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STATISTICAL QUALITY CONTROL

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Construct an attribute control chart. 8.1 BASIC IDEA ... Attributes Control Charts ... If the process is in control, this probability is constant over time. Example ... – PowerPoint PPT presentation

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Title: STATISTICAL QUALITY CONTROL


1
STATISTICAL QUALITY CONTROL
  • CHAPTER 8
  • BCT2053

2
CONTENT
  • 8.1 Basic Idea
  • 8.2 Control Charts for Variables and Mean
  • 8.3 Control Charts for Attributes

3
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

4
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.

5
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

6
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.

7
Typical Control Chart
Upper control limit
Center Line
Lower control limit
8
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.

9
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)

10
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)

11
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.

12
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.

13
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

14
R Chart
  • The values of D3 and D4 depend on the sample size
    (see table)

15
S Chart
  • The values of B3 and B4 depend on the sample size
    (see table)

16
  • The values of A2 depend on the sample size (see
    table)

17
  • The values of A3 depend on the sample size (see
    table)

18
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

19
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?

20
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.

21
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

22
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?

23
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

24
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?

25
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.

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