CONTROL CHARTS

If the chart indicates that the process is currently under control then it can be used with confidence to predict the future performance of the process. If the chart indicates that the process being monitored is not in control, the pattern it reveals can help determine the source of variation to be eliminated to bring the process back into control.

In statistical process control, the control chart, also known as the 'Shewhart chart' or 'process-behavior chart' is a tool used to determine whether a manufacturing or business process is in a state of statistical control or not.

A control chart is a specific kind of run chart that allows significant change to be differentiated from the natural variability of the process. This is key to effective process control and improvement.

The control chart is one of the seven basic tools of quality control (along with the histogram, Pareto chart, check sheet, cause-and-effect diagram, flowchart, and scatter diagram).

A control chart consists of the following:

• Points representing measurements of a quality characteristic in samples taken from the process at different times [the data]
• A centre line, drawn at the process characteristic mean which is calculated from the data
• Upper and lower control limits (sometimes called "natural process limits") that indicate the threshold at which the process output is considered statistically 'unlikely'

The chart may contain other optional features, including:

• Upper and lower warning limits, drawn as separate lines, typically two standard deviations above and below the centre line
• Division into zones, with the addition of rules governing frequencies of observations in each zone
• Annotation with events of interest, as determined by the Quality Engineer in charge of the process's quality
• If the process is in control, all points will plot within the control limits. Any observations outside the limits, or systematic patterns within, suggest the introduction of a new (and likely unanticipated) source of variation, known as a special-cause variation. Since increased variation means increased quality costs, a control chart "signaling" the presence of a special-cause requires immediate investigation.
• The control limits tell you about process behavior and have no intrinsic relationship to any specification targets or engineering tolerance. In practice, the long-term process mean (and hence the centre line) may not coincide exactly with the ideal value (or target) of the quality characteristic because equipment simply can't deliver the process characteristic at the desired level or because it's too costly to put the process on target.
• Control charts omit specification limits or targets because of the tendency of those involved with the process (e.g., machine operators) to focus on performing to specification when in fact the least-cost course of action is to keep process variation as low as possible. Attempting to make a process whose natural centre is not the same as the target increases process variability and costs significantly and is the cause of much inefficiency in operations. Process capability studies do examine the relationship between the natural process limits (the control limits) and specifications, however.
• The purpose of control charts is to allow simple detection of events that are indicative of actual process change. This can be difficult where the process characteristic is continuously varying; the control chart provides statistically objective criteria of change. When change is detected then if the change is good its cause should be identified and possibly become the new way of working, where the change is bad then its cause should be identified and eliminated. The purpose in adding warning limits or subdividing the control chart into zones is to provide early notification if something is amiss. Instead of immediately launching a process improvement effort to determine whether special causes are present, the Quality Engineer may temporarily increase the rate at which samples are taken from the process output until it's clear that the process is truly in control. Note that with three sigma limits, one expects to be signaled approximately once out of every 370 points on average, just due to common-causes.

The control chart is intended as a heuristic. Deming insisted that it is not a hypothesis test and is not motivated by the Neyman-Pearson lemma. He contended that the disjoint nature of population and sampling frame in most industrial situations compromised the use of conventional statistical techniques. Deming's intention was to seek insights into the cause system of a process ...under a wide range of unknowable circumstances, future and past.... He claimed that, under such conditions, 3-sigma limits provided ... a rational and economic guide to minimum economic loss... from the two errors:

1. Ascribe a variation or a mistake to a special cause when in fact the cause belongs to the system (common cause). (Also known as a Type I error)
2. Ascribe a variation or a mistake to the system (common causes) when in fact the cause was special. (Also known as a Type II error)

Types of Control charts

Mean Chart

In this chart the sample means are plotted in order to control the mean value of a variable

P-chart

A p-chart is an attributes control chart used with data collected in subgroups of varying sizes. Because the subgroup size can vary, it shows a proportion on nonconforming items rather than the actual count. P-charts show how the process changes over time. The process attribute (or characteristic) is always described in a yes/no, pass/fail, go/no go form. For example, use a p-chart to plot the proportion of incomplete insurance claim forms received weekly. The subgroup would vary, depending on the total number of claims each week. P-charts are used to determine if the process is stable and predictable, as well as to monitor the effects of process improvement theories. P-charts can be created using software programs like SQCpack and CHART runner.

Use p-charts when you can answer yes to these questions:

1. Do you need to assess system stability?
2. Is the data a count of nonconforming items per subgroup?
3. Can the counts be converted to proportions?
4. Are there only two outcomes to any given check?
5. Is the time order of subgroups preserved?

np chart

The use of attribute control charts arises when items are compared with some standard and then are classified as to whether they meet that standard or not.

The Np control chart is used to determine if the rate of nonconforming product is stable, and will detect when a deviation from stability has occurred.

There are those who argue that there should only be an Upper Control Limit (UCL), and NOT a Lower Control Limit (LCL) since rates of nonconforming product outside the LCL is actually a good thing. However, if we treat the LCL violations as another search for an assignable cause, we could learn where lower nonconformity rates lie and perhaps eliminate them further.

