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11
Quality ManagementQuality Managementand Controland Control
Presented by:Mohammad Saleh Owlia, Visiting Professor, University of Malaya
Adopted from:Operations Management for Competitive Advantage, Eleventh Edition (2006) Richard B. Chase, F. Robert Jacobs and Nicholas J. Aquilano
22
What is Quality?What is Quality?
33
Garvin’s Product Quality DimensionGarvin’s Product Quality Dimension Garvin’s Product Quality DimensionGarvin’s Product Quality Dimension
Performance
Features
Reliability
Conformance
Durability
Serviceability
Aesthetics
Perceived Quality
44
Service Quality DimensionsService Quality Dimensions Service Quality DimensionsService Quality DimensionsParasuraman, Zeithamel, and
Berry’s Service
Quality Dimensions
Tangibles
Service Reliability
Responsiveness
Assurance
Empathy
55
Total Quality ManagementTotal Quality Management
TQMTQM may be defined as managing the may be defined as managing the
entire organization so that it excels on entire organization so that it excels on
all dimensions of products and services all dimensions of products and services
that are important to the customer.that are important to the customer.
66
Quality SpecificationsQuality Specifications
Design quality (consumer’s view)Design quality (consumer’s view)– inherent value of the product in the inherent value of the product in the
marketplace and therefore, has strategic marketplace and therefore, has strategic implications.implications.
CConformance quality (producer’s view)onformance quality (producer’s view)– degree to which the product or servicedegree to which the product or service
design specifications are metdesign specifications are met
77
Costs of QualityCosts of QualityAppraisal costsAppraisal costs
Prevention costs
Internal failure costs
External Failure costs
inspection and testing
scrap, rework, yield loss, downtime
complaint adjustment, allowances, warranty work
quality planning and training
Co
st
pe
r g
oo
d u
nit
of
pro
du
ct
0 100%Quality level (q)Optimum
quality level
TotalqualitycostsInternal
and externalfailurecosts
Minimumtotal cost
Preventionand appraisalcosts
Quality Cost: Traditional ViewQuality Cost: Traditional View
1212
Phases of Quality Assurance
Acceptancesampling
Processcontrol
Continuousimprovement
Inspectionbefore/afterproduction
Correctiveaction duringproduction
Quality builtinto theprocess
The leastprogressive
The mostprogressive
1313
PDCA Cycle (Deming Wheel)PDCA Cycle (Deming Wheel)
1. Plan a change aimed at improvement.
1. Plan
2. Execute the change.
2. Do
3. Study the results; did it work?
3. Check
4. Institutionalize the change or abandon or do it again.
4. Act
1414
Ishikawa’s Basic Tools of QualityIshikawa’s Basic Tools of QualityIshikawa’s Basic Tools of QualityIshikawa’s Basic Tools of Quality
HistogramHistogramHistogramHistogram
Pareto ChartsPareto ChartsPareto ChartsPareto Charts
Cause & Effect Cause & Effect DiagramsDiagrams
Cause & Effect Cause & Effect DiagramsDiagrams
Check SheetsCheck SheetsCheck SheetsCheck Sheets
Scatter Scatter DiagramsDiagramsScatter Scatter
DiagramsDiagrams
FlowchartsFlowchartsFlowchartsFlowcharts
Control ChartsControl ChartsControl ChartsControl Charts
1515
HistogramsHistogramsN
um
be
r o
f Lo
ts
Data Ranges
Defectsin lot
0 1 2 3 4
Can be used to identify the frequency of quality defect occurrence and display quality performance.
Can be used to identify the frequency of quality defect occurrence and display quality performance.
Graphical representation of data in a bar chart format Graphical representation of data in a bar chart format
1616
Can be used to find when 80% of the problems may be attributed to 20% of thecauses.
Can be used to find when 80% of the problems may be attributed to 20% of thecauses.
Assy.Instruct.
Fre
quen
cy
Design Purch. Training Other
80%
Pareto ChartsPareto ChartsPareto ChartsPareto Charts
1717
Pareto ChartsPareto ChartsPareto ChartsPareto Charts
The Steps Used in Pareto Analysis The Steps Used in Pareto Analysis Include:Include:– Gathering categorical data relating to Gathering categorical data relating to
quality problems.quality problems.– Drawing a histogram of the data.Drawing a histogram of the data.– Focusing on the tallest bars in the Focusing on the tallest bars in the
histogram first when solving the problemhistogram first when solving the problem
1818
Cause and Effect Cause and Effect DiagramsDiagrams
Cause and Effect Cause and Effect DiagramsDiagrams
Cause and Effect (or Fishbone or Cause and Effect (or Fishbone or Ishikawa) DiagramIshikawa) Diagram– A diagram designed to help workers A diagram designed to help workers focus focus
on the causes of a problem rather than on the causes of a problem rather than the symptoms.the symptoms.
