Ch 8: Measuring and Controlling Quality
Defects (or Errors) per Million Opportunities
(Number of defects discovered / opportunities for error) * 1,000,000
Cpu
(USL - u (process average))/ 3 sigma (upper one-sided index)
Process Capability Index (Cp)
(Upper Specification Limit (USL) - Lower Specification Limit (LSL) / 6 sigma (sigma being the standard deviation of the process)
Non-conformances per unit (NPU)
(or Defects per Unit in manufacturing) = Total number of non-conformances / Number of units inspected 260/100 = 2.6 NPU
Proportion nonconforming
(or Proportion Defective in manufacturing) = Number of nonconforming units found / Number of units inspected. Usually displayed as a percentage. For example: (8 / 100)*100 = 8%
Cpl
(u (process average) - LSL)/3 sigma (lower one-sided index)
One often uses judgement about the nature of operations and the costs involved in making these decisions.
1: If the cost of investigating an operation to identify the cause of an apparent out-of-control condition is high, wider control limits should be adopted. Conversely, if the cost is low, narrower limits should be selected. 2: If the cost of the defective output generated by an operation is substantial, narrower control limits should be uses. Otherwise, wider limits should be selected. 3: If he cost of both types of errors are significant, wide control limits should be chosen and a larger sample size should be used. Also, more frequent samples should be taken to reduce the duration of any out-of-control condition that might occur. 4: If past experience with an operation indicates that an out-of-control condition arises quite frequently, narrower control limits should be considered. In the event that the probability of an out-of-control condition is small, wider limits might be preferred.
When a process is in statistical control, the points on a control chart fluctuate randomly between the control limits with no recognizable pattern:
1: No points are outside of the control limits. 2: The number of points above and below the center line is about the same. 3: the points seem to fall randomly above and below the center line. 4: Most points, but not all, are near the center line, and only a few are close to the control limits.
Process Capability Study
A carefully planned study designed to yield specific information about the performance of a process under specified operating conditions.
Three types of studies are often conducted
A process characterization A peak performance study A component variability study
A Repeatability and Reproducibility (R&R) Study
A study in a measurement system using statistical analysis. This study can quantify the error, uncertainty or maximum resolution of a test or inspection system
Throughput Yield (TY)
An estimate of the number of units that have no non-conformances: TY = e^-NPU
Nonconformance
Any defect or error associated with a unit of work
Variable Measurement
Applies to dimensional quantities such as length, weight, time, or any other value on a continuous scale of measurement
When implementing SPC, practitioners must consider the four issues
Basis for Sampling Sample Size Sampling Frequency Location of Control Limits
The steps in a process capability study are similar to those of any systematic investigation, and include the following
Choose a representative machine or segment of the process Define the process conditions Select a representative operator Provide materials that are of standard grade, with sufficient materials for uninterrupted study Specify the gauging or measurement method to be used Collect the measurements and interpret the data
Several reason why high rates occur
Complexity Defect Rate Inspection Rate
Hugging the Center Line
Control limits may be too wide, or miscalculated
Location of Control Limits
Control limits need not adhere to the statistical "3 standard deviations" formula. It may be desirable to use wider or narrower control limits to reduce the costs associated with drawing the wrong conclusions
Practical Guidelines
Cost models attempt to find the best combination of SPC design parameters (center line, control limits, sample size, and sampling interval) that minimize expected cost or maximize expected profit.