There is a difference between a "P Chart" and an "Np Chart". A P chart is one that shows the fraction defective (p), whereas the Np chart shows the NUMBER of defectives (Np). They are practically the same thing with the exception that an Np chart is used when the size of the subgroup (N) is constant, and a P chart is used when it is NOT constant.

Steps in Constructing an np Chart

• STEP #1 - Collect the data recording the number inspected (N) and the number of defective products (Np). Divide the data into subgroups. Usually, the data is grouped by date or by lot numbers. The subgroup size (N) should be over 50, and it is strongly recommended you stick with the constant sample size of 100 for subgroups.
• STEP #2 - Record the number of defectives on a chart or spreadsheet, along with the subgroup size.
• STEP #3 - Record the number of defectives for each subgroup and record on the data sheet. Then total both columns, from our example above you can see we had 272 defects, and 25 groups of 100 = 2500 total parts.

C chart

PURPOSE

Generates a (Poisson) counts control chart. The purpose of a c chart is to determine the stability of "counted" data when the opportunity is large compared to the actual number of defects (e.g. injuries per month or falls per month).

DESCRIPTION

A C chart is a data analysis technique for determining if a measurement process has gone out of statistical control. The C chart is sensitive to changes in the number of defective items in the measurement process. The “C” in C CONTROL CHART stands for “counts” as in defectives per lot. The C control chart consists of:

• Vertical axis = the number defective for each sub-group;
• Horizontal axis = sub-group designation.

The C chart assumes that each sub-group has an equal sample size (this sample size does not need to be specified). A sub-group is

• Typically a time sequence (e.g., the number of defectives in a daily production run where each day is considered a sub-group). If the
• Times are equally spaced, the horizontal axis variable can be generated as a sequence (e.g., LET X = SEQUENCE 1 N where N is the Number of sub-groups).

In addition, horizontal lines are drawn at the mean number of defectives and at the upper and lower control limits.

NOTES

• The distribution of the number of defective items is assumed to be Poisson. This assumption is the basis for the calculating the upper and lower control limits.
• The U CONTROL CHART is similar to the C CONTROL chart. The distinction is that the C CONTROL CHART is used when the material being measured is constant in area and the sub-groups have equal size. The U CONTROL CHART is used when either of these assumptions is not valid.
• The attributes of the 4 traces that make up the C control chart are controlled by the standard LINES, CHARACTERS, SPIKES, and BAR commands. Trace 1 is the response variable, trace 2 is the mean line, and traces 3 and 4 are the upper and lower control limits.
• Some analysts prefer to draw the response variable as a character or a spike rather than a connected line.

Application of control charts

Control charts are graphic illustrations of data collected from a process over time, thereby providing running records of performance. Examples of accounting processes where control charts are useful include the issuance of invoices and other accounting documents, the preparation of tax returns, and various auditing processes. Benefits of using control charts to monitor accounting processes include higher quality services, reduced costs, and higher profitability.

How Control Charts Work

Control charts are useful for analyzing and controlling repetitive processes because they help to determine when corrective actions are needed. Because they display running records of performance, control charts provide numerous types of information to management. For example, control charts are useful for:

1. Pinpointing errati or unpredictable processes;

2. Obtaining warning of impending trouble, such as an unexpected change in a process;

3. Evaluating product (service) consistency over time;

4. Decreasing performance variability in a process, thereby decreasing the level of post-process inspection of the output generated by the process;

5. Determining the cause of trouble when a process is generating output which has errors and mistakes; and

6. Knowing when a process is doing the best that can be expected from it. (1)

A control chart is a graph that contains a centerline, and upper and lower control limits. The centerline represents the process average. The control limits represent the upper and lower boundaries of acceptability around the centerline. The horizontal axis represents sample numbers or points in time, and the vertical axis represents measurements from samples.

Control charts are usually based on data collected from samples of a process. After a sufficient number of samples are drawn and the data is plotted on a control chart, the stability of the process is evaluated. A process which is stable is deemed to be "in control" whereas an "out of control" process is unstable, and therefore, unpredictable.

Many accounting and financial processes which are repetitive in nature can also be evaluated using similar charts. These processes might include:

1. Number of invoices processed per period;

2. Time required preparing a monthly statement;

3. Average age of accounts receivable;

4. Number of purchase discounts lost; and

5. Sales returns per salesperson, when commissions are based on the amount of gross sales.

Once accountants learn the basics of statistical quality control and how easy control charts are to prepare, they can readily identify other repetitive processes involved in the accounting function in which control charts will be useful as a control technique.

Benefits of Understanding Control Charts

Because many manufacturers are now using control charts to evaluate their processes, accountants have to understand statistical process control if they are going to continue to provide maximum services to their employers or clients. In addition, accountants will undoubtedly find many uses for control charts within their departments or firms. If the quality of accounting processes is improved by using statistical methods, firms should experience higher profitability. This increase in profitability will occur because of an increase in the quality of accounting services and a reduction in the costs incurred to provide the services. To remain competitive in today's environment, all departments, including accounting, must try to provide high quality services and products at the lowest possible cost.