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Control Charts

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Control Charts Chapter 5 Introduction In industrial processes, goals are to: - . We need to _____ an engineering process to ensure these goals are met. – PowerPoint PPT presentation

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Title: Control Charts


1
Control Charts
  • Chapter 5

2
Introduction
  • In industrial processes, goals are to
  • - .
  • We need to ___________ an engineering process to
    ensure these goals are met.
  • Examples
  • - monitor process for filling 16 oz cans
  • of pepsi
  • - maintain correct outside diameter of
  • ball point pens

3
Example
  • A 10-oz packaging line for a popular cereal has
    a target net weight of 10.5oz. Historically,
    process standard deviation is 0.1oz. The company
    monitors net weights by a random sample of 5
    boxes of cereal each hour. The mean net weights
    for 30 such subgroups is

4
Data
  • 10.56, 10.56, 10.46,10.46, 10.49, 10.52,
  • 10.53,10.47, 10.44, 10.54, 10.49, 10.52,
  • 10.53,10.50, 10.50, 10.48, 10.55, 10.68,
  • 10.67,10.62, 10.45, 10.47, 10.40, 10.43,
  • 10.47,10.50, 10.38, 10.43, 10.50, 10.51
  • The target net mean weight is µ010.5oz.

5
  • Let yi the weight of the ith box of cereal
    (i1,,5) at hour t. (t1,,30).
  • Let µ(t) be the process mean (the true mean
    weight at this time).
  • A model we can use is
  • ei is the random error associated with this box
    of cereal.
  • We assume here that the process variance s2 is
    constant.

6
Factors that may influence process
  • .
  • .
  • .
  • .
  • These factors change over time, which
  • will influence the true mean weight of
  • the cereal boxes.

7
Typical Drift in a Process Mean over time
  • µ(t)

µ0
t
8
Dealing with Process Changes
  • Do
  • Inspect ________ item and remove the unacceptable
    items. Very expensive, not always 100
    effective.
  • Produce batches of products, use statistics to
    determine if entire batch unacceptable.
  • Constantly monitor true mean weight, and adjust
    process whenever it begins to drift. Can use
    control charts here.
  • Create a process that cannot produce an
    unacceptable product. What we strive for.

9
Control Charts
  • Are used to
  • A random sample (a subgroup) is taken from
    process on a
  • As soon as data collected

10
A control chart for a process mean
  • Is equivalent to carrying out a hypothesis test
    at each time point. In cereal example
  • H0
  • H1
  • If we reject the null hypothesis at a specified
    level of significance (e.g. 5), we conclude the
    true mean weight of cereal boxes has moved away
    from the target value of 10.5 oz at that time
    point.

11
Control Limits of an . Chart
  • Upper Control Limit UCL
  • Lower Control Limit LCL

12
Cereal Example X-bar Chart
Out of control
UCL10.63
In control
µ0 10.5
In control
LCL10.37
Out of control
time
13
.. Chart of Cereal Box Weights
14
Conclusions for Cereal Example
  • The control chart suggests the process is
  • After this it is within control limits, but
    appears to be a downward trend.
  • Process

15
The np control chart
  • Instead of monitoring the mean of the process,
    for example, average weight of cereal packages,
    we may be interested in the
  • Here, we also use a control chart, but a slightly
    different one.

16
Brick Example
  • A study looked at the number of non-conforming
    bricks from a manufacturing process. It is known
    from historic data that the target proportion of
    non-conforming bricks is 0.06625. Process
    monitored by taking a random sample of 200 bricks
    every day for 16 days.
  • Each brick was classified as either
  • - conforming
  • - non-conforming.

17
  • Let p0 be the target proportion of nonconforming
    bricks.
  • Let yi be the number of nonconforming bricks on
    day i.
  • Expected value Eyinp0
  • Variance Varyinp0(1-p0).
  • As process stays in control, with same sample
    size each day, the expected value and variance
    stay constant.

18
An np control chart
  • Examines the
  • Is equivalent to carrying out a hypothesis test
    at each time point.
  • n is the number of items collected

19
In Brick Example
  • Our true hypotheses are
  • H0
  • H1
  • Our control limits take the form

20
In Brick Example
  • The control limits are

21
Brick Example
  • Check data and Figure 5.22 on page 330 in text.

22
Class Exercise
  • Airplanes approaching the runway for landing are
    required to stay within a certain distance (left
    and right) of the runway. Deviations are called
    exceedences. Each day, one airline randomly
    selects 200 flights and records the number in
    exceedence. The following data presents the
    number of flights in exceedence on each of 30
    days in a row.

23
  • 16 25 23 16 15 23 24 15 23 13
  • 21 19 23 28 30 19 18 15 18 10
  • 24 22 20 27 21 26 30 25 26 30
  • It is known historically that the
  • exceedence rate is 0.0985 for this
  • airline. Calculate the appropriate control
  • limits and plot the control chart.

24
  • Here n200

25
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