Quality Improvement PowerPoint presentation to accompany Besterfield, Quality Improvement, 9e Chapter 6- Control Charts for Variables
The Control Chart Techniques State of Introduction Control Specifications Process Capability Different Control Charts Outline
When you have completed this chapter you should: Know the three categories of variation and their sources. Understand the concept of the control chart method. Know the purpose of variable control charts. Know how to select the quality characteristics, the rational subgroup and the method of taking samples Learning Objectives
When you have completed this chapter you should: Be able to calculate the central value, trial control limits and the revised control limits for Xbar and R chart. Be able to explain what is meant by a process in control and the various out-of-control patterns. Know the difference between individual measurements and averages; control limits and specifications. Learning Objectives
When you have completed this chapter you should: Know the different situations between the process spread and specifications and what can be done to correct the undesirable situation. Be able to calculate process capability. Learning Objectives
variation • The variation concept is a law of nature in that no two natural items are the same. • The variation may be quite large and easily noticeable • The variation may be very small. It may appear that items are identical; however, precision instruments will show difference • The ability to measure variation is necessary before it can be controlled
Variation There are three categories of variation in piece part production: • Within-piece variation: Surface • Piece-to-piece variation: Among pieces produced at the same time • Time-to-time variation: Difference in product produced at different times of the day
Variation Sources of Variation in production processes: Measurement Instruments Operators Methods Materials PROCESS INPUTS OUTPUTS Human Inspection Performance Tools Machines Environment
Variation Sources of variation are: • Equipment: • Toolwear • Machine vibration • Electrical fluctuations etc. • Material • Tensile strength • Ductility • Thickness • Porosity etc.
Variation Sources of variation are: • Environment • Temperature • Light • Radiation • Humidity etc. • Operator • Personal problem • Physical problem etc.
Control Charts • Variable 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)
Control Charts Continuous Numerical Data Categorical or Discrete Numerical Data Control Charts Variables Attributes Charts Charts R P C X Chart Chart Chart Chart
Control Charts for Variables The control chart for variables is a means of visualizing the variations that occur in the central tendency and the mean of a set of observations. It shows whether or not a process is in a stable state.
Control Charts Figure 5-1 Example of a control chart
Control Charts Figure 6-1 Example of a method of reporting inspection results
Variable Control Charts The objectives of the variable control charts are: • For quality improvement • To determine the process capability • For decisions regarding product specifications • For current decisions on the production process • For current decisions on recently produced items
Control Chart Techniques • Procedure for establishing a pair of control charts for the average Xbar and the range R: • Select the quality characteristic • Choose the rational subgroup • Collect the data • Determine the trial center line and control limits • Establish the revised central line and control limits • Achieve the objective
Quality Characteristic • The Quality characteristic must be measurable. • It can expressed in terms of the seven basic units: • Length • Mass • Time • Electrical current • Temperature • Subatance • Luminosity
Rational Subgroup A rational subgroup is one in which the variation within a group is due only to chance causes. Within-subgroup variation is used to determine the control limits. Variation between subgroups is used to evaluate long-term stability.
Rational Subgroup • There are two schemes for selecting the subgroup samples: • Select subgroup samples from product or service produced at one instant of time or as close to that instant as possible • Select from product or service produced over a period of time that is representative of all the products or services
Rational Subgroup The first scheme will have a minimum variation within a subgroup. The second scheme will have a minimum variation among subgroups. The first scheme is the most commonly used since it provides a particular time reference for determining assignable causes. The second scheme provides better overall results and will provide a more accurate picture of the quality.
Subgroup Size • As the subgroup size increases, the control limits become closer to the central value, which make the control chart more sensitive to small variations in the process average • As the subgroup size increases, the inspection cost per subgroup increases • When destructive testing is used and the item is expensive, a small subgroup size is required
Subgroup Size • From a statistical basis a distribution of subgroup averages are nearly normal for groups of 4 or more even when samples are taken from a non-normal distribution • When a subgroup size of 10 or more is used, the s chart should be used instead of the R chart. • See Table 6-1 for (total) sample sizes
Data Collection Data collection can be accomplished using the type of figure shown in Figure 6-2. It can also be collected using the method in Table 6-2. It is necessary to collect a minimum of 25 subgroups of data. A run chart can be used to analyze the data in the development stage of a product or prior to a state of statistical control
Run Chart Figure 6-4 Run Chart for data of Table 6-2
Trial Central Lines Central Lines are obtained using:
Trial Control Limits Trial control limits are established at ±3 standard deviatons from the central value
Trial Control Limits In practice calculations are simplified by using the following equations where A2,D3 and D4 are factors that vary with the subgroupsize and are found in Table B of the Appendix.
Trial Control Limits Figure 6-5 Xbar and R chart for preliminary data with trial control limits
Figure 6-6 Trial control limits and revised control limits for Xbar and R charts
Achieve the Objective Figure 5-7 Continuing use of control charts, showing improved quality
Sample Standard Deviation Control Chart For subgroup sizes >=10, an s chart is more accurate than an R Chart.Trial control limits are given by:
State of Control Process in Control • When special causes have been eliminated from the process to the extent that the points plotted on the control chart remain within the control limits, the process is in a state of control • When a process is in control, there occurs a natural pattern of variation
State of Control Figure 6-9 Natural pattern of variation of a control chart
State of Control Types of errors: • Type I, occurs when looking for a special cause of variation when in reality a common cause is present • Type II, occurs when assuming that a common cause of variation is present when in reality there is a special cause
State of Control When the process is in control: • Individual units of the product or service will be more uniform • Since the product is more uniform, fewer samples are needed to judge the quality • The process capability or spread of the process is easily attained from 6ơ • Trouble can be anticipated before it occurs
State of Control When the process is in control: • The % of product that falls within any pair of values is more predictable • It allows the consumer to use the producer’s data • It is an indication that the operator is performing satisfactorily
Common Causes Special Causes 45
State of Control Figure 6-11 Frequency Distribution of subgroup averages with control limits
State of Control When a point (subgroup value) falls outside its control limits, the process is out of control. Out of control means a change in the process due to a special or assignable cause.A process can also be considered out of control even when the points fall inside the 3ơ limits
State of Control • It is not natural for seven or more consecutive points to be above or below the central line. • Also when 10 out of 11 points or 12 out of 14 points are located on one side of the central line, it is unnatural. • Six points in a row are steadily increasing or decreasing indicate an out of control situation
Patterns in Control Charts Figure 6-12 Some unnatural runs-process out of control
State of Control • Simplified rule: Divide space into two equal zones of 1.5σ. • Out of control occurs when two consecutive points are beyond 1.5σ. • See Figure 6-13
Patterns in Control Charts Figure 6-13 Simplified rule for out-of-control pattern
Out-of-Control Condition • Change or jump in level. • Trend or steady change in level • Recurring cycles • Two populations (also called mixture) • Mistakes
Out-of-Control Patterns Change or jump inlevel Trend or steady change in level Recurring cycles Two populations