– The diagram looks like the skeleton of a The diagram looks like the skeleton of a fish, with the problem being the head of the fish, with the problem being the head of the fish, major causes being the “ribs” of the fish, major causes being the “ribs” of the fish and subcauses forming smaller fish and subcauses forming smaller “bones” off the ribs.“bones” off the ribs.
1919
Cause & Effect DiagramCause & Effect Diagram
Effect
ManMachine
MaterialMethod
Environment
Possible causes:Possible causes: The results or effect
The results or effect
Can be used to systematically track backwards to find a possible cause of a quality problem (or effect)
Can be used to systematically track backwards to find a possible cause of a quality problem (or effect)
2020
Cause and Effect Cause and Effect DiagramsDiagrams
Cause and Effect Cause and Effect DiagramsDiagrams
2121
Billing Errors
Wrong Account
Wrong Amount
A/R Errors
Wrong Account
Wrong Amount
Monday
Can be used to keep track of defects or used to make sure people collect data in a correct manner.
Can be used to keep track of defects or used to make sure people collect data in a correct manner.
Check SheetsCheck SheetsCheck SheetsCheck Sheets
2222
Check SheetsCheck SheetsCheck SheetsCheck Sheets
Setting Up a Check SheetSetting Up a Check Sheet– Identify common defects occurring in the Identify common defects occurring in the
process.process.– Draw a table with common defects in the left Draw a table with common defects in the left
column and time period across the tops of column and time period across the tops of the columns to track the defects.the columns to track the defects.
– The user of the check sheet then places The user of the check sheet then places check marks on the sheet whenever the check marks on the sheet whenever the defect is encountered.defect is encountered.
2323
Check SheetsCheck SheetsCheck SheetsCheck Sheets
02468
1012
0 10 20 30
Hours of Training
De
fect
s
Can be used to illustrate the relationships between variables (Example: quality performance and training).
Can be used to illustrate the relationships between variables (Example: quality performance and training).
Scatter DiagramsScatter DiagramsScatter DiagramsScatter Diagrams
2525
Scatter DiagramsScatter DiagramsScatter DiagramsScatter Diagrams
Used to examine the relationships Used to examine the relationships between variables:between variables:Steps in Setting Up a Scatter PlotSteps in Setting Up a Scatter Plot– Determine your X (independent) and Y Determine your X (independent) and Y
(dependent) variables.(dependent) variables.– Gather process data relating to the variables Gather process data relating to the variables
identified in step 1.identified in step 1.– Plot the data on a two-dimensional Plot the data on a two-dimensional
Cartesian plane.Cartesian plane.– Observe the plotted data to see whether Observe the plotted data to see whether
there is a relationship between the variables.there is a relationship between the variables.
2626
Scatter DiagramsScatter DiagramsScatter DiagramsScatter Diagrams
Prevention in Costs and Conformance
2727
FlowchartsFlowchartsFlowchartsFlowcharts
Flowcharts:Flowcharts:Picture of a processPicture of a process
Allows a company to see process weaknessesAllows a company to see process weaknesses
Sometimes the first step in many process Sometimes the first step in many process improvement projects to see how the process improvement projects to see how the process existsexists
““You have to be able to know the process You have to be able to know the process before you can improve it”before you can improve it”
2828
Example: Process Flow Chart Example: Process Flow Chart
No, Continue…
Material Received
from Supplier
Inspect Material for
Defects Defects found?
Return to Supplier for
Credit
Yes
Can be used to find quality problems.
Can be used to find quality problems.
2929
FlowchartsFlowchartsFlowchartsFlowcharts
Basic Flowcharting Symbols
3030
FlowchartsFlowchartsFlowchartsFlowcharts
Steps in Flowcharting IncludeSteps in Flowcharting Include– Settle on a standard set of flowcharting Settle on a standard set of flowcharting
symbols to be used.symbols to be used.– Clearly communicate the purpose of the Clearly communicate the purpose of the
flowcharting to all the individuals involved in flowcharting to all the individuals involved in the flowcharting exercise.the flowcharting exercise.
