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Statistical Process Control

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 the two types, chance cause variation and assignable cause variation. Benefits of statistical process control include the ability to monitor a stable process and determine if changes occur due to factors other than random variation. When assignable cause variation does occur, the statistical analysis facilitates identification of the source, so that it can be eliminated.

Statistical process control also provides the ability 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. Control chart information can be used to determine the natural range of the process and to. Compare it with the specified tolerance range. If the natural range is wider, then either the specification range should be expanded, or improvements will be necessary to narrow the natural range.

 

We can expect the following key information from Shewhard control charts, which will become the basis for our action:

  • Average level of the quality characteristic

  • Basic variability of the quality characteristic

  • Consistency of performance

Benefits from control charting are derived from both attribute and variable 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. Control charts may be used as a predictive tool to indicate when changes are required in order to prevent the production of out of tolerance material. As an example, in a machining operation, tool wear can cause gradual increases or decreases in a part’s 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 to 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 the last check need to be inspected.

By monitoring the process during production, if problems do arise, the amount of defective material created is significantly less than when using batch production and subsequent inspection methods. An additional benefit of control charts is the ability 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 variable(s) or attribute(s) to monitor, setting up the control charts and data collection system, training personnel, and investigating and correcting the cause when data values fall outside control limits. As early as the 1940s, many companies found that the benefits of statistical process control far outweigh the related costs.

Selection of Variables

Given the benefits of control charting, one might be tempted to control chart every characteristic or process variable. The logic is if any 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 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 decrease, as quickly as the costs increase.

Some considerations for the selection of a control chart variable include:

  • Items that protect human safety.

  • Items that protect the environment or community.

  • Items that are running at a high defective rate.

  • Key process variables that impact the product.

  • Major sources of customer complaints.

  • Items that show adherence to applicable standards.

  • Items that are requested by key customers.

  • Variables that have caused processing difficulties.

  • Variables that can be measured by the person charting.

  • Items that can be counted by the person charting.

  • Items that contribute to high internal costs.

  • Variables that help control the process.
     

In an ideal case; one process variable is so critical that it is indicative of the process, as a whole. Key process input variables (KPlVs) may be analyzed to determine the degree of their effect on a process. Key process output variables (KPOVs) are ideal for determining process capability and for. Process monitoring using control charts. Design of experiments and analysis of variance may be used to identify the variables which are most significant to process control. Pareto analysis can be used to identify key internal and external losses.

Rational Sub-grouping

A control chart provides a statistical test to determine if the variation from sample-to-sample is consistent with the average variation within the sample. The key idea in the Shewhart control chart is the division of observations into what are called rational subgroups. The success of charting depends a great deal on the selection of these subgroups. Generally, subgroups are selected in a way that makes each subgroup as homogeneous as possible and that gives the maximum opportunity for variation from one subgroup to another. However, this selection depends upon a knowledge of the components of the total process variation.

 

Rational Subgrouping In production control charting, it is very important to maintain the order of production. 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.

 

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

The first subgroup consists of product produced as nearly as possible at one time. This method follows the rule for selection of rational subgroups by permitting a minimum chance for variation within a subgroup and a maximum chance for variation from subgroup-to-subgroup. Another subgroup option consists of product intended to be representative of 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 the 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 when 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 of 5 rather 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.

 

Control Chart Anatomy

Points to keep in mind while selecting a control chart:

  • Variables Data

  • For continuous data we can measure the average and the variation, thus X bar &R (Range) or X bar and S (Standard deviation) can be used

  • Attribute Data

Determine what are we measuring – Defects or Defectives

In case we are capturing defective data then determine if we are sampling for subgroup of equal sample size or not.

In case if we are capturing data for defects then determine if the opportunity for the defects are the same for each subgroup or not.

Based on the above, select the appropriate chart.

Control Chart Selection is based on the Data Type: 

  • If the data is variable data with the sub-group size as 1, we can use I-MR (Individuals Moving Range) Chart.

  • If the data is variable data with sub-group size more than 1 but less than 8, we can use X-Bar R (Mean and Range) Chart.

  • If the data is variable data with sub-group size more than 8, we can use X-Bar S (Mean and Standard Deviation) Chart.

  • If the data is attribute data, we capture Defectives and subgroup size is the same, we use np Chart.

  • If the data is attribute data, we capture Defectives and subgroup size is varying, we use p Chart.

  • If the data is attribute data, we capture Defects and subgroup size is the same, we use c Chart.

  • If the data is attribute data, we capture Defects and subgroup size is the varying, we use u Chart.



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