Handout MK. Pengawasan Mutu 2011/2012
n Statistical studies can be classified into two
types: enumerative and analytic.
n An analytic study considers the population in a
dynamic sense, and its objective is to predict
or improve a process or product in the future.
n In the quality management field, statistical
methods can be used for analyzing numerical
data focusing on results.
n “One picture is worth a thousand words”.
The primary goals of SPC
n Minimize production costs.
n Attain a consistency of products and services that
will meet production specifications and customer
n Create opportunities for all members of the
organization to contribute to quality improvement.
n Help both management and employees make
economically sound decision about actions affecting
Statistical tools used in QC
n Seven basic tools that have been used
successfully in food industries for decades:
§ Flow chart
§ Cause and effect diagram
§ Control chart
§ Check sheet
§ Pareto chart
§ Scatter diagram
n In a flowchart, the description
n A series of blocks with each of each process is written
block representing one
major process, that inside the blocks. Any other
describes an operation that significant information is
is studied or is used to plan usually written outside
stages of a project. blocks. Each block is
connected with an arrow to
n Flowcharts provide an show where that process
excellent form of
documentation for a leads.
process operation, and
often are useful when
examining how various
steps in an operation work
n A flowchart is important project development and
n It visually records the steps, decisions, and actions of
any manufacturing or service operation and defines
the system, its key points, activities and role
n A histogram is used to graphically summarize and
display the distribution of a process dataset.
n It can be constructed by segmenting the range of the
data into equal-sized bins (segments, groups, or
n The vertical axis of the histogram is the frequency
(the number of counts for each bin), and the
horizontal axis is labeled with the range of the
n The number of data points in each bin is determined
and the histogram constructed. The user defines the
Cause and Effect Diagram
n A problem is n A similar diagram can
systematically tracked be used to
back to possible causes. systematically search
n The diagram organizes for solutions to a
the search for the root problem.
cause of a problem.
Cause and Effect Diagram
n This diagram is created by Kaoru Ishikawa, one of the
founding fathers of modern management à Ishikawa
diagram/ fishbone diagram.
n Causes are arranged according to their level of importance or
detail, resulting in a depiction of relationships and hierarchy
n Cause-and-effect diagrams are typically constructed through
n The diagram are frequently arranged into the four most
common major categories:
– Manpower, methods, materials, and machinery (for
– Equipment, policies, procedures, and people (for
administration and planning)
Cause and Effect Diagram
Example Cause-Effect Diagram
n It is similar to a line graph
except that the data point
are plotted without a
connecting line drawn
n Scatter charts are suitable
for showing how data
points compare to each
n At least 2 measured objects
are needed for the query
(one for x-axis and one for y
n Scatter diagrams are used to study possible relationships
between 2 variables. Although these diagrams can’t prove
that one variable causes the other, they do indicate the
existence of a relationship. More than one measure object
can be used for the y-axis as long as the objects are of the
same type and scale.
n The purpose of scatter diagram is to display what happens to
one variable when the other variable is changed. The diagram
is to test the theory that the two variables are related.
n The slope of the diagram indicates the type of relationship
n The Pareto Principle is used n Pareto charts are used to
by business and industry to decide what steps need to
work to continually improve be taken for quality
n Quality improvement
involves tackling one issue
at a time. By addressing the
ones causing the most
can be made & monitored
for continuous progress.
n The number of occurrences or the costs of occurrences of
specific problems are charted on a bar graph. The largest bars
indicate the major problems and are used to determine the
priorities for problem solving.
n A Pareto chart graphically summarizes and displays the
relative importance of the differences between groups of
n A Pareto chart can be constructed by segmenting the range of
the data into groups.
n The number of data points in each group is determined and
the Pareto chart constructed; however, unlike the bar chart,
the Pareto chart is ordered in descending frequency
n A broken line graph proportion of defective
illustrates how a process pieces changes over time.
behaves over time.
n Samples are periodically
taken, checked, or
measured, and the results
are plotted on the chart.
n The charts can show how
the specific measurement
changes, how the variation
in measurement changes,
or how the
n A control chart is a graphic display of the actual
quality performance judged against a reference
frame showing a central line representing the
average quality value and upper and lower lines
called the upper control limit (UCL) and lower
control limit (LCL).
n Control charts are used to:
• find sources of special-cause variation (variation
that is caused by specific, fixable occurrences)
• measure the extent of common-cause variation
(variation that inherent in the process)
• maintain control of a process that is operating
n Types of control charts:
ØControl variable charts: X-bar and R charts
ØAttribute charts: p, np, c, and u charts
X-Bar and R-Charts
n The most commonly used of n They can be used for
the control charts and the controlling every step of
most valuable. production process, for the
n They are ideal tools to acceptance/ rejection of
improve product quality lots, and for early detection
and process control and of equipment or process
help to drastically reduce failure.
scrap and rework while
assuring the production of
only satisfactory products.
X-Bar and R Charts
n The X-bar and the R charts are used for control variables that
are expresses in the discrete numbers such as inches, pounds,
pH units, angstrom, percent solids, or degree of temperature
and so on.
n The R chart is developed from the ranges of each subgroup
data, which are calculated by subtracting the maximum and
the minimum value in each subgroup.
n Since the R chart indicates that the process variability is in
control, the X-bar chart can then be constructed. The center
line is mean of the sample means.
Example of X-Bar and R Charts
n The chart of a X-bar and R should not be used
with samples ≥10 or when the sample size is
n They are also used for control of defect analysis.
n They are particularly useful for controlling raw
material and finished product quality and for
analyzing quality comments in consumer letters.
n Attributes control charts are used when
measurements are too difficult to take, when
measurements do not apply to the situation (such as
visual checks for flaws), or when they are too costly
to take because of time lost.
n p chart
• It is the most commonly used attributes chart.
• The value p is the fraction, or percentage, of the number
items checked that are defective (unacceptable).
• Large samples of 50 or more are needed.
n np chart
• The np chart is sometimes used instead of the p chart
because it is easier; np is simply the number rather than
the fraction, of defective items in the sample.
• The p and np charts differ by that constant divisor, so they
do the same job with respect to control, process analysis,
n c chart
The c chart tracks the number of defects in constant size
units. There may be a single type of defect or different
types, but c chart tracks the total number of defects in
n u chart
• When samples of different size are taken, u is the
average number of defects per unit.
• The u chart is quite similar to the c hart in function.
Example p chart:
Example np chart
Example c chart
n Hubbard, M.R. 2003. Statistical Quality Control for the Food
Industry, 3rd Ed. Kluwer Academic/ Plenum Publisher. New York.
n Vosconcellos, A. 2004. Quality Assurance For The Food Industry.
CRC Press. Boca Raton.