– Observe the work being performed by Observe the work being performed by shadowing the workers performing the work.shadowing the workers performing the work.
– Develop a flowchart of the process.Develop a flowchart of the process.
3131
Control ChartsControl ChartsControl ChartsControl Charts
Control ChartsControl Charts– Control charts are used to determine Control charts are used to determine
whether a process will produce a product or whether a process will produce a product or service with consistent measurable service with consistent measurable properties. properties.
– Control charts are discussed in detail in Control charts are discussed in detail in Technical Note 7.Technical Note 7.
Example: Run ChartExample: Run Chart
0.440.460.48
0.50.520.540.560.58
1 2 3 4 5 6 7 8 9 10 11 12Time (Hours)
Dia
me
ter
Can be used to identify when equipment or processes are not behaving according to specifications.
Can be used to identify when equipment or processes are not behaving according to specifications.
Example: Control ChartExample: Control Chart
970
980
990
1000
1010
1020
0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
LCL
UCL
Can be used to monitor ongoing production process quality and quality conformance to stated standards of quality.
Can be used to monitor ongoing production process quality and quality conformance to stated standards of quality.
3434
Six Sigma QualitySix Sigma Quality
A philosophy and set of methods A philosophy and set of methods companies use to eliminate defects in companies use to eliminate defects in their products and processestheir products and processes
Seeks to reduce variation in the processes Seeks to reduce variation in the processes that lead to product defectsthat lead to product defects
The name, “six sigma” refers to the The name, “six sigma” refers to the variation that exists within plus or minus variation that exists within plus or minus six standard deviations of the process six standard deviations of the process outputsoutputs
6
3535
Six Sigma Quality (Continued)Six Sigma Quality (Continued)
Six Sigma allows managers to readily Six Sigma allows managers to readily describe process performance using a describe process performance using a common metric: Defects Per Million common metric: Defects Per Million Opportunities (DPMO)Opportunities (DPMO)
1,000,000 x
units of No. x
unit per error for iesopportunit ofNumber
defects ofNumber
DPMO
3636
Six Sigma Quality (Continued)Six Sigma Quality (Continued)
Example of Defects Per Million Example of Defects Per Million Opportunities (DPMO) calculation. Opportunities (DPMO) calculation. Suppose we observe 200 letters Suppose we observe 200 letters delivered incorrectly to the wrong delivered incorrectly to the wrong addresses in a small city during a addresses in a small city during a single day when a total of 200,000 single day when a total of 200,000 letters were delivered. What is the letters were delivered. What is the DPMO in this situation?DPMO in this situation?
Example of Defects Per Million Example of Defects Per Million Opportunities (DPMO) calculation. Opportunities (DPMO) calculation. Suppose we observe 200 letters Suppose we observe 200 letters delivered incorrectly to the wrong delivered incorrectly to the wrong addresses in a small city during a addresses in a small city during a single day when a total of 200,000 single day when a total of 200,000 letters were delivered. What is the letters were delivered. What is the DPMO in this situation?DPMO in this situation?
000,1 1,000,000 x
200,000 x 1
200DPMO
000,1 1,000,000 x
200,000 x 1
200DPMO
So, for every one million letters delivered this city’s postal managers can expect to have 1,000 letters incorrectly sent to the wrong address.
So, for every one million letters delivered this city’s postal managers can expect to have 1,000 letters incorrectly sent to the wrong address.
Cost of Quality: What might that DPMO mean in terms of over-time employment to correct the errors?
Cost of Quality: What might that DPMO mean in terms of over-time employment to correct the errors?
3838
Six Sigma Quality: DMAIC Six Sigma Quality: DMAIC
Cycle (Continued)Cycle (Continued) 1. Define (D)
2. Measure (M)
3. Analyze (A)
4. Improve (I)
5. Control (C)
Customers and their priorities
Process and its performance
Causes of defects
Remove causes of defects
Maintain quality
4242
Second PartSecond Part
Statistical Process ControlStatistical Process Control
4343
Statistical ThinkingStatistical Thinking
All work occurs in a system of All work occurs in a system of interconnected processesinterconnected processes
Variation exists in all processesVariation exists in all processes
Understanding and reducing variation are Understanding and reducing variation are the keys to successthe keys to success
4444
Sources of Variation in Production Sources of Variation in Production ProcessesProcesses
Materials
Tools
Operators Methods Measurement Instruments
HumanInspectionPerformance
EnvironmentMachines
INPUTS PROCESS OUTPUTS
4545
VariationVariation
Many sources of uncontrollable Many sources of uncontrollable variation exist (common causes)variation exist (common causes)
Special (assignable) causes of Special (assignable) causes of variation can be recognized and variation can be recognized and controlledcontrolled
Failure to understand these differences Failure to understand these differences can increase variation in a systemcan increase variation in a system
4646
Problems Created by Problems Created by VariationVariation
Variation increases unpredictability. Variation increases unpredictability.
