*SPC Objectives benefits Shewhart control charts Variations Common cause variation random variation Special nonrandom variation Variables Attribute Selection of Variable Rational Subgrouping Schemes Sources of Variability*

**Statistical Process Control Overview**

•Objectives and benefits

•Selection of variables

•Rational subgrouping

•Selection and application of control charts

•Analysis of control charts

•Pre-control

**Objectives and benefits**

Statistical process control (SPC) is a technique for applying statistical analysis to measure, monitor, and control processes.

•The major component of SPC is the use of control charting methods.

•The basic assumption made in SPC is that all processes are subject to variation.

This variation may be classified as one of two types,random or chance cause variation and assignable cause variation. Benefitsof statistical process control include the ability to monitor astable process and identify if changes occur that are due to factors other than random variation. When assignable cause variation does occur, the statistical analysis facilitates identification of the source so that it may be eliminated. The objectives of statistical process control are to determine process capability, monitor processes and identify whether the process is operating as expected or whether the process has changed and corrective action is required.

**•Variations and Control**

–**Common cause variation or random variation:** Natural variations in the output of a process, created by countless minor factors. Random variation is usually left alone.

–**Special cause or nonrandom variation:** A variation whose source can be identified to be nonrandom. When there is special nonrandom variation, we call it ‘out of control’. In this case, the cause(s) of nonrandom variation should be identified and corrected.

**Causes of Variation**

**Common Causes**

– Inherent to process

– Random

-Cannot be controlled

– Cannot be prevented

– Examples•weather•accuracy of measurements•capability of machine

•Are present all the time but impact varies

•Each contributes a small part of the total variation

•Viewing over time shows extent of variation

•Process is stable and predictable

•In control chart theory, if the process is only influenced by common cause variation, the process variation will follow a stable distribution, mostly normal distribution. So the process will be within control limits

**Special Causes**

•Exogenous to process

•Not random

•Controllable

•Preventable

•Examples–tool wear–“Monday”effect–poor maintenance

•Appear sporadically

•Out of the ordinary occurrence

•Typically one event has a large impact on variation

•When there is special cause variation, the process variation will not follow stable distribution, so the process variation will either be ‘out of control limits’or displace ‘nonrandom patterns’.

SPC Control limits are usually based on +/-3 σ, because in normal distribution, an observation outside +/-3σis a very rare event.

**Commonly Used Control Charts**

**•Variables data**

–x-bar and R-charts

–x-bar and s-charts

–Charts for individuals (x-charts)

**•Attribute data**

–For “defectives”(p-chart, np-chart)

–For “defects”(c-chart, u-chart)

** Shewhart control charts**

**Grant {1988) identifies benefits to be expected from the use of Shewhart control charts in providing information which becomes the basis for action. The information they provide is: **

. Basic variability of the quality characteristic

. Consistency of performance

. Average level of the quality characteristic

Control chart information can be used to determine the natural range of the process and to compare it with the specified tolerance range. Ifthe natural range is wider, then either the specification range should be expandedor the process needs engineering improvements to narrow the natural range.

Benefits from control charting are derived from both attributes and variables charts. Once the control chart shows that a process is in control and within specification limits, it is often possible to eliminate costs relating to inspection.

Interpretation of control charts may be used as a predictive tool to indicate when changes are required prior to production of out of tolerance material. As an example, in a machining operation, tool wear can cause gradual increases or decreases in a part dimension. Observation of a trend in the affected dimension allows the operator to replace the worn tool before defective parts are manufactured.

When the manufacturing method is lot production followed by lot inspection, if inspection finds out of tolerance parts, very little can be done other than scrap, rework or accept the defective parts. Using control charts, if the process changes, the process can be stopped and only the parts produced since thelast check need to be inspected. By monitoring the process during production, if problems do arise, the amount of defective material created is significantlyless than when using batch production and subsequent inspection methods.

An additional benefit of control charts is to monitor continuous improvement efforts. When process changes are made which reduce variation, the control chart can be used to determine if the changes were effective. The benefits of statistical process control are not without costs. Costs associated with SPC include the selection of the variables or attributes tomonitor, setting up the control charts and data collection system, training of operators, and investigation and correction when data values fall outside control limits. As early as the 1940’s, many companies found that the benefits of statistical process control far outweigh the related costs.

