MAR 3203 Chapter S6: Statistical Process Control

Statistical Process Control (SPC)

The application of statistical techniques to ensure that processes meet standards

• Objective is to provide a statistical signal when assignable causes of variation are present

• Variability is inherent in every process

• A process is in statistical control when the only source of variation are common (natural) causes after eliminating special (assignable) causes

Natural variations

The variability that affects every production process to some degree and is to be expected; also known as common cause

When natural variations form a normal distribution, they are characterized by the mean (measure of central tendency) and standard deviation (measure of dispersion)

When the distribution remains within limits, the process is said to be “in control”

Assignable variations

Can be traced to a specific reason with the objective to discover when assignable causes are present

Control charts

Helps distinguish between natural variations and variations due to assignable causes with three types of process outputs

1. In statistical control and capable of producing within control limits

2. In statistical control but not capable of producing within control limits

3. Out of control

Control charts for variables

Two charts that must be used together

• Characteristics that take any real value

• May be in whole or fractional numbers

• Continuous random variables

x̄-chart tracks changes in the mean
R-chart indicates a gain or loss of dispersion

Central limit theorem

States that regardless of the distribution of the population, the distribution of sample means drawn from the population will tend to follow a normal curve

Sampling distribution of means

Population distributions may differ (normal, beta, uniform) but the distribution of sample means always approaches a normal distribution

As sample size increases, the sampling distribution narrows

Sampling distribution has less variability than the process distribution

R-chart

Type of variables control chart that shows sample ranges over time—difference between smallest and largest values in sample

• Monitors variability

• Independent from the process mean

Process capability

A measure of the relationship between the natural variation of the process and the design specifications

• A process in statistical control does not necessarily meet the design specifications

Process capability ratio C_p

Determines whether a process meets design specifications

• A capable process must have a C_p of at least 1.0

• Does not look at how well the process is centered in the specification range

• Target value of C_p = 1.33 is used to allow for off-center processes

• Six sigma quality requires C_p = 2.0

Process capability index C_pk

Determines whether a process meets specifications based on the distance between the process mean and the nearest specification limit

• A capable process must have a C_pk of at least 1.0

• A capable process is not necessarily in the center of the specification, but falls within the limit at both extremes

Interpreting C_pk