Variation reduces capacity utilization. Variation reduces capacity utilization.
Variation makes it difficult to find root causes. Variation makes it difficult to find root causes.
Variation makes it difficult to detect potential Variation makes it difficult to detect potential problems early. problems early.
4747
Importance of Importance of Understanding VariationUnderstanding Variation
time
PREDICTABLE
?UNPREDECTIBLE
4848
Two Fundamental Two Fundamental Management MistakesManagement Mistakes
1.1. Treating as a special cause any fault, complaint, Treating as a special cause any fault, complaint, mistake, breakdown, accident or shortage when it mistake, breakdown, accident or shortage when it actually is due to common causesactually is due to common causes
2.2. Attributing to common causes any fault, complaint, Attributing to common causes any fault, complaint, mistake, breakdown, accident or shortage when it mistake, breakdown, accident or shortage when it actually is due to a special causeactually is due to a special cause
5050
• Number or percent of defective items in a lot.• Number of defects per item.• Types of defects.• Value assigned to defects (minor=1, major=5, critical=10)
• Length• Weight• Time
• Diameter• Tensile Strength• Strength of Solution
• Height• Volume• Temperature
Types of Data
“Things we count”
Variables Data
Attribute Data
“Things we measure”
5252
Process Control ChartsProcess Control Charts Process Control ChartsProcess Control Charts
Variables and Attributes
Variables Attributes
X (process population average) P (proportion defective)
X-bar (mean for average) np (number defective)
R (range) C (number conforming)
MR (moving range) U (number nonconforming)
S (standard deviation)
5757
Process Control ChartsProcess Control Charts Process Control ChartsProcess Control Charts
X-barX-bar and and RR Charts Charts– The The X-barX-bar chart is a process chart used to chart is a process chart used to
monitor the average of the characteristics being monitor the average of the characteristics being measuredmeasured. To set up an . To set up an X-barX-bar chart select chart select samples from the process for the characteristic samples from the process for the characteristic being measured. Then form the samples into being measured. Then form the samples into rational subgroups. Next, find the average rational subgroups. Next, find the average value of each sample by dividing the sums of value of each sample by dividing the sums of the measurements by the sample size and plot the measurements by the sample size and plot the value on the process control the value on the process control X-barX-bar chart. chart.
5858
Process Control ChartsProcess Control Charts Process Control ChartsProcess Control Charts
X-barX-bar and and RR Charts (continued) Charts (continued)– The The RR chart is used to monitor the variability or chart is used to monitor the variability or
dispersion of the processdispersion of the process. It is used in . It is used in conjunction with the conjunction with the X-barX-bar chart when the chart when the process characteristic is variable. To develop an process characteristic is variable. To develop an RR chart, collect samples from the process and chart, collect samples from the process and organize them into subgroups, usually of three to organize them into subgroups, usually of three to six items. Next, compute the range, six items. Next, compute the range, RR, by taking , by taking the difference of the high value in the subgroup the difference of the high value in the subgroup minus the low value. Then plot the minus the low value. Then plot the RR values on values on the the RR chart. chart.
5959
Process Control ChartsProcess Control Charts Process Control ChartsProcess Control Charts
X-bar and R Charts
6060
Example of x-Bar and R Charts: Example of x-Bar and R Charts: Required DataRequired Data
Sample Obs 1 Obs 2 Obs 3 Obs 4 Obs 51 10.682 10.689 10.776 10.798 10.7142 10.787 10.86 10.601 10.746 10.7793 10.78 10.667 10.838 10.785 10.7234 10.591 10.727 10.812 10.775 10.735 10.693 10.708 10.79 10.758 10.6716 10.749 10.714 10.738 10.719 10.6067 10.791 10.713 10.689 10.877 10.6038 10.744 10.779 10.11 10.737 10.759 10.769 10.773 10.641 10.644 10.72510 10.718 10.671 10.708 10.85 10.71211 10.787 10.821 10.764 10.658 10.70812 10.622 10.802 10.818 10.872 10.72713 10.657 10.822 10.893 10.544 10.7514 10.806 10.749 10.859 10.801 10.70115 10.66 10.681 10.644 10.747 10.728
6161
Example of x-bar and R charts: Step 1. Example of x-bar and R charts: Step 1. Calculate sample means, sample ranges, mean Calculate sample means, sample ranges, mean
of means, and mean of ranges.of means, and mean of ranges.
