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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

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

- 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

- 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

- 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

- 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 Capability

- Process limits
- Specification limits
- How do the limits relate to one another?

LO 2

Process Capability

LO 2

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

- 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

- Designed for an average of 60 psi
- Calculate Cpk

LO 2

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

- 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 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

- 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

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

x

m

z

-3

-2

-1

0

1

2

3

Standard deviation units or “z” units.

LO 3

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 ρ Charts

- Created for good/bad attributes
- Use simple statistics to create the control limits

LO 3

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

- 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

LO 3

How to Construct x and R Charts

LO 3

Example: The Data

LO 3

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