**Selection of Variable **

For the purpose of this discussion, the selection of a variable will be used to describe the statistic used with either variables or attributes data. Given the benefits of control charting, one might be tempted to control chart every characteristic of a given process. The logic to do so is that ifany characteristic changes, then the process can be stopped. This decision would also eliminate the need to determine if one characteristic is more important than another.

The risk of charting many parameters is that the operator will spend so much time and effort completing the charts, that the actual process becomes secondary. When a change does occur, it will most likely be overlooked. When more than a few charts are used for a process, the benefits may not increaseas quickly as the costs. As a result of diminishing returns, the point is reached where additional charts are not worthwhile.

In the ideal case, one process parameter is the most critical, and is indicative of the process as a whole. Some specifications identify this as a critical to quality (CTQ) characteristic. CTQ may also be identified as a key characteristic. QS-9000 (1998) defines two types of special characteristics: . Key Characteristic (not relating to safety or legal considerations) . Key Characteristic (with safety or legal consideration)

General Motors, Ford Motor Co., and Daimler Chrylser provide symbols to identify key characteristics and require the identified characteristics be included in control plans.

Key process input variables (KPIVs) may be analyzed to determine the degree of their effect on a process. For some processes, an input variable such as temperature, may be so significant that control charting is mandated.

Key process output variables (KPOVs) are candidates both for determining process capability and process monitoring using control charting.

Design of experiments (DOE) and analysis of variance (ANOV A) methods may also be used to identify variable(s) that are most significant to process control.

**Rational Subgrouping**

A control chart provides a statistical test to determine if the variation from sample to sample is consistent with the average variation withinthe sample. The key idea in the Shewhartcontrol chart is the division of observations into what are called rational subgroups. The success of charting depends in large measure on the selection of these subgroups.

Generally, subgroups are selected in a way that makes each subgroup as homogeneous as possible. This provides the maximum opportunity for estimating expected variation from one subgroup to another. However, this selection depends upon a knowledge of the components of the total process variation.

In production control charting, it is very important to maintain the order of production. Data from a charted process, which shows out of control conditions (and resulting opportunities for correction), may be mixed to create new X -R charts which demonstrate remarkable control. By mixing, chance causes are substituted for the original assignable causes as a basis for the differences among subgroups

**Subgrouping Schemes **

Where order of production is used as a basis for subgrouping, two fundamentally different approaches are possible:

. The first subgroup consists of product all produced as nearly as possible at one time. This method follows the rule for selection of rationalsubgroups by permitting a minimum chance for variation within a subgroup and a maximum chance for variation from subgroup to subgroup.

. One subgroup consists of product intended to be representativeof all the production over a given period of time; product may accumulate at the point of production, with a random sample chosen from all the product made since the last sample.

If subgrouping is by the first method and a change in process average takes place after one subgroup is taken and is corrected before the next subgroup, the change will not be reflected in the control chart. For this reason, the second method is sometimes preferred where one of the purposes of the control chart is to influence decisions on acceptance of product.

The choice of subgroup size should be influenced, in part, by the desirability of permitting a minimum chance for variation within a subgroup. In most cases, more useful information will be obtained from, say, five subgroups of5 than from one subgroup of 25. In large subgroups, such as 25, there is likely to be too much opportunity for a process change within the subgroup.

**Sources of Variability**

Much of the discussion of process capability will concentrate onthe analysis of sources of variability. It is worthwhile, therefore, to considerthe possible sources of variation in a manufactured product. The long term variation in a product will, for convenience, be termed the product {or process} spread. There will be some difference between the process spread and thelot-to-lot variation. One of the objectives of control charting is to markedly reduce the lot-to-lot variability.

The distribution of products flowing from different streams (machines, tanks, dies, etc.) may produce variabilities greater than those of individual streams. In order to eliminate this source of variability, it may be necessary to analyze each stream-to-stream entity separately. Another main objective of control charting isto reduce time-to-time variation.

Physical inspection measurements may be taken at a great many different points on a given unit. Such differences are referred to as within-piece variability. Significant positional variation may necessitate changes in material or machinery.

Another source of variability is the piece-to piece variation. Often, the inherent error of measurement is significant. This error consists of both human and equipment components. The remaining variability is referred to as the inherent process capability. It is the instant reproducibility of the machine and represents the ultimate capability operating under virtual laboratory conditions.

One very important factor still missing from this discussion of variability is the interaction that takes place between man and machine. This includes not only between the operator and the machine but also the inspectorand the measurement device.