($$) Appraisal Costs
Costs associated with efforts to ensure conformance to requirements, generally through measurement and analysis of data to detect non-conformances (inspections, which are costly
External Failure Costs
Costs due to customer complaints and returns Product recall costs and warranty claims Product liability costs
($$$) Internal Failure Costs
Costs incurred as a result of unsatisfactory quality found before the delivery of a product to the customer (this would be final inspection or final burn-in, quite expensive, since the product is now in its finished state)
Manufacturing classifications of defects
Critical Defect Major Defect Minor Defect
ISO 11462-1 standard addresses which elements
Definition of SPC goals Conditions for a successful SPC system Elements of the SPC system
Manufacturing, Variables Data
Diameters of machined ball bearings measured with a micrometer -> average diameter and the range of measurements (Statistical Process Control xbar and R-Chart) or standard deviation (Statistical Process Control x-bar and s-Charts) of a sample of ball bearings
Example of term indicator
For instance, though you cannot directly measure dissatisfaction, you can use the number of complaints or lost customers as indicators of dissatisfaction
Sudden shift in the Process Average
If eight consecutive points fall on one side of the center line, one could conclude that the mean has shifted
($) Prevention Costs
Investments made to keep non-conforming products from occurring and reaching the customer, including the following specific costs (designing in the quality in the product, this is usually the less expensive option)
Measurement System Evaluation
Low-technology instruments High-technology instruments Total observed variation in production output
Statistical Process Control (SPC)
Methodology for monitoring a process to identify special causes of variation and signal the need to take corrective action. SPC provides a means by which a firm can demonstrate its quality capability.
($,$$$) External Failure Costs
Occurs after poor-quality products reach the customer (this is the most expensive of all quality costs)
nonconforming Unit of Work
One unit of work that has one or more defects or errors
When special causes of variation are present, the process is said to be
Out of Control
Manufacturing, Attributes Data
Percentage of faucets that have cosmetic defects (Statistical Process Control Fraction Nonconforming (p) Chart)
Services
Percentage of orders filled accurately (Statistical Process Control Fraction Nonconforming (p) Chart), or the time taken to fill and ship a customer's order (Statistical Process Control x-bar and R-Chart)
For attribute data, the two important quality measures are
Proportion nonconforming Non-conformances per unit (NPU)
Prevention costs include (list)
Quality planning costs Process control costs Information systems costs Training and general management costs
When a worker or an inspector measures the same part multiple times the results will usually show some variability. Thus
Repeatability, or equipment variation (EV) Reproducibility, or appraiser variation (AV) A Repeatability and Reproducibility (R&R) Study
Internal Failure Costs includes (list)
Scrap and rework costs Costs of corrective action Downgrading costs Process failures
SMART, an acronym for good measurements
Simple (easy and cost-effective to obtain) Measurable (clear and un-ambiguous) Actionable (information to make good decisions for process management) Related (clearly related to what is important to customers - both external and internal - and for running the business)
When the variation in the process is due to common causes of variation alone, we say that the process is in
Statistical Control, or just Control
Definition of SPC goals
Such goals might include reducing variation around target values and compensating for process variation to ensure product conformity, reducing costs, indicating how the process is likely to behave in the future, and quantifying process capability
Sampling Frequency
Taking large samples on a frequent basis is desirable but clearly not economical. Samples should be close enough to provide an opportunity to detect changes in process characteristics as soon as possible and reduce the chances of producing a large amount of non-conforming output. However, they should not be so close that the cost of sampling outweighs the benefits that can be realized.
Appraisal Costs
Test and inspection costs Instrument maintenance costs Process measurement and control costs
First wrong conclusion
The belief that a special cause is present when in fact one does not exist
Process Capability
The capability of a process to produce output that conforms to specifications
Sample Size
The choice of sample size represents a trade-off between cost and information. Small sample sizes reduce costs associated with the time that workers must spend collecting data; however, they provide less statistical information. Large samples are more costly but allow smaller changes in process characteristics to be detected with higher probability
Precision
The closeness of repeated measurements to each other. Precision relates to the variance of repeated measurements
Accuracy
The difference between the true value and the observed average of a measurement
Complexity
The number of defects caught by an inspector decreases with more parts and less orderly arrangement
Unit of Work
The output of a process or an individual process step
Attribute Measurement
