STATISTICAL QUALITY CONTROL

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STATISTICAL QUALITY CONTROL

• CHAPTER 8
• BCT2053

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CONTENT

• 8.1 Basic Idea
• 8.2 Control Charts for Variables and Mean
• 8.3 Control Charts for Attributes

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OBJECTIVES

• At the end of this chapter, you should be able to
• Understand the statistical process control using
  control charts
• Construct a variable control chart
• Construct an attribute control chart

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8.1 BASIC IDEA

• Statistical quality control (SQC) is a method of
  visually monitoring manufacturing processes.
• With the use of control charts and collecting few
  but frequent samples, this method can effectively
  detect changes in the process that may affect its
  quality.
• Under the assumption that a manufactured product
  has variation and this variation is affected by
  several process parameters, when SQC is applied
  to "control" each parameter the final result
  trend to be a more controlled product.
• SQC can be very cost efficient, as it usually
  requires collection and charting data already
  available, while "product control"
• requires accepting, rejecting,
  reworking and scrapping
• products that already went through the
  whole process.

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History

• Statistical process control was pioneered by
  Walter A. Shewart and taken up by W. Edwards
  Deming with significant effect by the Americans
  during World War II to improve industrial
  production.
• Deming was also instrumental in introducing SQC
  methods to Japanese industry after that war.
• Shewart created the basis for the control chart
  and the concept of a state of statistical control
  by carefully designed experiments.
• While Dr. Shewart drew from pure mathematical
  statistical theories, he understood data from
  physical processes never produce a "normal
  distribution curve" (a Gaussian distribution,
  also commonly referred to as a "bell curve").
• He discovered that observed variation in
  manufacturing data did not always behave the same
  way as data in nature.
• Dr. Shewart concluded that while every process
  displays variation, some processes display
  controlled variation that is natural to the
  process, while others display uncontrolled
  variation that is not present in the process
  causal system at all times

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Control Chart

• A graphical tool for monitoring the activity of
  an ongoing process
• Sometimes referred as Shewart control charts
• The value of the quality characteristics to be
  monitored is plotted along the vertical axis,
  while the horizontal axis represents the samples
  or subgroups (in order of time) from which the
  quality characteristics is found
• Samples of a certain size (say 4 or 5 items) are
  selected and the quality characteristics is
  calculated based on the number of items in the
  sample.

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Typical Control Chart
Upper control limit
Center Line
Lower control limit
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Typical Control Chart

• Center Line
• Represents the average value of characteristic
  that is being plotted
• Is an indication of where the process is centered
• Upper Control Limit Lower Control Limit
• Used to make decisions regarding the process
• If the points plot within the control limits and
  do not exhibit any identifiable pattern, the
  process is said to be in statistical control.
• If the points plot outside the control limits or
  if an identifiable nonrandom pattern, the process
  is said to be out of statistical control.

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Basic Principal of Control Chart

• The values of the statistic plotted on a control
  chart are assumed to have an approximately normal
  distribution with process mean and
  process standard deviation
• The lower and upper limits are chosen so that the
  probability of the sample points falling between
  them is almost 1 if the process in statistical
  control
• Typical Control limits are placed at 3 sd away
  from the mean of statistic being plotted
• Normal distribution theory states that a sample
  statistic will fall within the limits 99.74 of
  the time if the process is in the control.
  (recall Chebychev theorem when k3)

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Benefit of Using Control Charts

• Serves as a guide to indicate when something is
  possibly wrong with a process such that the
  corrective action is needed
• The pattern of plot may provide diagnostic
  information about plausible causes and hence
  plausible types of remedial actions that may be
  taken
• Used to determine when an exhibited variability
  is normal and inherent such that no corrective
  action is necessary. (when to leave a process
  alone)

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Benefit of Using Control Charts

• If the process in statistical control, one can
  estimate the capability of the process and hence
  its ability to meets customer requirements. This
  will also help product and process design.
• Used as a base for instituting and measuring
  quality improvement. It also can provide useful
  information regarding actions to take for quality
  improvement.

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Types of Control Chart

• Variables Control Charts
• The quality characteristics are variables and
  numerical values can obtained for each
• Examples average length, average diameter,
  average tensile strength, average resistance,
  average service time.
• Attributes Control Charts
• The quality characteristics are the proportion of
  nonconforming items, the number of
  nonconformities in a unit, and the number of
  demerits per unit.

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8.2 Variables Control Charts

• R Chart or S Chart
• Used to control the variability in a process
• R for range
• S Standard deviation
• Chart
• Used to control the process mean

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R Chart

• The values of D3 and D4 depend on the sample size
  (see table)

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S Chart

• The values of B3 and B4 depend on the sample size
  (see table)

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• The values of A2 depend on the sample size (see
  table)

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• The values of A3 depend on the sample size (see
  table)

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Example

• The quality engineer in charge of a salt
  packaging process is concerned about the moisture
  content in packages of salt and want to determine
  whether the process is in statistical control.
• Assume that 5 packages of salt are sampled every
  15 minutes for 8 hours, and that the moisture
  content in package is measured as a percentage of
  total weight

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Example, cont

• Compute the R Chart upper and lower control
  limits and plot the R Chart. Is the process
  variation in control?
• Use to compute the Chart upper and lower
  control limits and plot the Chart. Is the
  process mean in control?
• Compute the S Chart upper and lower control
  limits and plot the S Chart. Is the process
  variation in control?
• Use to compute the Chart upper and lower
  control limits and plot the Chart. Is the
  process mean in control?
• Which is better, the R chart or S chart?

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8.3 Attribute Control Chart

• The p chart
• Used when the quality characteristics being
  measured on each unit has only 2 possible values
  (usually defective not defective).
• The c chart
• Used when the quality characteristics is a count
  of the number of defects or flaws in a given unit.

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The p chart

• p is the probability that a given unit is
  defective (proportions). If the process is in
  control, this probability is constant over time

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Example

• In the production of silicon wafers, 30 lots of
  size 500 are sampled and the proportion of
  defective wafers is calculated for each sample.
• Compute the upper and lower control limits for
  the p chart.
• Plot the chart.
• Does the process appear to be in control?

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The c chart

• The number of defects follow a Poisson
  Distribution where is the total number of
  flaws per unit
• If the process is in control, the value of
  is constant over time

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Example

• Rolls of sheets aluminum, used to manufacture
  cans, are examines for surface flaws. The table
  presents the number of flaws in 40 samples of 100
  m square each.
• Compute the upper and lower control limit for the
  c chart.
• Plot the c chart.
• Does the process appear to be in control?

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Summary

• The Shewart control charts are the most powerful
  of the commonly used tools for statistical
  quality control.
• When common causes are the only causes of
  variation, the process is said to be in state of
  statistical control or in control.

Thank You