chapter 10: statistical quality control Flashcards
Statistical quality control
uses statistical techniques and sampling to monitor and test the quality of goods and services
provides an economical way to evaluate the quality of products and meet the expectations of the customers
The part of statistical quality control that occurs during production
statistical process control
phases of statistical quality control in a company
from least progressive, to most progressive
- Inspection
before and after production
–> Acceptance sampling
- Corrective action during production
–> Statistical process
control
- Quality built into the
process
–> Continuous improvement and Six Sigma
locations of use of acceptance sampling and statistical process control within production
inputs: acceptance sampling
transformation: statistical process control
outputs: acceptance sampling
Inspection
an appraisal activity that compares the quality of a good or service to a standard
Statistical Process Control Planning Steps
- Define the quality characteristics important to customers, and how each is measured
- a. for each characteristic, determine a quality control point
b. for each characteristic, plan how inspection is to be done, how much to inspect, and whether centralized or on-site
c. for each characteristic, plan the corrective action
Defining the Quality Characteristics (step 1)
define, in sufficient detail, what is to be controlled
Different characteristics may require different approaches for control purposes
–> Only those characteristics that can be measured are candidates for control
the only characteristics candidates for control
those hat can be measured
Determine a Quality Control Point (step 2. a.)
what are the typical inspection points?
At the beginning of the process
At the end of the process
At the operation where a characteristic of interest to customers is first determined
when is customer satisfaction and company’s image most at stake?
At the end of the process
How Inspection Is to Be Done (step 2. b.)
usually technical and needs engineering knowledge.
How Much to-Inspect (step 2. c.)
what is the range of inspection?
can range from no inspection whatsoever to inspection of each unit
why do low cost, high-volume items such as paper clips, nails, and pencils often require little inspection?
(1) the cost associated with passing defective items is quite low
(2) the processes that produce these items are usually highly reliable
–> defects are rare
do items that have large costs associated with passing defective products often require more intensive inspection?
yeee
why is the goal in inspection not catch every single defect?
what is the goal then?
because it would be mostly economically inefficient to do so
the goal is the see where the equilibrium would be between comparing the total cost of inspection and the cost of passing defectives
–> the equilibrium, on a graph, shows the total minimal cost, and the amount of inspection
operations with a high proportion of human involvement necessitate more or less inspection than mechanical operations?
why’
more inspection than mechanical operations
because the latter tend to be more reliable
statistical process control (SPC)
concerns itself with statistical evaluation of the product in the production process
the operator takes periodic samples from the process and compares them with predetermined limits
The main task in SPC is to distinguish assignable from random variation
random variation
common variability of the process (Deming)
–> if we were to correct, the result would be negligible
natural variation in the output of a process, created by countless minor factors
assignable variation
special variation (Deming)
the main sources of assignable variation can usually be identified (assigned to a specific cause) and eliminated
The variability of a sample statistic is described by what?
its sampling distribution
the central limit theorem
states that as the sample size increases, the distribution of sample averages approaches a Normal distribution regardless of the shape of the sampled population
The larger the sample size, the narrower the sampling distribution
the likelihood that a sample statistic is close to the true value in the population is higher for large samples or for small samples?
why?
large samples
central limit theorem
limits selected within which most values of a sample statistic should fall if its variations are random
serves in distinguishing between random and assignable variation of a sampling statistic
typical limits are +2 standard deviations or +3 standard deviations
who developed the control chart
Walter Shewhart
control chart
a time-ordered plot of a sample statistic, with limits
used to distinguish between random and assignable variation
it has upper and lower limits, called control limits
purpose of a control chart
to monitor process output to see if it is random
A necessary (but not sufficient) condition for a process to be deemed “in control,” or stable using a control chart
all the data points have to fall between the upper and lower control limits
which proportion of the values will fall within + or - 3 standard deviations of the mean of the distribution?
99.7%
control limits
The dividing lines between random and assignable deviations from the mean of the distribution
the two control limits in control charts
the upper control limit (UCL) which is the largest acceptable value
the lower control limit (LCL) which is the lowest acceptable value
difference between control limits and specification limits
Control limits are based on the characteristic of the process
specification limits are based on the desired characteristic of the product
which proportion of the values will fall within + or - 2 standard deviations of the mean of the distribution?
95.5%
Type I error
not finding sample values that fall that outside of the + or - 2 standard deviations
concluding that the process has not shifted, when it has
downside of using wider limits (for ex, using + or - 3 standard deviation instead of + or - 2 standard deviation)?
make it more difficult to detect assignable variations (i.e., a shift in the process) 扩they are present
Type 2 error
not finding sample values that fall that outside of the + or - 3 standard deviations
concluding that the process has not shifted, when it has
The steps taken to design control charts
- Determine a sample size n (usually between 2 and 20)
- Obtain 20 to 25 samples of size n
–> Compute the appropriate sample statistic for each sample (e.g., sample mean)
- Establish preliminary control limits using appropriate formulas and graph them
- Plot the sample statistic values on the control chart, and note whether any points fall outside the control limits
- If you find no points outside control limits, assume that there is no assignable cause and therefore the process is stable and in control
–> if there are points outside, investigate and correct assignable causes of variation; then repeat the process from Step 2 on
the larger the n, the larger or smaller the probability of Type II error?
