OVERVIEW OF CONTROL CHART DEVELOPMENT | Six Sigma and Beyond: Statistical Process Control, Volume IV

In this section, we will discuss a general procedure and concerns for constructing and interpreting control charts. Some of the preparatory steps have already been discussed in the previous sections. The detailed discussion for specific charts will be found in Chapters 8, 9, and 10.

So, the question is, where does one begin? The answer of course lies with the level of preparation that one has undergone in identifying and characterizing the process and its needs. Some of the early issues and concerns in the development of control charts are:

Normalize the process.
State the purpose of the control chart.
Collect data from the process.
- Select the characteristic for study.
  - Customer's concerns
  - Process inefficiencies
  - Causal relationships
  - Operation parameters
- Establish a sampling plan.
  - Sample size
    - Risk
    - Type of data
  - Sampling frequency
- Recognize and assess measurement error.
- Ensure the integrity of the data.
Calculate control limits from the process data.
Interpret the process variation for stability and control.
Interpret the process data for capability.
Plan process improvement activities.
Continue the process improvement cycle.

NORMALIZE THE PROCESS

Unless the process has been normalized, control charts may show the operations to be unstable and inconsistent. Before developing a control chart, try to solve the obvious problems and concerns in the operational process or product design. Standardize the materials, tools, and setups within the specifications. Maintain a process log as a record of all significant process events (e.g., tool changes, machine rehabilitations, material lot changes, operator replacements ). Make the process log sheets a part of regular manufacturing practices.

The managerial environment should also be normalized. Decide by whom, when, and how the control chart data are to be collected, measured, processed , analyzed , and communicated. Unless these factors are discussed and established as a part of the production routine, the charts will not work. Implementation of control charts and process improvements is not spontaneous .

STATE THE PURPOSE OF THE CONTROL CHART

Before choosing the type, decide on the goal and purpose of the control chart. Because each type of control chart has its own advantages and disadvantages, it is important to select the chart type that is best suited to the job.

Control charts are divided into two general categories: variables -type control charts and attribute-type control charts. Table 7.1 identifies some of the most common charts and their categories.

Table 7.1: Common Charts and Their Categories
Data Type	Chart Name	Plotted Values
Variables	Xbar and R Chart Xbar and s Chart X and Moving R Chart Median and R Chart	Sample means and ranges Sample means and standard deviations Individual observations and moving ranges Sample medians and ranges
Attribute	p chart np chart c chart u chart	Proportion of defective units in the sample Number of defective units in the sample Number of defects per inspection unit Average number of defects per production unit

Variable-Type Control Charts

Variable-type control charts depend on variable data. Some of the general characteristics of these charts are:

They require continuous or measured data.
They provide very detailed information.
They are characteristic specific.
They are very sensitive to changes in the process.
They require a relatively small sample size (5 to 10 measurements per subgroup ).
They require skillful interpretation.

Attribute-Type Control Charts

Attribute-type control charts depend on attribute data. Some of the general characteristics of these charts are the following:

They require count-type data (unacceptable product must be observed ).
They summarize the overall quality level.
They are less sensitive to changes in the process.
They require a relatively large sample size (3 to 5 defective parts must be observed in each subgroup).
They are easy to construct and interpret.

Reasons to Construct a Variable-Type Control Chart

There are many reasons to construct a variable control chart, some of which are:

To learn about special variation, including when to take action and when to leave a process alone
To judge a process's ability to meet specifications (capability analysis)
To gain information about how to improve the manufacturing process
To add insight concerning the need to change measurement methods or material acceptance criteria

Reasons to Construct an Attribute-Type Control Chart

There are several reasons that an attribute chart should be constructed , some of which are:

To define the reject rate
To discover changes in the average quality level or rate of production
To call attention to exceptionally poor or superior quality production periods and to discover their causes
To find places and characteristics that may benefit from the use of variable-type control charts
To monitor many characteristics of process variation after a set of variable-type control charts have been eliminated

COLLECT DATA FROM THE PROCESS

To do any analysis for any process, one begins with data. To generate a control chart, one needs appropriate and applicable data as well. The process begins as follows :

