Statistical Process Control Chapter 4S

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Statistical Process ControlChapter 4S

• Learning Objectives
• Identify sources of variation
• Explain statistical process control
• Develop control charts for variables
• R chart,X chart
• Develop control charts for attributes
• P chart, c chart
• Explain acceptance sampling
• Producers consumers risk

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Statistical Quality Control (SPC)

• 1. Measures performance of a process
• 2. Uses mathematics (i.e., statistics)
• 3. Involves collecting, organizing,
  interpreting data
• 4. Objective Regulate product quality
• 5. Used to
• Control the process as products are produced
• Inspect samples of finished products

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Types of Statistical Quality Control
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Quality Characteristics
Attributes
Variables

• 1. Characteristics that you measure, e.g.,
  weight, length
• 2. May be in whole or in fractional numbers
• 3. Continuous random variables

• 1. Characteristics for which you focus on defects
• 2. Classify products as either good or bad,
  or count defects
• e.g., radio works or not
• 3. Categorical or discrete random variables

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Statistical Process Control (SPC)

• 1. Statistical technique used to ensure process
  is making product to standard
• 2. All process are subject to variability
• Natural causes Random variations
• Assignable causes Correctable problems
• Machine wear, unskilled workers, poor material
• 3. Objective Identify assignable causes
• 4. Uses process control charts

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Process Control Charts
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Control Chart Purposes

• 1. Show changes in data pattern
• e.g., trends
• Make corrections before process is out of control
• 2. Show causes of changes in data
• Assignable causes
• Data outside control limits or trend in data
• Natural causes
• Random variations around average

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Theoretical Basis of Control Charts
Central Limit Theorem
As sample size gets large enough (³ 30) ...
sampling distribution becomes almost normal
regardless of population distribution.
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Theoretical Basis of Control Charts
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Theoretical Basis of Control Charts
Properties of normal distribution
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Control Chart Types
R and X charts go hand in hand when monitoring
variables because they measure two critical
parameters 1. Central tendency
2. Dispersion
Continuous Numerical Data
Categorical or Discrete Numerical Data
Control
Charts
Variables
Attributes
Charts
Charts
R

P
C
X
Chart
Chart
Chart
Chart
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Statistical Process Control Steps
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X Chart

• 1. Type of variables control chart
• Interval or ratio scaled numerical data
• 2. Shows sample means over time
• 3. Monitors process average and tells whether
  changes have occurred. These changes may due to
• 1. Tool wear
• 2. Increase in temperature
• 3. Different method used
  in the second shift
• 4. New stronger material
• 4. Example Weigh samples of coffee compute
  means of samples Plot

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X Chart Control Limits
From Table S4.1
Sample Range at Time i
Sample Mean at Time i
Samples
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R Chart

• 1. Type of variables control chart
• Interval or ratio scaled numerical data
• 2. Shows sample ranges over time
• Difference between smallest largest values in
  inspection sample
• 3. Monitors variability in process, it tells us
  the loss or gain in dispersion. This change may
  be due to
• 1. Worn bearing
• 2. A loose tool
• 3. An erratic flow of
  lubricant to machine
• 4. Sloppiness of
  machine operator
• 4. Example Weigh samples of coffee compute
  ranges of samples Plot

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R Chart Control Limits
From Table S4.1
Sample Range at Time i
Samples
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p Chart

• 1. Type of attributes control chart
• Nominally scaled categorical data
• e.g., good-bad
• 2. Shows of nonconforming items
• 3. Example Count defective chairs divide by
  total chairs inspected Plot
• Chair is either defective or not defective

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p Chart Control Limits
z 2 for 95.5 limits z 3 for 99.7 limits
Defective Items in Sample i
Size of sample i
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c Chart

• 1. Type of attributes control chart
• Discrete quantitative data
• 2. Shows number of nonconformities (defects) in a
  unit
• Unit may be chair, steel sheet, car etc.
• Size of unit must be constant
• 3. Example Count defects (scratches, chips
  etc.) in each chair of a sample of 100 chairs
  Plot

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c Chart Control Limits
Use 3 for 99.7 limits
Defects in Unit i
Units Sampled
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Process Capability Cpk

• Assumes that the process is
• under control
• normally distributed

If Cpk index goes above 1 the process becomes
more and more target oriented with fewer defects.
If Cpk is 1 the process variation is centered
within the control limits. However, if it is less
than 1, the process will not produce within the
specified limits
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What Is Acceptance Sampling?

• 1. Form of quality testing used for incoming
  materials or finished goods
• e.g., purchased material components
• 2. Procedure
• Take one or more samples at random from a lot
  (shipment) of items
• Inspect each of the items in the sample
• Decide whether to reject the whole lot based on
  the inspection results

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What Is an Acceptance Plan?

• 1. Set of procedures for inspecting incoming
  materials or finished goods
• 2. Identifies
• Type of sample
• Sample size (n)
• Criteria (c) used to reject or accept a lot
• 3. Producer (supplier) consumer (buyer) must
  negotiate

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Operating Characteristics Curve

• 1. Shows how well a sampling plan discriminates
  between good bad lots (shipments)
• 2. Shows the relationship between the probability
  of accepting a lot its quality

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OC Curve100 Inspection
P(Accept Whole Shipment)
100
Return whole shipment
Keep whole shipment
0
Cut-Off
Defective in Lot
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OC Curve with Sampling
P(Accept Whole Shipment)
Probability is not 100 Risk of keeping bad
shipment or returning good one.
100
Keep whole shipment
Return whole shipment
0
Cut-Off
Defective in Lot
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AQL LTPD

• 1. Acceptable quality level (AQL)
• Quality level of a good lot
• Producer (supplier) does not want lots with fewer
  defects than AQL rejected
• 2. Lot tolerance defective (LTPD)
• Quality level of a bad lot
• Consumer (buyer) does not want lots with more
  defects than LTPD accepted

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Producers Consumers Risk

• 1. Producer's risk (a)
• Probability of rejecting a good lot (Type I
  Error)
• Probability of rejecting a lot when fraction
  defective is AQL
• 2. Consumer's risk (ß)
• Probability of accepting a bad lot (Type II
  Error)
• Probability of accepting a lot when fraction
  defective is LTPD

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OC Curve Risk
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OC Curves for Different Sampling Plans
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Average Outgoing Quality
Where Pd true percent defective of the lot
Pa probability of accepting the
lot N number of items in the
lot n number of items in the
sample The maximum value of on the AOQ curve
correspond to the highest average percent
defective or the lowest average quality for the
plan It is called the Average Outgoing Quality
Limit (AOQL)
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Developing a Sample Plan

• 1. Negotiated between producer (supplier) and
  consumer (buyer)
• 2. Both parties attempt to minimize risk
• Affects sample size cut-off criterion
• 3. Methods
• MIL-STD-105D Tables
• Dodge-Romig Tables