STATISTICAL STATISTICAL PROCESS CONTROLPROCESS CONTROL

Handout MK. Pengawasan Mutu 2011/2012

SPCSPC Statistical studies can be classified into two

types: enumerative and analytic. 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.

In the quality management field, statistical In the quality management field, statistical methods can be used for analyzing numerical methods can be used for analyzing numerical data focusing on results.data focusing on results.

““One picture is worth a thousand words”.One picture is worth a thousand words”.

The primary goals of SPCThe primary goals of SPC

Minimize production costs.Minimize production costs. Attain a consistency of products and services that Attain a consistency of products and services that

will meet production specifications and customer will meet production specifications and customer expectations.expectations.

Create opportunities for all members of the Create opportunities for all members of the organization to contribute to quality improvement.organization to contribute to quality improvement.

Help both management and employees make Help both management and employees make economically sound decision about actions affecting economically sound decision about actions affecting the process.the process.

Statistical tools used in QC applicationsStatistical tools used in QC applications

Seven basic tools that have been used Seven basic tools that have been used successfully in food industries for decades:successfully in food industries for decades: Flow chartFlow chart Cause and effect diagramCause and effect diagram Control chartControl chart HistogramHistogram Check sheetCheck sheet Pareto chartPareto chart Scatter diagramScatter diagram

Flow ChartFlow Chart A series of blocks with each A series of blocks with each

block representing one block representing one major process, that major process, that describes an operation that describes an operation that is studied or is used to plan is studied or is used to plan stages of a project.stages of a project.

Flowcharts provide an Flowcharts provide an excellent form of excellent form of documentation for a documentation for a process operation, and process operation, and often are useful when often are useful when examining how various examining how various steps in an operation work steps in an operation work together.together.

In a flowchart, the description In a flowchart, the description of each process is written of each process is written inside the blocks. Any other inside the blocks. Any other significant information is significant information is usually written outside usually written outside blocks. Each block is blocks. Each block is connected with an arrow to connected with an arrow to show where that process show where that process leads.leads.

Flow ChartFlow Chart

A flowchart is important project development and A flowchart is important project development and documentation tool.documentation tool.

It visually records the steps, decisions, and actions of It visually records the steps, decisions, and actions of any manufacturing or service operation and defines any manufacturing or service operation and defines the system, its key points, activities and role the system, its key points, activities and role performances.performances.

HistogramHistogram A histogram is used to graphically summarize and

display the distribution of a process dataset. It can be constructed by segmenting the range of the

data into equal-sized bins (segments, groups, or classes).

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 response variable.

The number of data points in each bin is determined and the histogram constructed. The user defines the bin size.

HistogramHistogram

Cause and Effect DiagramCause and Effect Diagram

A problem is A problem is systematically tracked systematically tracked back to possible causes. back to possible causes.

The diagram organizes The diagram organizes the search for the root the search for the root cause of a problem.cause of a problem.

A similar diagram can A similar diagram can be used to be used to systematically search systematically search for solutions to a for solutions to a problem.problem.

This diagram is created by Kaoru Ishikawa, one of the founding fathers of modern management Ishikawa diagram/ fishbone diagram.

Causes are arranged according to their level of importance or detail, resulting in a depiction of relationships and hierarchy of events.

Cause-and-effect diagrams are typically constructed through brainstorming techniques.

The diagram are frequently arranged into the four most common major categories:– Manpower, methods, materials, and machinery (for

manufacturing)– Equipment, policies, procedures, and people (for administration

and planning)

Cause and Effect DiagramCause and Effect Diagram

Cause and Effect DiagramCause and Effect Diagram

Example Cause-Effect DiagramExample Cause-Effect Diagram

Scatter DiagramScatter Diagram It is similar to a line graph It is similar to a line graph

except that the data point except that the data point are plotted without a are plotted without a connecting line drawn connecting line drawn between them.between them.

Scatter charts are suitable Scatter charts are suitable for showing how data for showing how data points compare to each points compare to each other.other.

At least 2 measured objects At least 2 measured objects are needed for the query are needed for the query (one for x-axis and one for (one for x-axis and one for y-axis)y-axis)

Scatter DiagramScatter Diagram Scatter diagrams are used to study possible relationships Scatter diagrams are used to study possible relationships

between 2 variables. Although these diagrams can’t prove that between 2 variables. Although these diagrams can’t prove that one variable causes the other, they do indicate the existence of one variable causes the other, they do indicate the existence of a relationship. More than one measure object can be used for 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.the y-axis as long as the objects are of the same type and scale.

The purpose of scatter diagram is to display what happens to The purpose of scatter diagram is to display what happens to one variable when the other variable is changed. The diagram is one variable when the other variable is changed. The diagram is to test the theory that the two variables are related.to test the theory that the two variables are related.

The slope of the diagram indicates the type of relationship that The slope of the diagram indicates the type of relationship that exist.exist.

Pareto ChartsPareto Charts The Pareto Principle is used The Pareto Principle is used

by business and industry to by business and industry to work to continually improve work to continually improve quality.quality.

Quality improvement Quality improvement involves tackling one issue involves tackling one issue at a time. By addressing the at a time. By addressing the ones causing the most ones causing the most difficulty, improvements difficulty, improvements can be made & monitored can be made & monitored for continuous progress.for continuous progress.

Pareto charts are used to Pareto charts are used to decide what steps need to decide what steps need to be taken for quality be taken for quality improvement.improvement.

Pareto ChartsPareto Charts The number of occurrences or the costs of occurrences of The number of occurrences or the costs of occurrences of

specific problems are charted on a bar graph. The largest bars specific problems are charted on a bar graph. The largest bars indicate the major problems and are used to determine the indicate the major problems and are used to determine the priorities for problem solving.priorities for problem solving.