The presence or absence of non-conformances in a unit of work, or The presence or absence of non-conformances in a unit of work, or the number of non-conformances in a unit of work. Often collected by visual inspection and expressed as proportions and counts. Collecting attribute data is usually easier because an assessment can usually be done more quickly by a simple inspection or count, whereas variable data require the use of some type of measuring instrument. However, attribute measurement requires a much larger sample size than variable measurement to obtain the same amount of statistical information. This difference can become significant when inspection of each item is time-consuming or expensive
Basis for Sampling
The purpose of a control chart is to identify the variation in a system that may change over time. In determining the method of sampling, samples should be chosen to be as homogenous as possible so that each sample reflects the system of common causes or assignable causes that may be present at that point in time. Also, the chance of observing differences between samples should be high, the chance of observing differences within a sample should be low. Samples that satisfy these criteria are called rational subgroups
Repeatability, or equipment variation (EV)
The variation in multiple measurements of a quality characteristic by an individual worker or inspector using the same instrument. Repeatability indicates how consistent a measuring instrument is. It is influenced by the condition of the measurement instrument, environmental conditions such as noise or lighting, the workers overall health and eyesight, and the process used to take the measurement such as how the part is positioned in the gage
Reproducibility, or appraiser variation (AV)
The variation when using the same measuring instrument by different individuals to measure the same parts. Reproducibility indicates how consistent workers or inspectors are in using measurement instruments. It is influenced by the training of workers in the use of the instrument, clarity of the directions or procedures of the measurement process, calibration of gages between workers, gage maintenance, and worker health
Measurement System
The workers who take the measurements + the instructions they use + the instruments they use
Elements of the SPC system
These address the processes an organization should implement and actions it should take to ensure that a successful SPC system includes both operational sand support activities. These elements include a process documentation and control plan, definition of process targets and limits, data collection, measuring equipment, data recording and analyses, process control, short- and long-term process capability assessment, communication of results, and process improvement implementation and project management activities
Conditions for a successful SPC system
These conditions include integration with a formal quality management system, management support, use of information for data-driven decisions and management reviews, and ensuring the competence of those who will be using the tools.
Process Performance Indexes
Used if the process include special causes of variation, which represents the actual, rather than the ideal, performance in a non-controlled environment. In reality, this makes little sense; many experts do not recommend this because it is important to control a process and remove special causes in order to achieve high levels of quality and customer satisfaction
SPC was first proposed by
Walter Shewhart in the 1920s
Second wrong conclusion
When special causes are present but are not signaled in the control chart.
Defect Rate
When the product defect is low, inspectors tend to miss more defects than when the defect rate is higher
Defect
a term most often used in Manufacturing
Error
a term most often used in Services
Measurements must be both
accurate and precise
Cycles
are short, repeated patterns in the chart, alternating high peaks and low valleys
Costs of corrective action
arising from time spent determining the causes of failure and correcting production problems
A component variability study
assesses the relative contribution of different sources of total variation. A component variability study uses a designed experiment to evaluate the sources of variability
Test and inspection costs
associated with incoming materials, work-in-process, and finished goods, including equipment costs and salaries (inspectors, supervisors, quality managers and quality engineers)
Efficient national and international trade requires weights and measures organizations that
assure uniform and accurate measures used in trade, national or regional measurement standards laboratories, standards development organizations, and accredited and internationally recognized calibration and testing laboratories
How can Complexity, Inspection Rate, and Inspection Rate be mitigated?
by using automated technology, or minimizing the number of quality characteristics that must be inspected, reducing time pressures, using repeated inspections by other inspectors, and improving the design of the workspace to facilitate the inspection task
SPC relies on
control charts
Product recall costs and warranty claims
cost of repair or replacement as well as associated administrative costs
Process control costs
costs spent on analyzing production processes and implementing process control plans
High-technology instruments
depend on modern electronics, microprocessors, lasers or advanced optics
A peak performance study
determines how a process performs when only common causes of variation are present. Typically this is done over a short time interval under carefullycontrolled conditions.
Instrument maintenance costs
due to calibration and repair of measuring instruments
Good data and measurement systems are the basis for
effective quality control as well as for quality improvement.
