MGMT 382
Jeremy T. Navarre, Ph.D.
Quality Control
Chapter 10
Quality Control
Quality control is a process that measures output relative to
a standard that may or may not necessitate corrective
action.
If results are acceptable compared to the specified
standard, no corrective action is required whereas results
not meeting the standard yield corrective action(s).
Quality Assurance & Control
Quality assurance relies on inspection of lots, or batches,
and is referred to as acceptance sampling.
Quality control processes that occur simultaneous to
production are referred to as statistical process control.
Quality Control
Quality control evaluates the quality of conformance related
to a process.
Specifically, quality control evaluates whether a process
conforms to the intended design of the process.
Statistical Process Control
Statistical process control employs statistical analyses to
evaluate if a process conforms to the intended design or, in
contrast, is out of control and, consequently, requires
corrective action.
Process Variability
Process variability may be derived from random, or
common, variability, which is deemed acceptable based on
specified criteria.
Assignable, or special, variation includes variation derived
from an identifiable and meaningful phenomenon or
phenomena.
Assignable Variation
Statistical process control focuses on assignable variation,
which is deemed inherently problematic, is identifiable, does
not conform to the intended design and able to be
corrected.
Assignable variation is typically identified from a sampling
distribution’s statistical characteristics.
Central Limit Theorem
The central limit theorem states that as the sample size
increases, the distribution of sample means approaches a normal
distribution regardless of the shape of the sampled population.
As the sample distribution becomes increasingly concentrated,
the likelihood that a sample statistic is close to the true value in
the population is higher for larger samples relative to smaller
samples.
Statistical Process Control
Control Process
Define
 Define Characteristics to be Controlled
Measure
 Define Measurement Procedures
Compare
 Compare Measurement Results to
Specified Standards or Level of Standard
Evaluate
 Interpret Results Based on Established
Criteria for Control Status
Correct
 Employ Corrective Measures, or Don’t
Monitor
 Sample and Monitor Effectiveness
Statistical Process Control
Statistical Process Control
Central Limit Theorem
Control limits, lower and upper, establish parameters that
effectively differentiate between random and nonrandom
variation.
Notably, there exists the potential that Type I or Type II
errors are prevalent.
Type I and Type II Errors
A Type I error occurs when a sample statistic indicates
assignable, or special, variation is present when only
random, or common, variation is present.
 A Type II error occurs when a sample statistic indicates
assignable, or special, variation is not present when, in fact,
assignable, or special, variation is present.
Control Charts
Control charts, mean and attribute, are useful tools to
visualize how sample statistics relate to control measures, or
parameters.
Typically, control limits are referred to as either an upper
control limit (UCL) or a lower control limit (LCL).
Mean Control Limits
Upper Control Limit (UCL)
Lower Control Limit (LCL)
An upper control limit is an upper bound
above the average of sample means, 𝑥.
A lower control limit is a lower bound below
the average of sample means, 𝑥.
 UCL = 𝑥 + 𝑧𝜎𝑥
 LCL = 𝑥 − 𝑧𝜎𝑥
 where
 where
𝜎𝑥 = 𝜎/ 𝑛, or standard deviation of sample
means
σ = estimated process standard deviation
n = sample size
z = number of standard deviations yielding control
limits
𝑥 = average of sample means
𝜎𝑥 = 𝜎/ 𝑛, or standard deviation of sample
means
σ = estimated process standard deviation
n = sample size
z = number of standard deviations yielding control
limits
𝑥 = average of sample means
P-chart Control Limits
Upper Control Limit (𝑼𝑪𝑳𝒑 )
Lower Control Limit (𝑳𝑪𝑳𝒑 )
An upper control limit is an upper bound above
the average fraction defective in a population, p.
 A lower control limit is a lower bound below the
average fraction defective in a population, p.
