Statistical Applications in Quality and Productivity Management

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Statistical Applications in Quality and
Productivity Management

• Sections 1 8. Skip 5.

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Introductory Notes

• Quality is an important concept for effective
  competition in our global economy.
• Quality refers to both goods and services (good
  examples on page 752).
• Some tools control charts, Pareto diagrams, and
  histograms (and understanding of random
  variables).

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18.1 Total Quality Management (TQM)

• Global Marketplace
• USA companies have been interested in quality
  since the middle to late 1950s.
• The systematic approach to management that
  emphasizes quality and continuous improvement of
  products and services is called Total Quality
  Management. See page 753.

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Demings 14 Points A Theory of Management

• Japan as a model.
• Shewhart-Deming Cycle Figure 18.1

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18.2 Six Sigma Management

• Quality improvement from Motorola 1980s.
• Create processes that result in no more than 3.4
  defects per million.
• Ddefine
• Mmeasure (the CTQ characteristics)
• Aanalyze (why defects occur)
• Iimprove (often with experiments)
• CControl (maintain benefits)

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18.3 The Theory of Control Charts

• Control chart shows the plot of data over time.
• The data being plotted is related to quality.
• The control chart gives insight into variability.
• Use the control chart to improve the process.
• Different types of data have different types of
  control chart.

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Variation

• To separate the special (assignable) causes of
  variation from chance (common causes).
• Special causes of variation are correctable
  without changing the system.
• Reducing variation from common causes requires
  that the system be changed (by management).

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Control Limits

• Typically calculate /- 3 standard deviations of
  the measure of interest (mu, proportion, range,
  etc.).
• Upper Control Limit (UCL) process average plus
  3 standard deviations.
• Lower Control Limit (LCL) process average minus
  3 standard deviations.
• A process that produces data outside of the
  control lines is said to be out of control.

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Out of Control

• First thing identify sources of variation.
• Hopefully we can find the assignable cause(s).
• Figure 18.3, page 757
• Panel A stablein control
• Panel B special cause detected in 2 places
• Panel C not in control, in a trend
• Define Trend, page 757.

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In Control--Stable

• Only common cause variation.
• Is the common cause variation small enough to
  satisfy the buyers of the product?
• Yes monitor process.
• No change process.

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18-4 Control Chart for the Proportion of
Nonconforming ItemsThe p Chart

• p chart is an attribute chart shows the
  results of classifying sample observations as
  conforming or nonconforming.
• The p chart shows the results, i.e. the
  proportion of nonconforming items in a sample.

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Theory

• p chart is based on binomial distribution.
• Use formulae 18.2 and 18.3 to calculate the upper
  and lower control limits

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Mechanics

• Negative values of LCL mean that there is no LCL.
• Subgroup means number of days that samples were
  taken.
• The formulas work out nicer if the sample size is
  the same for each subgroup as is demonstrated in
  Table 18.1.
• PHStat and Minitab will produce control charts.

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Example 18.1

• Making sponges.
• data k32 (the proportion was calculated 32
  times).
• The sample sizes were different for each sample.
• Figure 18.6 and 18.7
• One instance of special cause variation.
• Minitab calculates new control limits for each
  day.

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18.5 The Red Bead Experiment Understanding
Process Variability

• This experiment demonstrates some aspects of
  production and quality control.
• In the experiment the workers must produce
  white beads. A red bead is nonconforming.
• The inspectors count the red beads.
• Production input is 80/20 white to red ratio.
• Production tools are limited.

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Lessons learned from the Experiment

• Processes have variation.
• Worker performance is primarily determined by the
  system.
• Only managers can change the system.
• Some workers will be above average and some will
  be below average.

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18.6 Control Chart for an Area of
OpportunityThe c Chart

• Instead of looking at the proportion of
  nonconforming items, look at the number of
  nonconforming items per unit.
• The area of opportunity is called a unit.
• In considering the number of typos on a page, the
  page is the unit.
• In considering the number of flaws in a square
  foot of carpet, the unit is the square foot of
  carpet.

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Theory of the c Chart

• The probability distribution is Poisson.
• If the size of the unit remains constant, the
  normal probability distribution can be used to
  derive the formulae in 18.3.
• In other words, the 3 in Formulae 18.3 is
  theoretically derived.

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Example using Table 18.4

• Number of complaints per week for 50 weeks.
• Unit week.
• k 50.
• c-bar sum of complaints / 50.
• LCL does not exist.
• Figure 18.9 out of control due to trend.
• Obvious managerial question is ___.

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18.7 Control Charts for the Range and the Mean

• Instead of measuring qualities such as
  defective or Nonconforming, we often want to
  measure quantities.
• Variables control charts are used with
  quantities.
• Variables control charts are used in pairs
• one for variability the range chart.
• One for the process average the x-bar chart.

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The R Chart

• Examine the Range chart first.
• In control? Use it to develop mean chart.
• Out of control? Use it to achieve control. Mean
  chart is not useful until in control.
• Formulae 18.4 and 18.5 define the control limits.
  The constants are found in Table E.13. What do
  we need to know?

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Example from Table 18.5

• How much time is required to move luggage from
  lobby to guest room?
• Examine 5 deliveries per day for 28 days.
• Calculate the average time per day and the daily
  range.
• Examine R chart. In control?

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The x-bar Chart

• Formulae 18.6 and 18.7 show that you need
  x-bar-bar and the average range.
• The A factors are found in Table E.13.

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Figure 18.11

• The x-bar control chart for luggage delivery
  times.
• In control?
• Since the R-chart and X-bar-chart show processes
  that are in control if a change is desired,
  management must change the process.

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18.8 Process Capability

• Answers the question can our process satisfy
  the quality requirements of our customers?
• To answer this question, we must know
• what the customers expect.
• that our process is in control.

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3 Approaches to Capability

• Process Capability is the ability of a process to
  consistently meet requirements.
• Use the specification limits to calculate the
  probability of falling within specifications.
• Calculate the Cp index.
• Calculate the Cpk index.

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Probability of Falling within Spec.

• Process must be in control.
• You will need x-bar-bar, R-bar, n, d2, and the
  customer specification limits.
• Customer specification limits are called LSL and
  USL.
• Need to assume that the population of measured
  valuesthe x valuesis approximately normally
  distributed.
• Use formulae 18.8.

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The Cp Index

• An overall measure of ability to meet
  specification.
• Cp is the most common index used.
• Formula 18.9.
• Ratio of (1) distance between specification
  limits and (2) actual process spread.
• Bigger is better less than 1 is not good.

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Problems with Cp

• This index shows potential capability. Since it
  does not consider x-bar, the actual capability is
  in question.
• Most optimistic assumption is that the process is
  operating near the center of the control area,
  i.e. near x-bar-bar.
• Many companies require values near 2.0very
  strict control!

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The Cpk Index

• Cpk min CPL, CPU
• CPL and CPU are capability indices that show the
  process capability relative to the actual
  operation of the process.
• Formulae 18.10.
• Bigger is better.
• The minimum CP is the conservative value of
  process capability.