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Statistical Process Control (SPC)

- Chapter 6

Course Overview

Operations and Operations Strategy

Products, Processes, Quality

Operations Planning Control

Facilities and Work Systems

Mathematical Tools for Operations

Product Design

Project Management

Process Design

Linear Programming

Just-in-Time

Quality Management

Statistical Process Control

Assuring Customer-Based Quality

Product launch activities Revise periodically

Statistical Process Control Measure monitor

quality

Ongoing activity

Statistical Process Control (SPC)

Basic SPC Concepts

SPC for Variables

Types of Measures

Variation

Attributes

Mean charts

Range charts

Objectives

Variables

? and ? known

First steps

? unknown, ? known

?, ? unknown

Variation in a Transformation Process

Variation

Variation

- Inputs
- Facilities
- Equipment
- Materials
- Energy

Variation

- Variation in inputs create variation in outputs
- Variations in the transformation process
- create variation in outputs

Variation in a Transformation Process

Customer requirements are not met

- Inputs
- Facilities
- Equipment
- Materials
- Energy

- Variation in inputs create variation in outputs
- Variations in the transformation process
- create variation in outputs

Variation

- All processes have variation.
- Common cause variation is random variation that

is always present in a process. - Assignable cause variation results from changes

in the inputs or the process. The cause can and

should be identified. - Assignable cause variation shows that the process

or the inputs have changed, at least temporarily.

Objectives of Statistical Process Control (SPC)

- Find out how much common cause variation the

process has - Find out if there is assignable cause variation.
- A process is in control if it has no assignable

cause variation - Being in control means that the process is stable

and behaving as it usually does.

First Steps in Statistical Process Control (SPC)

- Measure characteristics of goods or services that

are important to customers - Make a control chart for each characteristic
- The chart is used to determine whether the

process is in control

Types of Measures (1)Variable Measures

- Continuous random variables
- Measure does not have to be a whole number.
- Examples time, weight, miles per gallon, length,

diameter

Types of Measures (2)Attribute Measures

- Discrete random variables finite number of

possibilities - Also called categorical variables
- The measure may depend on perception or judgment.
- Different types of control charts are used for

variable and attribute measures

Examples of Attribute Measures

- Good/bad evaluations
- Good or defective
- Correct or incorrect
- Number of defects per unit
- Number of scratches on a table
- Opinion surveys of quality
- Customer satisfaction surveys
- Teacher evaluations

SPC for VariablesThe Normal Distribution

- ? the population mean
- the standard deviation
- for the population
- 99.74 of the area under the normal curve is

between - ? - 3? and ? 3?

SPC for Variables The Central Limit Theorem

- Samples are taken from a distribution with mean ?

and standard deviation ?. - k the number of samples
- n the number of units in each sample
- The sample means are normally distributed
- with mean ? and standard deviation
- when k is large.

Control Limits for the Sample Mean when ? and ?

are known

- x is a variable, and samples of size n are taken

from the population containing x. - Given ? 10, ? 1, n 4
- Then
- A 99.7 confidence interval for is

Control Limits for the Sample Mean when ? and ?

are known (2)

- The lower control limit for is

Control Limits for the Sample Mean when ? and ?

are known (3)

- The upper control limit for is

Control Limits for the Sample Mean when ? is

unknown, ? is known

- Example 6.1, page 179
- Given 25 samples, 4 units in each sample,
- ? 0.14. ?? is not given.
- k 25, n 4
- For i 1,...,k, the observations in sample i are

- For the ith sample, the sample mean is

Control Limits for the Sample Mean when ? is

unknown, ? is known (2)

- Compute the mean for each sample. For example,

- Compute

Control Limits for the Sample Mean when ? is

unknown, ? is known (3)

- Use instead of ? in the formulas for LCL and

UCL.