Accuracy is measured as the amount of
error in a measurement in proportion to the total size of the measurement
Information systems costs
expended to develop data requirements and measurements
The lack of accuracy reflects a systematic bias in the measurement such as
gage that is not properly calibrated, worn, or used improperly by the worker
Metrology is also vital to
global competitiveness
Quality control seeks to ensure that processes perform in a stable and predictable fashion by
identifying when corrective action is needed
Training and general management costs
including internal and external training programs, clerical staff expenses, and miscellaneous supplies
Managers usually react to high failure costs by
increasing inspection
If special causes are present, the control chart will
indicate them, and corrective action can be taken quickly
Process Capability (indexes)
is measured by computing numerical indexes. The distribution of process output (length, time, weight, etc.) can differ in both location and spread relative to the specifications
Cp
is the ratio of the specification range to the process variation.
if the variation in the measurement system is high
it is difficult to separate the true variation in the process from the variation in the measurement system, resulting in misleading conclusions about quality
The overall increase of inspection typically results of
little, if any, improvement in overall quality or profitability
Quality costs are the responsibility of
management
Low-technology instruments
manual devices such as gages and rulers
Scrap and rework costs
material, labor, and overhead
Many government regulations (such as those in Drugs, Biologics, and Medical Devices) and commercial contracts require regulated organizations or contractors to verify that
measurements are traceable to a reference standard.
Timely
measurements need to be available and communicated to workers and managers when they need the results from the measurements
Cpk
minimum (Cpu or Cpl)
Metrology is the science
of measurement and is defined broadly as the collection of people, equipment, facilities, methods, and procedures used to assure the correctness or adequacy of measurements
Major Defect
one not critical but likely to result in failure or to materially reduce the usability of the unit for its intended purpose
Minor Defect
one not likely to materially reduce the usability or the item for its intended purpose, nor have any bearing on the effective use or operation of the unit.
Critical Defect
one that judgement and experience indicate will surely result in hazardous or unsafe conditions for individuals using, maintaining, or depending on the product and will prevent proper performance of the product
Metrology is vital in
our daily lives
Low precision is the result of
random variation that is built into the instrument, such as friction among its parts
Product liability costs
resulting from legal actions and settlements
Costs due to customer complaints and returns
rework on returned items, cancelled orders, and freight premiums
A control chart is
run chart to which two horizontal lines, called control limits are added; the Upper Control Limit (UCL) and the Lower Control Limit (LCL).
Quality planning costs
salaries of individuals associated with quality planning and problem-solving teams, the development of new procedures, new equipment design, and reliability studies
Most control charts today are implemented via
software; nevertheless, they are quite easy to do by hand
Thus, an objective of quality assurance is to minimize measurement error. In many industries, in-process measures are collected through
some type of manual inspection process. Processes that rely on visual interpretation of product characteristics or manual reading of gauges and instruments may encounter error rates of from 10 to 50 percent
A process characterization
study is designed to determine how a process performs under actual operating conditions, which may include both common and special causes of variation. It is typically performed over a moderately long time interval to capture any and all variations that might occur
Downgrading costs
such as revenue lost when selling a product at a lower price because it does not meet specifications
The difference between Accuracy and Precision is often illustrated by
target
The term indicator is often used for measurements
that are not a direct or exclusive measure of performance
Measurement is
the act of collecting data to quantify the values of product, service, process, and other business metrics
The only information needed to conduct a process characterization study is
the mean, standard deviation, and histogram of a sample of measurements
If there is little variation in the measurement system
the observed measurements reflect the true variation in the process
Trends
the result of some cause that gradually affects the measurement and causes the points on a control chart to gradually move up or down
Control limits are chosen statistically
to provide a high probability that points will fall between these limits if the process is in control.
Measures and indicators refer
to the numerical results obtained from measurement
Total observed variation in production output
true process variation + variation due to measurement
dashboards
typically consist of a small set of measures (five to six) that provide a quick summary of process performance
Process failures
unplanned machine downtime or unplanned equipment repair
The ISO standard ISO 11462-1 provides guidance for organizations wishing to
use SPC to meet statistical methods
In practice, an increase in prevention
usually generates larger savings in all other cost categories
Calibration is the process of
verifying the capability and performance of an item of measuring and test equipment compared to traceable measurement standards
To evaluate the Process Capability
we need the specifications for the output, and statistical information about the actual process performance
Process measurement and control costs
which involve the time spent by workers to gather and analyze quality measurements
