Statistical Process Control

What is Statistical Process Control? W. Edwards Deming The main message of Deming’s 14 items list is that poor quality occurs as a result of the system and so should be corrected by the management. Deming also stressed that variation in output should be reduced by identifying particular causes that differ from random variation.

What is Statistical Process Control? Joseph M. Juran Juran was geared towards what customers want. He asserted that 80 percent of quality gaps can be corrected by management through quality planning, control, and improvement. Philip B. Crosby Introduced the concept of zero defects and stressed prevention. He pointed out that the cost of achieving higher quality also reduces costs, hence quality is free

What is Statistical Process Control? Statistical Process Control (SPC) monitor standards, makes measurements, and takes corrective action while a product or service is being produced. Samples of process outputs are examined. If they are within acceptable limits and no present discernible pattern, the process is permitted to continue. If they fall outside the specified limits or a discernible pattern is detected, the process is stopped and the assignable cause located and removed (Corrective action is taken). Acceptance sampling is used to determine acceptance or rejection of material evaluated by a sample.

What is Statistical Process Control? All processes are subject to a certain degree of variability. Walter Shewhart, in 1920s, distinguished between the common and special causes of variation. These causes are also known as natural and assignable causes of variation. A process is said to be operating in statistical control when the only source of variation is natural (common) causes.

What is Statistical Process Control? A process must first be brought to statistical control by detecting and eliminating the assignable causes of variation. Then its performance is predictable and its ability to meet customer expectations can be assessed. The objective of a process control system is to provide a statistical signal when assignable causes of variation are present.

Natural and Assignable Variations Natural Variations: Affect almost every production process and are to be expected Although individual values are different, as a group they form a pattern that can be described as a distribution. As long as the distribution output measures remain within specific limits, the process is said to be in control and natural variations are tolerated.

Natural and Assignable Variations Can be traced to a specific reason. If assignable causes of variation are present, the process output is not stable over time and is not predictable. Factors such as: machine wear, misadjusted equipment, fatigued or untrained workers or new batches of raw materials are all potential sources of assignable variations.

Control Charts Control Charts are graphic presentation of data over time that show upper and lower limits for the process we want to control. Control charts are constructed in such a way that new data can be compared with past performance data. Sample of the process output are taken and the average of the samples are plotted on a chart that has the acceptable limits on it.

Samples Samples: Because of the natural and assignable causes, statistical process control uses averages of small samples (often between 4 and 8 items) Individual items tend to be too erratic to make trends quickly visible.

Each of these represents one sample of five boxes of cereal Samples To measure the process, we take samples and analyze the sample statistics following these steps Each of these represents one sample of five boxes of cereal (a) Samples of the product, say five boxes of cereal taken off the filling machine line, vary from each other in weight Frequency Weight #

The solid line represents the distribution Samples The solid line represents the distribution (b) After enough samples are taken from a stable process, they form a pattern called a distribution Frequency Weight

Samples (c) There are many types of distributions, including the normal (bell-shaped) distribution, but distributions do differ in terms of central tendency (mean), standard deviation or variance, and shape Weight Central tendency Variation Shape Frequency

Samples (d) If only natural causes of variation are present, the output of a process forms a distribution that is stable over time and is predictable Prediction Weight Time Frequency

Samples Prediction ? (e) If assignable causes are present, the process output is not stable over time and is not predicable Weight Time Frequency

Process Control (a) In statistical control and capable of producing within control limits Frequency Lower control limit Upper control limit (b) In statistical control but not capable of producing within control limits This slide helps introduce different process outputs. It can also be used to illustrate natural and assignable variation. (c) Out of control (weight, length, speed, etc.) Size

Types of Data Variables Attributes Characteristics that can take any real value May be in whole or in fractional numbers Continuous random variables Defect-related characteristics Classify products as either good or bad or count defects Categorical or discrete random variables Once the categories are outlined, students may be asked to provide examples of items for which variable or attribute inspection might be appropriate. They might also be asked to provide examples of products for which both characteristics might be important at different stages of the production process.

Central Limit Theorem Regardless of the distribution of the population, the distribution of sample means drawn from the population will tend to follow a normal curve The mean of the sampling distribution (x) will be the same as the population mean m This slide introduces the difference between “natural” and “assignable” causes. The next several slides expand the discussion and introduce some of the statistical issues. The standard deviation of the sampling distribution (sx) will equal the population standard deviation (s) divided by the square root of the sample size, n

Population and Sampling Distributions Three population distributions Beta Normal Uniform Distribution of sample means Standard deviation of the sample means = sx = s n Mean of sample means = x | | | | | | | -3sx -2sx -1sx x +1sx +2sx +3sx 99.73% of all x fall within ± 3sx 95.45% fall within ± 2sx