Control Limits for the Sample Mean when ? and ?

are unknown

- Example 6.1 (continued), page 180
- Given 25 samples, 4 units in each sample
- ? and ? are not given
- k 25, n 4

Control Limits for the Sample Mean when ? and ?

are unknown (2)

- Compute the mean for each sample. For example,

- Compute

Control Limits for the Sample Mean when ? and ?

are unknown (3)

- For the ith sample, the sample range is
- Ri (largest value in sample i )
- - (smallest value in sample i )
- Compute Ri for every sample. For example,
- R1 16.02 15.83 0.19

Control Limits for the Sample Mean when ? and

? are unknown (4)

- Compute , the average range
- We will approximate by , where
- A2 is a number that depends on the sample
- size n. We get A2 from Table 6.1, page 182

Control Limits for the Sample Mean when ? and

? are unknown (5)

- n the number of units in each sample
- 4.
- From Table 6.1,
- A2 0.73.
- The same A2 is used
- for every problem
- with n 4.

Control Limits for the Sample Mean when ? and

? are unknown (6)

- The formula for the lower control limit is
- The formula for the upper control limit is

Control Chart for

The variation between LCL 15.74 and UCL

16.16 is the common cause variation.

Common Cause andSpecial Cause Variation

- The range between the LCL and UCL, inclusive, is

the common cause variation for the process. When - is in this range, the process is in

control. - When a process is in control, it is predictable.

Output from the process may or may not meet

customer requirements. - When is outside control limits, the process

is out of control and has special cause

variation. The cause of the variation should be

identified and eliminated.

Control Limits for R

- From the table,
- get D3 and D4
- for n 4.
- D3 0
- D4 2.28

Control Limits for R (2)

- The formula for the lower control limit is
- The formula for the upper control limit is

Statistical Process Control (SPC)

Review of Specification Limits

- The target for a process is the ideal value
- Example if the amount of beverage in a bottle

should be 16 ounces, the target is 16 ounces - Specification limits are the acceptable range of

values for a variable - Example the amount of beverage in a bottle must

be at least 15.8 ounces and no more than 16.2

ounces. - The allowable range is 15.8 16.2 ounces.
- Lower specification limit 15.8 ounces or LSL

15.8 ounces - Upper specification limit 16.2 ounces or USL

16.2 ounces

Control Limits vs. Specification Limits

- Control limits show the actual range of variation

within a process - What the process is doing
- Specification limits show the acceptable common

cause variation that will meet customer

requirements.

Process is Capable Control Limits arewithin or

on Specification Limits

Upper specification limit

UCL

X

LCL

Lower specification limit

Process is Not Capable One or BothControl

Limits are Outside Specification Limits

UCL

Upper specification limit

X

LCL

Lower specification limit

Capability and Conformance Quality

- A process is capable if
- It is in control and
- It consistently produces outputs that meet

specifications. - This means that both control limits for the mean

must be within the specification limits - A capable process produces outputs that have

conformance quality (outputs that meet

specifications).

Capable Transformation Process

- Inputs
- Facilities
- Equipment
- Materials
- Energy

Outputs Goods Services that meet specifications

Capable Transformation Process

Process Capability Ratio

- Use to determine whether the process is

capable when ? target. - If , the process is capable,
- If , the process is not capable.

Example

- Given Boffo Beverages produces 16-ounce bottles

of soft drinks. The mean ounces of beverage in

Boffo's bottle is 16. The allowable range is 15.8

16.2. The standard deviation is 0.06. Find

and determine whether the process is capable.

Example (2)

- Given ? 16, ? 0.06, target 16
- LSL 15.8, USL 16.2
- The process is capable.

Process Capability Index Cpk

- If Cpk gt 1, the process is capable.
- If Cpk lt 1, the process is not capable.
- We must use Cpk when ? does not equal the target.

Cpk Example

- Given Boffo Beverages produces 16-ounce bottles

of soft drinks. The mean ounces of beverage in

Boffo's bottle is 15.9. The allowable range is

15.8 16.2. The standard deviation is 0.06. Find

and determine whether the process is

capable.

Cpk Example (2)

- Given ? 15.9, ? 0.06, target 16
- LSL 15.8, USL 16.2
- Cpk lt 1. Process is not capable.

Statistical Process Control (SPC)

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