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Chapter 9A. Process Capability and Statistical Process Control. Learning Objectives. Explain what statistical quality control is. Calculate the capability of a process. Understand how processes are monitored with control charts for both attribute and variable data.

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chapter 9a
Chapter 9A

Process Capability and Statistical Process Control

learning objectives
Learning Objectives
  • Explain what statistical quality control is.
  • Calculate the capability of a process.
  • Understand how processes are monitored with control charts for both attribute and variable data
types of situations where spc can be applied
Types of Situations where SPC can be Applied
  • How many paint defects are there in the finish of a car?
  • How long does it take to execute market orders?
  • How well are we able to maintain the dimensional tolerance on our ball bearing assembly?
  • How long do customers wait to be served from our drive-through window?

LO 1

basic forms of variation
Basic Forms of Variation
  • Assignable variation: caused by factors that can be clearly identified and possibly managed
    • Example: a poorly trained employee that creates variation in finished product output
  • Common variation: variation that is inherent in the production process
    • Example: a molding process that always leaves “burrs” or flaws on a molded item

LO 1

variation around us
Variation Around Us
  • When variation is reduced, quality is improved
  • However, it is impossible to have zero variation
    • Engineers assign acceptable limits for variation
    • The limits are know as the upper and lower specification limits
      • Also know as upper and lower tolerance limits

LO 1

taguchi s view of variation
Taguchi’s View of Variation
  • Traditional view is that quality within the range is good and that the cost of quality outside this range is constant
  • Taguchi views costs as increasing as variability increases, so seek to achieve zero defects and that will truly minimize quality costs

LO 1

process capability
Process Capability
  • Taguchi argues that tolerance is not a yes/no decision, but a continuous function
  • Other experts argue that the process should be so good the probability of generating a defect should be very low

LO 2

process capability1
Process Capability
  • Process limits
  • Specification limits
  • How do the limits relate to one another?

LO 2

capability index c pk
Capability Index (Cpk)
  • Capability index (Cpk) shows how well parts being produced fit into design limit specifications
  • Also useful to calculate probabilities

LO 2

example capability
Example: Capability
  • Data
    • Designed for an average of 60 psi
      • Lower limit of 55 psi, upper limit of 65 psi
    • Sample mean of 61 psi, standard deviation of 2 psi
  • Calculate Cpk

LO 2

the cereal box example
The Cereal Box Example
  • We are the maker of this cereal. Consumer Reports has just published an article that shows that we frequently have less than 15 ounces of cereal in a box.
  • Let’s assume that the government says that we must be within ± 5 percent of the weight advertised on the box.
  • Upper Tolerance Limit = 16 + .05(16) = 16.8 ounces
  • Lower Tolerance Limit = 16 – .05(16) = 15.2 ounces
  • We go out and buy 1,000 boxes of cereal and find that they weight an average of 15.875 ounces with a standard deviation of .529 ounces.

LO 2

cereal box process capability
Cereal Box Process Capability
  • Specification or Tolerance Limits
    • Upper Spec = 16.8 oz
    • Lower Spec = 15.2 oz
  • Observed Weight
    • Mean = 15.875 oz
    • Std Dev = .529 oz

LO 2

what does a c pk of 4253 mean
What does a Cpk of .4253 mean?
  • An index that shows how well the units being produced fit within the specification limits.
  • This is a process that will produce a relatively high number of defects.
  • Many companies look for a Cpk of 1.3 or better… 6-Sigma company wants 2.0!

LO 2

process control procedures
Process Control Procedures
  • Attribute (Go or no-go information)
    • Defectives refers to the acceptability of product across a range of characteristics.
    • Defects refers to the number of defects per unit which may be higher than the number of defectives.
    • p-chart application
  • Variable (Continuous)
    • Usually measured by the mean and the standard deviation.
    • X-bar and R chart applications

LO 3

slide17

Statistical

Process

Control

(SPC) Charts

UCL

Normal Behavior

LCL

1 2 3 4 5 6

Samples over time

UCL

Possible problem, investigate

LCL

1 2 3 4 5 6

Samples over time

UCL

Possible problem, investigate

LCL

1 2 3 4 5 6

Samples over time

LO 3

control limits are based on the normal curve
Control Limits are based on the Normal Curve

x

m

z

-3

-2

-1

0

1

2

3

Standard deviation units or “z” units.

LO 3

control limits

x

Control Limits

We establish the Upper Control Limits (UCL) and the Lower Control Limits (LCL) with plus or minus 3 standard deviations from some x-bar or mean value. Based on this we can expect 99.73% of our sample observations to fall within these limits.

99.73%

LCL

UCL

LO 3

process control with attribute measurement using charts
Process Control with Attribute Measurement: Using ρ Charts
  • Created for good/bad attributes
  • Use simple statistics to create the control limits

LO 3

interpreting control charts
Interpreting Control Charts

1 – 2- 5- 7 Rule

  • 1 point above UCL or 1 point below LCL
  • 2 consecutive points near the UCL or 2 consecutive points near the LCL
  • 5 consecutive decreasing points or 5 consecutive increasing points
  • 7 consecutive points above the center line or 7 consecutive points below the center line

LO 3

process control with variable measurements using x and r charts
Process Control with Variable Measurements: Using x and R Charts
  • In variable sampling, we measure actual values rather than sampling attributes
  • Generally want small sample size
    • Quicker
    • Cheaper
  • Samples of 4-5 are typical
  • Want 25 or so samples to set up chart

LO 3

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