A Pareto chart graphically summarizes and displays the relative importance of the differences between groups of data.

A Pareto chart can be constructed by segmenting the range of the data into groups.

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 magnitude.

Control ChartsControl Charts A broken line graph A broken line graph

illustrates how a process illustrates how a process behaves over time.behaves over time.

Samples are periodically Samples are periodically taken, checked, or taken, checked, or measured, and the results measured, and the results are plotted on the chart.are plotted on the chart.

The charts can show how The charts can show how the specific measurement the specific measurement changes, how the variation changes, how the variation in measurement changes, in measurement changes, or how the or how the

proportion of defective proportion of defective pieces changes over time. pieces changes over time.

Control ChartsControl Charts

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).

Control ChartsControl Charts

Control charts are used to:Control charts are used to:• find sources of special-cause variation (variation find sources of special-cause variation (variation

that is caused by specific, fixable occurrences)that is caused by specific, fixable occurrences)• measure the extent of common-cause variation measure the extent of common-cause variation

(variation that inherent in the process)(variation that inherent in the process)• maintain control of a process that is operating maintain control of a process that is operating

effectively.effectively.

Control ChartsControl Charts

Types of control charts:Types of control charts:Control variable charts: X-bar and R chartsControl variable charts: X-bar and R chartsAttribute charts: Attribute charts: pp, , npnp, , cc, and , and uu charts charts

X-Bar and R-ChartsX-Bar and R-Charts The most commonly used of The most commonly used of

the control charts and the the control charts and the most valuable.most valuable.

They are ideal tools to They are ideal tools to improve product quality improve product quality and process control and and process control and help to drastically reduce help to drastically reduce scrap and rework while scrap and rework while assuring the production of assuring the production of only satisfactory products.only satisfactory products.

They can be used for They can be used for controlling every step of controlling every step of production process, for the production process, for the acceptance/ rejection of acceptance/ rejection of lots, and for early detection lots, and for early detection of equipment or process of equipment or process failure.failure.

X-Bar and R ChartsX-Bar and R Charts The X-bar and the R charts are used for control variables that The X-bar and the R charts are used for control variables that

are expresses in the discrete numbers such as inches, pounds, are expresses in the discrete numbers such as inches, pounds, pH units, angstrom, percent solids, or degree of temperature pH units, angstrom, percent solids, or degree of temperature and so on.and so on.

The R chart is developed from the ranges of each subgroup The R chart is developed from the ranges of each subgroup data, which are calculated by subtracting the maximum and data, which are calculated by subtracting the maximum and the minimum value in each subgroup.the minimum value in each subgroup.

Since the R chart indicates that the process variability is in Since the R chart indicates that the process variability is in control, the X-bar chart can then be constructed. The center control, the X-bar chart can then be constructed. The center line is mean of the sample means.line is mean of the sample means.

Example of X-Bar and R ChartsExample of X-Bar and R Charts

The chart of a X-bar and R should not be used with samples ≥10 or when the sample size is not constant.

Attribute ChartsAttribute Charts

They are also used for control of defect analysis.They are also used for control of defect analysis. They are particularly useful for controlling raw They are particularly useful for controlling raw

material and finished product quality and for material and finished product quality and for analyzing quality comments in consumer letters.analyzing quality comments in consumer letters.

Attributes control charts are used when Attributes control charts are used when measurements are too difficult to take, when measurements are too difficult to take, when measurements do not apply to the situation (such as measurements do not apply to the situation (such as visual checks for flaws), or when they are too costly visual checks for flaws), or when they are too costly to take because of time lost.to take because of time lost.

Attribute ChartsAttribute Charts p p chartchart

• It is the most commonly used attributes chart. It is the most commonly used attributes chart. • The value The value pp is the fraction, or percentage, of the number is the fraction, or percentage, of the number

items checked that are defective (unacceptable). items checked that are defective (unacceptable). • Large samples of 50 or more are needed.Large samples of 50 or more are needed.

npnp chart chart • The The npnp chart is sometimes used instead of the chart is sometimes used instead of the pp chart chart

because it is easier; because it is easier; npnp is simply the number rather than the is simply the number rather than the fraction, of defective items in the sample.fraction, of defective items in the sample.

• The p and The p and npnp charts differ by that constant divisor, so they do charts differ by that constant divisor, so they do the same job with respect to control, process analysis, etc.the same job with respect to control, process analysis, etc.

Attribute ChartsAttribute Charts cc chart chart

The The cc chart tracks the number of defects in constant size chart tracks the number of defects in constant size units. There may be a single type of defect or different units. There may be a single type of defect or different types, but types, but cc chart tracks the total number of defects in chart tracks the total number of defects in each unit.each unit.

uu chart chart• When samples of different size are taken, When samples of different size are taken, uu is the is the

average number of defects per unit.average number of defects per unit.• The The uu chart is quite similar to the chart is quite similar to the cc hart in function. hart in function.

Example Example pp chart: chart:

Example Example npnp chart chart

Example Example cc chart chart

ReferencesReferences Hubbard, M.R. 2003. Statistical Quality Control for the Food Hubbard, M.R. 2003. Statistical Quality Control for the Food

Industry, 3Industry, 3rdrd Ed. Kluwer Academic/ Plenum Publisher. New Ed. Kluwer Academic/ Plenum Publisher. New York.York.

Vosconcellos, A. 2004. Quality Assurance For The Food Vosconcellos, A. 2004. Quality Assurance For The Food Industry. CRC Press. Boca Raton.Industry. CRC Press. Boca Raton.