Philippine Institute of Pure and Applied Chemistry

Philippine Institute of Pure and Applied Chemistry CONTROL CHARTS Dr. Ronald M. Fabicon

Learning Objectives The Control Chart Techniques State of Introduction Control Specifications Process Capability Six Sigma Different Control Charts Control Charts in Analytical Laboratories OUTLINE

LEARNING OBJECTIVES When you have completed this part of the training course 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

When you have completed this part of the training course you should: Be able to calculate the central value, trial control limits and the revised control limits for X bar 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 training 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. Know the statistical meaning of 6σ LEARNING OBJECTIVES

VARIATION The variation concept is a law of nature in that no two natural items in any category are the same.

VARIATION • 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.

VARIATION There is also a reported variation which is due to the inspection activity. Variation due to inspection should account for one tenth of the four other sources of variation.

VARIATION Variation may be due to chance causes (random causes) or assignable causes. When only chance causes are present, then the process is said to be in a state of statistical control. The process is stable and predictable.

Is a plot of a parameter being monitored (at the y-axis) versus run number (x-axis) Lines in the control chart: Mean line Warning Limits Critical/Action Limits CONTROL CHART

CONTROL CHART

Upper Critical Limit (UCL) = x + 3s Upper Warning Limit (UWL) = x + 2s Mean = x Lower Warning Limit (LWL) = x - 2s Lower Critical Limit (UCL) = x - 3s CONTROL CHART

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 CHART 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 Example of a control chart

Control Charts Figure 5-1 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 X bar 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 CHARACTERISTICS • The Quality Characteristic must be measurable. • It can expressed in terms of the seven basic units: • Length • Mass • Time • Electrical current • Temperature • Substance • Luminosity, etc

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.

DATA COLLECTION 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

TRIAL CENTRAL LINES Central Lines are obtained using:

TRIAL CONTROL LIMITS Trial control limits are established at ±3 standard deviations 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 subgroup size and are found in Table B of the Appendix.

TRIAL CONTROL LIMITS - SAMPLE pH meters in a certain analytical laboratory are calibrated daily at the start of the working day (8:00 AM). A standard pH 7.000 solution was read using the instrument at the end of the day. The following data were collected over a 25 day period. Determine center line and trial control limits.

TRIAL CONTROL LIMITS - SAMPLE

REVISED CENTRAL LINES

ACHIEVING THE QUALITY OBJECTIVE Continuing use of control charts, showing improved quality

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 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 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 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

OUT OF CONTROL CONDITIONS • Change or jump in level. • Trend or steady change in level • Recurring cycles • Two populations (also called mixture) • Mistakes

PATTERNS IN CONTROL CHARTS Some unnatural runs-process out of control

Philippine Institute of Pure and Applied Chemistry