– process variation
– control charts
– process capability
Variation is present in every process as a result of a combination of four variables:
(1) operator variation (due to physical and emotional conditions),
(2) equipment variation (due to wear and tear),
(3) materials variation (due to thickness, moisture content, and old and new materials), and
(4) environmental variation (due to changes in temperature,
light, and humidity).
Variation is either expected or unexpected, and it results from common causes, special causes, or structural causes.
Common causes of variation affect the standard deviation of a process and are caused by factors internal to a process. These causes, which are present in all processes, are also called chance (random) causes.
Chance causes are small in magnitude and are difficult to identify. Examples of common random causes include worker availability, number and complexity of orders, job schedules, equipment testing, work-center schedules, changes in raw materials, truck schedules, and worker performance.
Examples of special (assignable) causes include equipment break-downs, operator changes, new raw materials, new products, new competition, and new customers.
Examples of structural causes include sudden sales / production volume increase due to a new product or a new customer, seasonal sales, and sudden increase in profits.
It shows whether a process is in a stable state and is used to improve the process quality.
It has been stated that 80 to 85 percent of quality problems are due to management or the quality system and that 15 to 20 percent of problems are due to operators or workers. Supervisors, operators, and technicians can correct the unnatural variation. Control charts can be drawn for variables and attributes.
It measures the quality of a particular characteristic, such as length, time, or temperature.
Once true process capability is obtained, effective specifications can be determined. The figure below shows the sequence of events taking place with the control chart.
Variable data consist of measurements such as weight, length, width, height, time, and temperature. Variable data contain more information than attribute data. Variable control charts can decrease the difference between customer needs and process
It is used where measurements are not possible, such as for color, missing parts, scratches, or damage. Quality characteristics for a product can be translated into a go/no-go decision, as follows.
Go/No-Go Decision for Product Quality
– Go conforms to specifications.
– No-go does not conform to specifications.
(1) the chart for nonconforming units
(2) the chart for nonconformities
A nonconforming unit is a product or service containing at least one nonconformity.
A nonconformity is a departure of quality characteristic from its intended level that is not meeting a specification requirement.
1) Type I error is called producer’s risk (alpha risk), which is the probability that a conforming (good quality) product will be rejected as poor quality product and not sold to customers.
This product meets the established acceptable quality level. This results in an incorrect decision to reject something when it is acceptable.
This results in an incorrect decision to accept something when it is unacceptable. Type II error occurs when statistical quality data fails to result in the scrapping or reworking of a defective product.
When a process is in control (stable), there is a natural pattern of variation, and only chance causes of variation are present. Small variations in operator performance, equipment performance, materials, and environmental characteristics are expected and are considered to be part of a stable process.
Further improvements in the process can be achieved only by changing the input factors, that is, operator, equipment, materials, and environment. These changes require action by management through quality improvement ideas.
When an observed measurement falls outside its control limits, the process is said to be out of control (unstable). This means that an assignable cause of variation is present. The unnatural, unstable variation makes it impossible to predict future variation. The assignable causes must be found and corrected before a natural, stable process can continue.
The process capability index (PCI), which indicates whether a process is capable of meeting customer expectations, must be equal to or greater than 1 to meet customer expectations.
A PCI of less than 1 means that the process does not meet customer expectations.
The PCI is computed in several ways:
PCI = (UL – LL) / (6 x Standard Deviation of a Process)
where UL is upper specification limit and LL is lower specification limit.
Upper specification limit means some data points will be above the central line in a control chart. Lower specification limit means some data points will be below the central line in a control chart.
Capability ratio (Cp) is specification tolerance width divided by the process capability.
Specification tolerance width refers to variability of a parameter permitted above or below a nominal value. Cp is a widely used PCI.