Sample Obs 1 Obs 2 Obs 3 Obs 4 Obs 5 Avg Range1 10.682 10.689 10.776 10.798 10.714 10.732 0.1162 10.787 10.86 10.601 10.746 10.779 10.755 0.2593 10.780 10.667 10.838 10.785 10.723 10.759 0.1714 10.591 10.727 10.812 10.775 10.73 10.727 0.2215 10.693 10.708 10.79 10.758 10.671 10.724 0.1196 10.749 10.714 10.738 10.719 10.606 10.705 0.1437 10.791 10.713 10.689 10.877 10.603 10.735 0.2748 10.744 10.779 10.11 10.737 10.75 10.624 0.6699 10.769 10.773 10.641 10.644 10.725 10.710 0.13210 10.718 10.671 10.708 10.85 10.712 10.732 0.17911 10.787 10.821 10.764 10.658 10.708 10.748 0.16312 10.622 10.802 10.818 10.872 10.727 10.768 0.25013 10.657 10.822 10.893 10.544 10.75 10.733 0.34914 10.806 10.749 10.859 10.801 10.701 10.783 0.15815 10.660 10.681 10.644 10.747 10.728 10.692 0.103
Averages 10.728 0.220400
6262
Example of x-bar and R charts: Step 2. Example of x-bar and R charts: Step 2. Determine Control Limit Formulas and Determine Control Limit Formulas and
Necessary Tabled ValuesNecessary Tabled Values
x Chart Control Limits
UCL = x + A R
LCL = x - A R
2
2
R Chart Control Limits
UCL = D R
LCL = D R
4
3
n A2 D3 D42 1.88 0 3.273 1.02 0 2.574 0.73 0 2.285 0.58 0 2.116 0.48 0 2.007 0.42 0.08 1.928 0.37 0.14 1.869 0.34 0.18 1.82
10 0.31 0.22 1.7811 0.29 0.26 1.74
6363
Example of x-bar and R charts: Steps 3&4. Example of x-bar and R charts: Steps 3&4. Calculate x-bar Chart and Plot ValuesCalculate x-bar Chart and Plot Values
10.601
10.856
=).58(0.2204-10.728RA - x = LCL
=).58(0.220410.728RA + x = UCL
2
2
10.550
10.600
10.650
10.700
10.750
10.800
10.850
10.900
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sample
Mea
ns
UCL
LCL
6464
Example of x-bar and R charts: Steps 5&6. Example of x-bar and R charts: Steps 5&6. Calculate R-chart and Plot ValuesCalculate R-chart and Plot Values
0
0.46504
)2204.0)(0(R D= LCL
)2204.0)(11.2(R D= UCL
3
4
0.000
0.100
0.200
0.300
0.400
0.500
0.600
0.700
0.800
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Sample
RUCL
LCL
6565
UCL
LCL
Samples over time
1 2 3 4 5 6
UCL
LCL
Samples over time
1 2 3 4 5 6
UCL
LCL
Samples over time
1 2 3 4 5 6
Normal Behavior
Possible problem, investigate
Possible problem, investigate
•Interpreting Control Charts
•Interpreting Control Charts
6666
Process Control ChartsProcess Control Charts Process Control ChartsProcess Control Charts
Implications of a Process Out of ControlImplications of a Process Out of Control– If a process loses control and becomes If a process loses control and becomes
nonrandom, the process should be nonrandom, the process should be stopped immediately. stopped immediately.
– In many modern process industries where just-in-In many modern process industries where just-in-time is used, this will result in the stoppage of time is used, this will result in the stoppage of several work stations. several work stations.
– The team of workers who are to address the The team of workers who are to address the problem should use a structured problem solving problem should use a structured problem solving process.process.