Select the characteristic for study. Before collecting data, decide on a specific characteristic to monitor. This will be the focus of the control chart. Consider focusing on the following:
- Customers' concerns should be given top priority for study. Any subsequent production operations or the end-item users are considered customers.
- Production inefficiencies (scrap, rework , unfulfilled production schedules, etc.) should be studied with control charts. A production department's Pareto charts may help determine the most frequent troublesome areas.
- Study causal relationships because they may be easier to monitor and may provide faster feedback than do resultant performance characteristics. A fishbone diagram helps organize cause and effect relationships and a scatter diagram helps verify the relationships.
- Use production parameters and data collection points early in the process to prevent defects and defectives; they are leading indicators of quality outcomes .
Establish a sampling plan. Determine the amount and frequency of data collection.
- Establish sample size. Determine the amount of information that should be included in each subgroup. Consider the following cautions :
- Risk. When the sample size is large, the control chart will respond to changes in the process with great sensitivity. This is called "confidence." Balance the benefits of increasing the sample size against the increase in costs for data collection. A reduced sample size may cost less, but it increases the risk of an ineffective control chart.
- Type of data. Different types of data require different amounts of data for each subgroup. Variables-type data are very efficient and pack a lot of information into each measurement. Therefore, samples sizes for variable-type control charts are relatively small (approximately 5 to 10 measurements per subgroup). The selected sample size must be constant for variable-type control charts.
- Attribute data are not as efficient as variables data. They require a larger sample size to achieve similar levels of confidence. The sample size should be large enough to permit 3 to 5 defective parts to be observed in each subgroup. Although equal subgroup sizes are not required for some attribute-type control charts (p and u charts), the most quickly produced control charts (np and c charts) do require equal sample sizes.
Determine the sampling frequency.
- The purpose of any control chart is to detect changes in the process over time. The length of time between subgroups should be small enough that difference between the observed subgroups and the unobserved is considered insignificant. During the initial study period, there may be no time between subgroups (100% sampling). As information and confidence are gained , the time between subgroups may be increased.
- A meaningful and regular sampling frequency can be based on production volume rather than time (e.g., collecting a subgroup every 1000 parts rather than every 2 hours).
Recognize and assess measurement error.

Control charts require a standard procedure. Data must have the same meaning for all people at all times. Analyze the measurement process and quantify the magnitude of measurement error. Too much measurement error will cause the control chart to miss meaningful changes in the process.
Insure the integrity of the data.

Collect the measurements consistently and honestly. The most sophisticated analysis technique cannot draw a valid conclusion from false data. Time and training must be assigned for the collection and analysis of data.

CALCULATE CONTROL LIMITS FROM THE PROCESS DATA

To be able to figure out the voice of the process or the behavior of the process, control limits must be calculated. Control limits are calculated from observed process data. They indicate the amount of variation expected if only common causes of variation are operating in the process. Control limits are not specifications and should never be based on the product specifications. (In fact, control limits may be calculated when there are no specifications.) Specific steps and formulas for the different control limits are given in later chapters and in the appendix for the specific control charts.

INTERPRET THE PROCESS VARIATION FOR STABILITY AND CONTROL

If all of the data points are within the control limits and the data follow a random pattern, the process is stable and in control (see Figure 7.1).

Figure 7.1: A stable and in-control process.

When the control chart does not meet the above criteria, special causes of variation are present, and the system is out of control. The causes of the special variation must be studied and understood. Be careful: a process that is out of control is not stable and does not follow the expected pattern. Sometimes a process is out of control because improvements have been made. These out-of-control conditions must be understood and made a part of the regular process. At other times, an out-of-control process is a change for the worse . Identify and eliminate the causes of deterioration.

INTERPRET THE PROCESS DATA FOR CAPABILITY

The C _p index is appropriate for processes in which the mean is equal to the target value (midway between the specification limits). Processes with C _p = 1 produce about 2700 out-of-specification items per million, but this number decreases dramatically as C _p increases.

The C _pk index is appropriate for all processes, but it is especially useful when the mean is off target. (In case the mean is on target, C _p and Cpk are equivalent.) Processes with C _pk = 1 produce about 1350 out-of-specification items per million on the side nearest to target (and fewer on the other side), and again this number decreases dramatically as C _pk increases.

Both C _p and C _pk are only indices of process capability. However, they imply the probability of an item's being beyond specifications (and the ppm beyond specifications).

A 3-sigma process has C _pk = 1, whereas a 6-sigma process has C _pk = 2. In general, the distance from the process mean to the nearest specification limit in a k-sigma process is k ƒ .

Process capability compares the estimated distribution of a product to its specifications. Calculate the percentage of the distribution in and out of specifications (see Figure 7.2). Most organizations define a capable process as one that has a minimum of 99.73% of the population within specifications. If we add the long-term shift of 1.5 plus or minus sigma then we get a 93.32% accountability. The 6-sigma approach, on the other hand, defines the capability of the long term as a 4.5 sigma plus or minus 1.5 sigma (99.99966%).

Figure 7.2: A pictorial view of a distribution with specifications and the z-values.

Most processes may be described by the normal curve, but there are some that do not follow the normality criteria. A capability study is valid only if the process is stable and in control. If the process control charts show changing conditions, the process is out of control. Because out-of-control processes have different characteristics at different times, it is useless to estimate their capability levels. (Any calculation or conclusion made is useful only for the data used to perform that calculation; no generalization is possible.) The confidence level of such a study is zero (0).

PLAN PROCESS IMPROVEMENT ACTIVITIES

Improvement activities must be made a part of the regular manufacturing process. They must be deliberately planned, scheduled, and evaluated. The process must be pushed out of control by people's decisions and actions to improve.

CONTINUE THE PROCESS IMPROVEMENT CYCLE

For most companies in the 21st century, the corporate mission is to continually improve products and services to satisfy the customer. These improvements require constant work, even when all parts are within specifications. Common variation should be reduced so that the process approaches the best possible distribution.