the smaller
The sample mean (x_) control chart
used to monitor the process mean
control chart for the sample mean
how do we find the centre line used in a sample mean (x_) control chart?
estimated by taking a few samples, computing their mean, and then averaging these means
called the grand mean
calculating the control limits using the standard deviation of the process, σ
Upper Control Limit (UCLx_) = x_ + z · (σ of x_ / √n)
Lower Control Limit (LCLx_) = x_ - z · (σ of x_ / √n)
σ of x_: Standard deviation of the sampling distribution of the sample mean
σ: Process standard deviation
n: sample size
z: Standard Normal deviate (usually z = 3)
x_: Average of sample means = Grand mean
A second approach to calculating the control limits
to use the sample range (i.e., Maximum value - Minimum value in the sample)
formulas to find the limits using the sample ranges
UCL = x_ + A2R_
LCL: x_ - A2R_
A2: get from the table
R_: average of sample ranges of a few samples
The sample range (R) control chart
used to monitor process dispersion or spread
how to find the limits using the sample range (R) control chart
UCLR = D4R_
LCLR = D3R_
D3 and D4 are taken from the table
individual unit (X) control chart
Control chart for individual unit used to monitor single observations (n = 1)
finding the limits for the individual unit (X) control chart
UCLx = X_ + zσ
LCLx = X_ - zσ
X_: the mean of a few individual observations (that estimates the process mean)
z: the standard Normal deviate
σ: the process standard deviation
moving range (MR) control chart
used to calculate the differences between consecutive observations in single unit samples
we want to control the dispersion or spread
finding the limits for the moving range (MR) control chart
UCLR = D4R_
LCLR = D3R_
D3 and D4 are taken from the table
R_: the average of the moving ranges
when are control charts for attributes used?
when the process characteristic is counted rather than measured
two types of attribute control charts
one for the fraction of defective items in a sample (p-chart)
one for the number of defects per unit (c-chart)
when is a p-chart appropriate?
when the data consist of two categories of items
When the data consist of multiple samples of n observations each (e.g., 15 samples pf n = 20 each)
what is a p-chart?
the control chart for the sample proportion of defectives
used to monitor the proportion of defective items generated by the process
when is a c-chart appropriate?
When only the number of occurrences per unit of measure can be counted
–> non-occurrences cannot be counted
When the goal is to control the number of occurrences of defects per unit product
The centre line on a p-chart
the average proportion of defectives in the population, p
The standard deviation of the p-chart
σp = (sqrt(p · (1 - p)) / n
control limits for the p chart
UCLp = p + z · σp
LCLp = p - z · σp
When the goal is to control the number of occurrences of defects per unit product, which chart do we use?
the c-chart
what is the distribution for the c-chart
the poisson distribution
the limits using the c-chart
UCL = c + z · (c)^(1/2)
LCL = c - z · (c)^(1/2)
c: mean number of defects per unit product
(c) ^(1/2): the standard deviation
what must we do after the stability of a process has been established?
it is necessary to determine if the process is capable of producing output that is within an acceptable range
–> The capability of a process
what are the three focal points we need for process capability
Design specification
control limits
Process variability
Design specification
a range of values into which a product must fall in order to be acceptable
Process variability
the actual variability in a process for a product
process capability
he ability of a process to meet the design specification
capability analysis
measuring the process capability
determines whether the process output falls within the design specification
when is a process said to be capable
when the process output falls within the design specification
process capability ratio
Cp = (design specification width) / process width
= (upper design specification - lower design specification ) / 6σ
ratio must be at least 1 for the process to be gyu
what measure do we use when the process is not centered between design specification limits, or if there is no design specification limit on one side
Cpk
Cpk formula
Cpk = (Upper design specification - Process mean) / 3σ
and
(Process mean - lower design specification) / 3σ
the smaller of the two ratios is the the Cpk
the Cpk has to be bigger than 1
Six Sigma quality
refers to the goal of achieving process variability so small that the half width of design specification equals six standard deviations of the process
the difference in the objective between Six Sigma quality and Continuous improvement
Six Sigma quality: Product and process perfection
Continuous improvement: Product and process improvement
the difference in the tools used between Six Sigma quality and Continuous improvement
Six Sigma quality: Statistical
Continuous improvement: Simple data analysis
the difference in the methodology used between Six Sigma quality and Continuous improvement
Six Sigma quality: Define, measure, analyze, improve, control (DMAIC)
Continuous improvement: Plan, do, study, act (PDSA)
the difference in the team leaders between Six Sigma quality and Continuous improvement
Six Sigma quality: Black belt
Continuous improvement: Champion
the difference in the training between Six Sigma quality and Continuous improvement
Six Sigma quality: long/formal
Continuous improvement: short/informal
the difference in the culture change between Six Sigma quality and Continuous improvement
Six Sigma quality: usually enforced
Continuous improvement: sometimes enforced
the difference in the project time frame between Six Sigma quality and Continuous improvement
Six Sigma quality: moths/years
Continuous improvement: days/weeks
Design of experiments
involves performing experiments by changing levels of factors to measure their influence on output and identifying best levels for each factor
