Chapter 9a
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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

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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


Process capability2

Process Capability

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


Example probabilities

Example: Probabilities

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


Chapter 9a

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


Example control chart design

Example: Control Chart Design

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


Example calculations

Example: Calculations

LO 3


Control chart evidence for investigation

Control Chart Evidence for Investigation

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


How to construct x charts if standard deviation known

How to Construct x Charts if Standard Deviation Known

LO 3


How to construct x and r charts

How to Construct x and R Charts

LO 3


Example the data

Example: The Data

LO 3


Chapter 9a

LO 3


Example calculations and chart

Example: Calculations and Chart

LO 3


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