6767
Process Control ChartsProcess Control ChartsProcess Control ChartsProcess Control Charts
Control Charts for AttributesControl Charts for Attributes– We now shift to charts for attributes. These We now shift to charts for attributes. These
charts deal with binomial and Poisson charts deal with binomial and Poisson processes that are not measurements. processes that are not measurements.
– We will now be thinking in terms of defects and We will now be thinking in terms of defects and defectives rather than diameters or widths.defectives rather than diameters or widths.
A defect is an irregularity or problem with a larger A defect is an irregularity or problem with a larger unit. unit.
A defective is a unit that, as a whole, is not A defective is a unit that, as a whole, is not acceptable or does not meet specifications.acceptable or does not meet specifications.
6868
Process Control ChartsProcess Control Charts Process Control ChartsProcess Control Charts
pp Charts for Proportion Defective Charts for Proportion Defective– The The pp chart is a process chart that is used to chart is a process chart that is used to
graph the proportion of items in a sample that graph the proportion of items in a sample that are defective (nonconforming to specifications)are defective (nonconforming to specifications)
– pp charts are effectively used to determine when charts are effectively used to determine when there has been a shift in the proportion there has been a shift in the proportion defective for a particular product or service. defective for a particular product or service.
– Typical applications of the Typical applications of the pp chart include things chart include things like late deliveries, incomplete orders, and like late deliveries, incomplete orders, and clerical errors on written forms.clerical errors on written forms.
6969
Process Control ChartsProcess Control Charts Process Control ChartsProcess Control Charts
npnp Charts Charts– The The npnp chart is a graph of the number of chart is a graph of the number of
defectives (or nonconforming units) in a defectives (or nonconforming units) in a subgroup. The subgroup. The npnp chart requires that the chart requires that the sample size of each subgroup be the same sample size of each subgroup be the same each time a sample is drawn. each time a sample is drawn.
– When subgroup sizes are equal, either the When subgroup sizes are equal, either the pp or or npnp chart can be used. They are essentially chart can be used. They are essentially the same chart.the same chart.
7070
Example of Constructing a Example of Constructing a pp-Chart: -Chart: Required DataRequired Data
1 100 42 100 23 100 54 100 35 100 66 100 47 100 38 100 79 100 1
10 100 211 100 312 100 213 100 214 100 815 100 3
7171
Statistical Process Control Formulas:Statistical Process Control Formulas:Attribute Measurements (Attribute Measurements (pp-Chart)-Chart)
p =Total Number of Defectives
Total Number of Observations
ns
)p-(1 p = p
p
p
z - p = LCL
z + p = UCL
s
s
Given:
Compute control limits:
7272
1. Calculate the sample proportions, p (these are what can be plotted on the p-chart) for each sample.
Sample n Defectives p1 100 4 0.042 100 2 0.023 100 5 0.054 100 3 0.035 100 6 0.066 100 4 0.047 100 3 0.038 100 7 0.079 100 1 0.01
10 100 2 0.0211 100 3 0.0312 100 2 0.0213 100 2 0.0214 100 8 0.0815 100 3 0.03
Example of Constructing a Example of Constructing a pp-chart: -chart: Step 1Step 1
7373
2. Calculate the average of the sample proportions.
0.036=1500
55 = p
3. Calculate the standard deviation of the sample proportion
.0188= 100
.036)-.036(1=
)p-(1 p = p n
s
Example of Constructing a Example of Constructing a pp-chart: -chart: Steps 2&3Steps 2&3
7474
4. Calculate the control limits.
3(.0188) .036
UCL = 0.0924LCL = -0.0204 (or 0)
p
p
z - p = LCL
z + p = UCL
s
s
Example of Constructing a Example of Constructing a pp-chart: -chart: Step 4Step 4
7575
Example of Constructing a Example of Constructing a pp-Chart: -Chart: Step 5Step 5
5. Plot the individual sample proportions, the average of the proportions, and the control limits
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15
Observation
p
UCL
LCL
Sample n Defectives p1 100 4 0.042 100 2 0.023 100 5 0.054 100 3 0.035 100 6 0.066 100 4 0.047 100 3 0.038 100 7 0.079 100 1 0.01
10 100 2 0.0211 100 3 0.0312 100 2 0.0213 100 2 0.0214 100 8 0.0815 100 3 0.03
7676
Process CapabilityProcess CapabilityProcess CapabilityProcess Capability
Process Stability and CapabilityProcess Stability and Capability– Once a process is stable, the next Once a process is stable, the next
emphasis is to ensure that the process is emphasis is to ensure that the process is capable.capable.
