Assignment 6 (Chapter 10)
Quality Control
McGraw-Hill/Irwin
Copyright © 2012 by The McGraw-Hill Companies, Inc. All rights reserved.
- You should be able to:
List and briefly explain the elements in the control process
Explain how control charts are used to monitor a process, and the concepts that underlie their use
Use and interpret control charts
Perform run tests to check for nonrandomness in process output
Assess process capability
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- Quality Control
- A process that evaluates output relative to a standard and takes corrective action when output doesn’t meet standards
- If results are acceptable no further action is required
- Unacceptable results call for correction action
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- Inspection
- An appraisal activity that compares goods or services to a standard
- Inspection issues:
How much to inspect and how often
At what points in the process to inspect
Whether to inspect in a centralized or on-site location
Whether to inspect attributes or variables
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- Typical Inspection Points:
- Raw materials and purchased parts
- Finished products
- Before a costly operation
- Before an irreversible process
- Before a covering process
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- Effects on cost and level of disruption are a major issue in selecting centralized vs. on-site inspection
- Centralized
- Specialized tests that may best be completed in a lab
- More specialized testing equipment
- More favorable testing environment
- On-Site
- Quicker decisions are rendered
- Avoid introduction of extraneous factors
- Quality at the source
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- Quality control seeks
- Quality of Conformance
- A product or service conforms to specifications
- A tool used to help in this process:
- SPC
- Statistical evaluation of the output of a process
- Helps us to decide if a process is “in control” or if corrective action is needed
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- Two basic questions: concerning variability:
Issue of Process Control
- Are the variations random? If nonrandom variation is present, the process is said to be unstable.
Issue of Process Capability
- Given a stable process, is the inherent variability of the process within a range that conforms to performance criteria?
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- Variation
Random (common cause) variation:
Natural variation in the output of a process, created by countless minor factors
Assignable (special cause) variation:
A variation whose cause can be identified.
A nonrandom variation
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- SPC involves periodically taking samples of process output and computing sample statistics:
- Sample means
- The number of occurrences of some outcome
- Sample statistics are used to judge the randomness of process variation
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- Sampling Distribution
- A theoretical distribution that describes the random variability of sample statistics
- The normal distribution is commonly used for this purpose
- Central Limit Theorem
- The distribution of sample averages tends to be normal regardless of the shape of the process distribution
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- Sampling and corrective action are only a part of the control process
- Steps required for effective control:
- Define: What is to be controlled?
- Measure: How will measurement be accomplished?
- Compare: There must be a standard of comparison
- Evaluate: Establish a definition of out of control
- Correct: Uncover the cause of nonrandom variability and fix it
- Monitor: Verify that the problem has been eliminated
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- Control Chart
- A time ordered plot of representative sample statistics obtained from an ongoing process (e.g. sample means), used to distinguish between random and nonrandom variability
- Control limits
- The dividing lines between random and nonrandom deviations from the mean of the distribution
- Upper and lower control limits define the range of acceptable variation
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Each point on the control chart represents a sample of n observations
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- Type I error
- Concluding a process is not in control when it actually is.
- The probability of rejecting the null hypothesis when the null hypothesis is true.
- Manufacturer’s Risk
- Type II error
- Concluding a process is in control when it is not.
- The probability of failing to reject the null hypothesis when the null hypothesis is false.
- Consumer’s Risk
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- Variables generate data that are measured
- Mean control charts
- Used to monitor the central tendency of a process.
- “x- bar” charts
- Range control charts
- Used to monitor the process dispersion
- R charts
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- Used to monitor the central tendency of a process
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- Used to monitor process dispersion
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- To determine initial control limits:
- Obtain 20 to 25 samples
- Compute appropriate sample statistics
- Establish preliminary control limits
- Determine if any points fall outside of the control limits
- If you find no out-of-control signals, assume the process is in control
- If you find an out-of-control signal, search for and correct the assignable cause of variation
- Resume the process and collect another set of observations on which to base control limits
- Plot the data on the control chart and check for out-of-control signals
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- Attributes generate data that are counted.
- p-Chart
- Control chart used to monitor the proportion of defectives in a process
- c-Chart
- Control chart used to monitor the number of defects per unit
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- When observations can be placed into two categories.
Good or bad
Pass or fail
Operate or don’t operate
- When the data consists of multiple samples of several observations each
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- Use only when the number of occurrences per unit of measure can be counted; non-occurrences cannot be counted.
Scratches, chips, dents, or errors per item
Cracks or faults per unit of distance
Breaks or Tears per unit of area
Bacteria or pollutants per unit of volume
Calls, complaints, failures per unit of time
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- At what points in the process to use control charts
- What size samples to take
- What type of control chart to use
- Variables
- Attributes
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- Once a process has been determined to be stable, it is necessary to determine if the process is capable of producing output that is within an acceptable range
- Tolerances or specifications
- Range of acceptable values established by engineering design or customer requirements
- Process variability
- Natural or inherent variability in a process
- Process capability
- The inherent variability of process output (process width) relative to the variation allowed by the design specification (specification width)
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Lower
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Upper
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Process variability (width) is less than the specification width
Lower
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Upper
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Process variability (width) matches specifications width
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Upper
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Process variability (width)
exceeds specifications
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- Used when a process is not centered at its target, or nominal, value
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- Simplify
- Standardize
- Mistake-proof
- Upgrade equipment
- Automate
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- Quality is a primary consideration for nearly all customers
- Achieving and maintaining quality standards is of strategic importance to all business organizations
- Product and service design
- Increase capability in order to move from extensive use of control charts and inspection to achieve desired quality outcomes
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