 𝑈𝐶𝐿𝑝 = 𝑝 + 𝑧𝜎𝑝
 𝐿𝐶𝐿𝑝 = 𝑝 − 𝑧𝜎𝑝
 where
 where
𝜎𝑝 =
𝑝(1−𝑝)
,
𝑛
or standard deviation of sample
distribution
n = sample size
z = number of standard deviations yielding
control
limits
𝑝 = estimated average proportion of defects in
population, p
𝜎𝑝 =
𝑝(1−𝑝)
,
𝑛
or standard deviation of sample
distribution
n = sample size
z = number of standard deviations yielding control
limits
𝑝 = estimated average proportion of defects in
population, p
C-chart Control Limits
Upper Control Limit (𝑼𝑪𝑳𝒄 )
Lower Control Limit (𝑳𝑪𝑳𝒄 )
An upper control limit is an upper bound above
the average occurrence of defects per unit in a
sample.
 A lower control limit is a lower bound below the
average occurrence of defects per unit in a sample.
𝑈𝐶𝐿𝑐 = 𝑐 + 𝑧 𝑐
 where
n = sample size
z = number of standard deviations yielding
control limits
𝑐 = occurrence of defects per unit in sample
 𝐿𝐶𝐿𝑐 = 𝑐 − 𝑧 𝑐
 where
n = sample size
z = number of standard deviations yielding
control limits
𝑐 = occurrence of defects per unit in sample
Application of Charts
P-Chart (𝐔𝐂𝐋𝐩 & 𝐋𝐂𝐋𝐩 )
C-Chart (𝐔𝐂𝐋𝐜 & 𝐋𝐂𝐋𝐜 )
P-charts are prescribed when:
C-Charts are prescribed when:
 Binary Observations
 Occurrences Per Unit are Counted
 0,1
 Arrivals Per Hour
 Pass/Fail
 Calls Per Hour
 Examples…
 Examples…
Process Capability
Process capability refers to the capability of yielding output
within specified parameters, which is imperative for
organizations producing products or providing services.
Among the aspects of variability to be measured and
evaluated are specifications, control limits and process
variability.
Specifications
Specifications, also referred to as tolerances, indicate a
range of values that individual output values must fall within.
Examples…
Control Limits
Control limits are statistical limits that reflect the extent to
which sample statistics, such as means and ranges, can vary
due to randomness.
Examples…
Process Variability
Process variability represents the natural, or inherent,
variability of a process and is measured via standard
deviation.
Process Capability
Processes may yield output that are within parameters
prescribed by control limits while not adhering to
specifications. In this case, the process may not be capable
of meeting specified specifications.
Determining whether a process is capable of adhering to
specifications, a capability index is computed and evaluated.
Process Capability Index, 𝑪𝒑
Process capability index is computed via:
Process capability index, 𝐶𝑝 =
𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 (𝑠𝑝𝑒𝑐.) 𝑢𝑛𝑖𝑡(𝑠)
𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑢𝑛𝑖𝑡 (𝑠)
or
𝑢𝑝𝑝𝑒𝑟 𝑠𝑝𝑒𝑐. − 𝑙𝑜𝑤𝑒𝑟 𝑠𝑝𝑒𝑐.
6𝜎 𝑜𝑓 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑢𝑛𝑖𝑡(𝑠)
Process Capability Index, 𝑪𝒑𝒌
If the process mean is not perfectly centered between the specification
range, the modified capability index is computed via:
𝐶𝑝𝑘 =
𝑢𝑝𝑝𝑒𝑟 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛 − 𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑚𝑒𝑎𝑛
3𝜎
and
𝐶𝑝𝑘 =
𝑝𝑟𝑜𝑐𝑒𝑠𝑠 𝑚𝑒𝑎𝑛 −𝑙𝑜𝑤𝑒𝑟 𝑠𝑝𝑒𝑐𝑖𝑓𝑖𝑐𝑎𝑡𝑖𝑜𝑛
3𝜎
Process Capability Improvement
Process capability can be improved through a reduction in
process variability, which may be accomplished through
simplification, standardization and automation.
Quality Control
Questions…