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Chapter 9 - Quality and Statistical Process Control
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Terms in this set (55)
Natural Variation
Variation that occurs in a process as a result of pure randomness
(a.k.a.
Common Cause Variation
)
Assignable Cause Variation
Variation that occurs because of a specific change in input or in environmental variables.
Input Variables
The variables in a process that are under the control of management.
Environmental Variables
Variables in a process that are not under the control of management but nevertheless might impact the outcome of the process
Outcome Variables
Measures describing the quality of the output of the process.
Set of Specifications
A set of rules that determine if the outcome variable of a unit is defective or not.
Root Cause
A root cause for a defect is a change in an input or an environmental variable that initiated a defect.
Goal of Management
Input variables and environmental variables will always be subject to some common cause variation. Goal is to keep variation small and design the process so that this variation does not translate in large variations in outcome variables and ultimately defects.
Robust
The ability of a process to tolerate changes in input and environmental variables without causing the outcomes to be defective.
Statistical Process Control (SPC)
A framework in operations management built around the empirical measurement and the statistical analysis of input, environmental, and outcome variables.
4 Steps of Statistical Process Control (SPC)
1. Capability of Process
2. Conformance Analysis
3. Investigating for Assignable Cause
4. Eliminating Assignable Cause
Capability of Process
Measuring the current amount of outcome variation in the process and comparing how this variation relates to the outcome specifications and thus the likelihood of making a defect.
Conformance Analysis
Monitoring process & identifying instances in which the outcome variation is
abnormal
, suggesting the occurrence of some assignable cause variation in input or environmental variables.
Investigating for Assignable Cause
Investigating the root cause of an assignable cause variation by finding the input or environmental variable(s) that caused the variation.
Eliminating Assignable Cause
Avoiding the recurrence in the future of similar assignable cause variations and/or changing the process so that it is sufficiently robust to not have its quality be affected by such events in the future.
Abnormal
A variation is abnormal if it is not behaving in line with past data; this allows us to conclude that we are dealing with an
assignable cause variation
and are not just facing randomness in the form of
common cause variation
Lower Specification Limit (LSL)
The
smallest
outcome value that does not trigger a defective unit.
Upper Specification Limit (USL)
The
largest
outcome value that does not trigger a defective unit.
Process Capability Index
The ratio between the width of the specification interval of the outcome variable and the variation in the outcome variable.
tells us how many standard deviations we can move away from the statistical mean before causing a defect
Process Capability Index (Equation)
= (USL - LSL)/(6 x Standard Deviation)
Six-Sigma Process
A process that has 6 standard deviations on either side of the mean and the specification limit
Defect Probability
the statistical probability with which a randomly chosen flow unit does not meet specifications
3 Steps for Defect Probability
1. Find probability that unit falls below LSL
2. Find probability that unit falls above USL
3. Add the results of step 1 & 2
Parts Per Million (PPM)
the expected number of defective parts in a random sample of 1 million
= Defective Probability x 1,000,000
3 Sigma Process
Where Process Capability Index = 1
Target Variation
The largest amount of variation in a process that does not exceed a given defect probability
Control Charts
plot data over time in graph to show a representation of variation in the process
X-Bar Charts
A special control chart in which we track the mean of a sample
X-Bar
the average of a sample
gets less noisy the bigger the daily sample size
Upper Control Limit (UCL)
Line in control chart that provides the
largest
value that is still acceptable without being abnormal
Lower Control Limit (LCL)
Line in control chart that provides the
smallest
value that is acceptable without being an abnormal variation
X-Double-Bar
the average of a set of sample averages
Estimated Standard Deviation of All Parts
the standard deviation that is computed across all parts
Estimated Standard Deviation for X-Bar (Equation)
Standard Deviation of all parts/Square root of sample size
Control Limits
measures to what extent the process is behaving the same way it did in the past
Specification Limits
measures to what extent the process meets the specifications of the customer
Control vs Specification Limits
it is possible that the outcome of the process is within the control limits but outside the specification limits.
~in this case, the process capability is low and defects occur regularly as a result of common cause variation
Fishbone Diagram
A structured way to brainstorm about the potential root causes that have led to a change in an outcome variable.
(this is done by mapping out all
input
and
environmental variables
)
(a.k.a.
Cause-Effect Diagram
&
Ishikawa Diagram
)
"Five Whys"
Brainstorming technique that helps employees to find the root cause of a problem.
~employees are encouraged to ask "why did this happen?" at least 5 times (Toyota)
Pareto Diagram
Graphical way to identify the most important causes of process defects.
~to create one, we need to collect data on the number of defect occurrences as well as the associated defect types.
Pareto Principle
(80-20 rule): 20% of the causes account for 80% of the problems
Robust Process
A process that can tolerate variation in input variables and environmental variables without leading to a defect.
Strategies for Robust Process
1.
Over-engineering
- make the process so that it can do well, even under very exceptional conditions
2.
Fool-proofing
- change the work in such a way that the operator attempting to make a mistake, can't, and realizes they have done something wrong.
3.
Early warning signs on input/environmental variables
- there typically exists some time lag between the occurrence of variation in the outcome variable and the defect
Event Tree
Visual representation of binary outcome variables. It supports the defect probability calculations by connecting the defects in the process to an overall outcome measure.
Example where all steps have to function correctly
3 steps to make a unit, each step has 2 possible outcomes (good or defect). Therefore, because they're are 3 outcome variables and each with 2 possible outcomes, the event tree distinguishes between 8 (2x2x2) different scenarios.
~any single mistake leads to defect
~only one scenario (all 3 steps done correctly) that leads to a good unit
Example where as long as defect is caught/fixed at any step, there can still be a good outcome
3 steps, 2 values at each step, 8 (2x2x2) possible outcomes but only one outcome leads to a defect, and that's if the defect is missed at every step, otherwise even with a defect at 2 steps out of 3, there is still a good outcome.
P-Chart
Special control chart used for dealing with binary outcomes. Has all features of X-Bar Chart, yet does not require a continuous outcome variable.
requires larger sample sizes, especially if defects rarely occur
(a.k.a.
Attribute-Based Control Chart
)
Estimated Standard Deviation for P-Chart (Equation)
Square root of: [P-Bar(1-P-Bar)/Sample Size]
UCL for P-Chart (Equation)
= P-Bar + (3 x Estimated Standard Deviation)
LCL for P-Chart (Equation)
= P-Bar - (3 x Estimated Standard Deviation)
Binary
measure capability of the process as the percentage of units produced correctly.
(wastes a lot of info)
Binary/Capability Analysis
~PPM
~Yield Calculations
Binary/Conformance Analysis
use P-Chart
Parametric/Capability Analysis
use Six-Sigma
Parametric/Conformance Analysis
use X-Bar
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