– Process capability refers to the ability of a Process capability refers to the ability of a process to produce a product that meets process to produce a product that meets specifications.specifications.
7777
Process CapabilityProcess Capability
Process limitsProcess limits
Tolerance limitsTolerance limits
How do the limits relate to one another?How do the limits relate to one another?
7878
If the process capability of a normally If the process capability of a normally distributed process is .084, the process is distributed process is .084, the process is in control, and is centered at .550. What in control, and is centered at .550. What are the upper and lower control limits for are the upper and lower control limits for
this process? this process?
Process Capability = 6
6 = .084 = .014
UCL = .550 + 3(.014)= .592
LCL = .550 - 3(.014) = .508
7979
X4.90 4.95 5.00 5.05 5.10 5.15
cm
Tolerance band
Process capability (6 )LTL UTL
Outputout of spec
Outputout of spec
Process outputdistribution
5.010
s
Process Capability Chart
8080
This process is CAPABLE of producing all good output.
ä Control the process.
This process is NOT CAPABLE.
ä INSPECT - Sort out the defectives
××
LowerTolerance
Limit
UpperTolerance
Limit
Process Capability
8181
Process Capability Index, CProcess Capability Index, Cpkpk
3
X-UTLor
3
LTLXmin=C pk
Shifts in Process Mean
Capability Index shows how well parts being produced fit into design limit specifications.
As a production process produces items small shifts in equipment or systems can cause differences in production performance from differing samples.
8282
Given:Given:
process mean = 1.0015process mean = 1.0015
= .001= .001
LTL = .994LTL = .994
UTL = 1.006UTL = 1.006
Process Capability Index- ExampleProcess Capability Index- Example
3Upper Tol Limit - X
3
X - Lower Tol Limit–OR{
Cpk
=
Smaller of:
Cpk= min
1.0015 -.994 1.006 - 1.0015
3(.001) 3 (.001)or
Cpk= min [2.5 or 1.5] = 1.5
–
8383
LTL UTL
Cpk = 1.0
LTL UTL
Cpk = 0.60
LTL UTL
Cpk = 1.33
LTL UTL
Cpk = 0.80
(f)
LTL UTL
Cpk = 1.0
(d)
LTL UTL
Cpk = 3.0
Process Capability: Cpk Varieties
8686
Acceptance SamplingAcceptance SamplingAcceptance SamplingAcceptance Sampling
Acceptance SamplingAcceptance Sampling– A statistical quality control technique used A statistical quality control technique used
in deciding to accept or reject a shipment in deciding to accept or reject a shipment of input or output.of input or output.
– Acceptance sampling inspection can range Acceptance sampling inspection can range from 100% of the Lot to a relatively few from 100% of the Lot to a relatively few items from the Lot items from the Lot (N=2)(N=2) from which the from which the receiving firm draws inferences about the receiving firm draws inferences about the whole shipment.whole shipment.
8787
Acceptance SamplingAcceptance SamplingPurposesPurposes– Determine quality levelDetermine quality level– Ensure quality is within predetermined levelEnsure quality is within predetermined level
AdvantagesAdvantages– EconomyEconomy– Less handling damageLess handling damage– Fewer inspectorsFewer inspectors– Upgrading of the inspection jobUpgrading of the inspection job– Applicability to destructive testingApplicability to destructive testing– Entire lot rejection (motivation for improvement) Entire lot rejection (motivation for improvement)
8888
Acceptance SamplingAcceptance Sampling
DisadvantagesDisadvantages– Risks of accepting “bad” lots and rejecting Risks of accepting “bad” lots and rejecting
“good” lots“good” lots– Added planning and documentationAdded planning and documentation– Sample provides less information than 100-Sample provides less information than 100-
percent inspection percent inspection
9090
Statistical Sampling Statistical Sampling TechniquesTechniques
Statistical Sampling Statistical Sampling TechniquesTechniques
nn and and c c – The bottom line in acceptance sampling is The bottom line in acceptance sampling is
that acceptance sampling plans are that acceptance sampling plans are designed to give us two things: designed to give us two things: nn and and cc, , where where nn = the sample size of a particular sampling plan = the sample size of a particular sampling plan
cc = the maximum number of defective pieces for = the maximum number of defective pieces for a a sample to be rejected