control?

97. R Chart and Mean Chart Hotel Data
Sample Sample Day Average Range

98. Mean Chart Control Limits Solution
From Table E.9
(n = 5)

99. Mean Chart Control Chart Solution
Minutes
UCL 8 _ _ 6 X 4 2
LCL 1 2 3 4 5 6 7
Day

100. R Chart and Mean Chart in PHStat
PHStat | Control Charts | R & Xbar Charts …
Excel Spreadsheet for the Hotel Room Example

101. Process Capability
Process Capability is the Ability of a Process to Consistently Meet Specified Customer-Driven Requirements
Specification Limits are Set by Management in Response to Customer’s Expectations
The Upper Specification Limit (USL) is the Largest Value that Can Be Obtained and Still Conform to Customer’s Expectation
The Lower Specification Limit (LSL) is the Smallest Value that is Still Conforming

102. Estimating Process Capability
Must Have an In-Control Process First
Estimate the Percentage of Product or Service Within Specification
Assume the Population of X Values is Approximately Normally Distributed with Mean Estimated by and Standard Deviation Estimated by

103. Estimating Process Capability
(continued)
For a Characteristic with an LSL and a USL
where Z is a standardized normal random variable

104. Estimating Process Capability
(continued)
For a Characteristic with Only a LSL
where Z is a standardized normal random variable

105. Estimating Process Capability
(continued)
For a Characteristic with Only a USL
where Z is a standardized normal random variable

106. Process Capability Example
You’re manager of a 500-room hotel. You have instituted a policy that 99% of all luggage deliveries must be completed within 10 minutes or less. For 7 days, you collect data on 5 deliveries per day. Is the process capable?

107. Process Capability: Hotel Data
Sample Sample Day Average Range

108. Process Capability: Hotel Example Solution
Therefore, we estimate that 99.38% of the luggage deliveries will be made within the 10 minutes or less specification. The process is capable of meeting the 99% goal.

109. Capability Indices
Aggregate Measures of a Process’ Ability to Meet Specification Limits
The larger (>1) the values, the more capable a process is of meeting requirements
Measure of Process Potential Performance
Cp>1 implies that a process has the potential of having more than 99.73% of outcomes within specifications

110. Capability Indices Measures of Actual Process Performance
(continued)
Measures of Actual Process Performance
For one-sided specification limits
CPL (CPU) >1 implies that the process mean is more than 3 standard deviations away from the lower (upper) specification limit

111. Capability Indices For two-sided specification limits
(continued)
For two-sided specification limits
Cpk = 1 indicates that the process average is 3 standard deviations away from the closest specification limit
Larger Cpk indicates larger capability of meeting the requirements

112. Process Capability Example
You’re manager of a 500-room hotel. You have instituted a policy that all luggage deliveries must be completed within 10 minutes or less. For 7 days, you collect data on 5 deliveries per day. Compute an appropriate capability index for the delivery process.

113. Process Capability: Hotel Data
Sample Sample Day Average Range

114. Process Capability: Hotel Example Solution
Since there is only the upper specification limit, we need to only compute CPU. The capability index for the luggage delivery process is .8337, which is less than 1. The upper specification limit is less than 3 standard deviations above the mean.

115. Thank You