Chapter 7- Additional SPC Techniques for Variables Quality Improvement Chapter 7- Additional SPC Techniques for Variables PowerPoint presentation to accompany Besterfield, Quality Improvement, 9e 1

Outline Continuous and Batch Processes Multi-Vari Chart Short-Run SPC Gauge Control 2

Learning Objectives When you have completed this chapter you should be able to: Explain the difference between discrete, continuous, and batch processes. Construct and use a group chart. Construct a multi-vari chart. Calculate the central line and control limits of a specification chart 3

Learning Objectives-Continued When you have completed this chapter you should be able to: Calculate the central line and central limits for a Zbar & W and Z & MW charts Explain how to use precontrol for set up and run activities. Determine a PTPC chart Understand the concept of GR&R 4

Continuous Processes Usually operates 24 hrs a day, 7 days a week, stops for scheduled maintenance. Often involves a conveyor or moving assembly line Associated with product involving hazardous materials

Continuous Processes Examples Paper-making machines Oil refineries Soft drinks (continuous then discrete) Control charts for each value (multiple stream output)

Continuous Processes It is extremely important to have knowledge about the process and objectives for the control chart. When it is difficult to obtain samples from a location, sensors may be helpful to collect data, compare to control limits, and automatically control the process.

Continuous & Batch Processing A good example of a continuous process is depicted by the paper-making process. They operate 24 hrs a day, 7 days a week, and stop only for scheduled maintenance or emergencies.Observed values are taken in the machine direction(md) or cross-machine direction (cd). 8

Continuous & Batch Processing If the flow of pulp is controlled by 48 valves, then 48 md control charts would be required to control each valve.In this case it is very important for the practitioner to be knowledgeable about the process and have definite objectives for the control chart. 9

FIGURE 7-1 Paper-Making Machine

FIGURE 7-2 Paper Web and Observed Valves for md and cd Control Charts MD = machine direction CD = Cross-machine direction FIGURE 7-2 Paper Web and Observed Valves for md and cd Control Charts

Group Chart Eliminates the need for a chart for each stream; however, it does not eliminate the need for measurements at each stream Uses the same methodology outlined in Chapter 6, 25 subgroups for each stream. Use lowest and highest averages for Xbar chart and the highest range for the R chart. Each stream has a number.

Group Chart Any out-of-control situation would call for corrective actions We have the out-of-control situation when the same value streams gives the highest or lowest value r times in succession

Group Chart Each stream has the same target Same variation See Table 7-1 for the r values The technique is applicable to machines, test equipment, operators, or suppliers as long as: Each stream has the same target Same variation Variation is as close to normal as required by conventional Xbar and R charts.

Batch Processes Paint, soft drinks, bread, soup, etc SPC of batches has two forms: Within batch variation Only one observed value of a particular quality characteristic can be obtained They need to be obtained at different locations within the batch Between-batch variation Does not always occur

FIGURE 7-3 Example of Multiple Streams: A Four-Spindle Filling Machine

Batch Chart It is not a control chart, it might be more appropriately called a run chart Can provide information for effective quality improvement

Batch Chart Figure 7-4 Batch chart for different batches with differet specifications

Multi-Vari Chart For detecting different types of variation that are found in products and services The chart will lead to a problem solution much faster than other techniques Shows the different types of variation within a single unit or service (within unit variation, unit-to-unit variation, time-to-time variation)

Multi-Vari Chart Procedure: Select 3 to 5 consecutive units Plot the highest and lowest observed value of each piece Draw a line between them Repeat the process

Short-Run SPC Specification Chart Used for small lot sizes – common in JIT Gives some measure of control and a method of quality improvement Central line and control limits are established using the specification σ = (USL-LSL) / 6 Cp JIT = Just in time USL – LSL instead of range

Specification Chart Cp is unknown since we do not have enough data This is an approximation. Do 25.00 +/- .12 These limits represent what we would like the process to do.

Cp = 1, 1.33, .67 FIGURE 7-7 Comparison for Different Capabilities for Specification Chart

Deviation Chart Deviation Chart The plotted points are the deviation from the target Even though the target changes, the central line for the X chart is always zero Because the target changes, we require the variance (S2) of the different targets or nominal to be identical. This requirement is verified by ANOVA or by using Target changes from different runs with different targets ANOVA = Analysis of variances Slide 18

Deviation Chart Advantages: Provide the opportunity to convey enhanced information Can plot different quality characteristics on the same chart Can use this on Xbar R charts too.

Deviation Chart Example 7.2, 7.3 HW 5, 6, 7 Figure 7-8 Deviation chart for individuals (X’s) and moving range(R’s)

Short-Run SPC

ZBar and W Charts Very good for short runs Different quality characteristics such as length, width etc. may be plotted on the same chart Can be used to monitor an operator’s daily performance Can track an entire part history Subgroup size MUST remain constant Calculations are more involved

Zbar and W Charts Those are very good for short runs LCLr < R < UCLr D3Rbar < R < D4Rbar D3 < R/Rbar < D4 LCL xbar < X bar < UCLxbar Xbarbar – A2Rbar < Xbar < Xbarbar + A2Rbar etc

Zbar and W Charts Figure 7-10 Zbar chart W Chart CL = 1 and UCL = D4, LCL = D3 Since the scale and CLs are the same, we can plot different characteristics Figure 7-10 Zbar chart

Z and MW Charts MW chart uses the absolute value CL always the same MW chart uses the absolute value Individuals values are plotted

FIGURE 7-11 Central Lines and Control Limits for Z and MW Charts

Precontrol Was developed originally with machining operations in mind. Operator faced with the problem of first setting up the machine and then deciding if the machine is ready for full production. Small lot sizes with each piece taking a long time to produce.

Precontrol Well suited for machining operations where one can devise simple feedback algorithms to bring the process back on target. Requires operators who are very knowledgeable about the process.

Precontrol Steps for the construction: Be sure that the process capability is less than the specifications. PC lines are established to divide the tolerance into five zones (Figure 7-12) The PC procedure has two stages: Start-up Run Cp>1 This is management’s responsibility

Precontrol Show for spec of 3.15 +/- .1 mm For Cp >1.33 middle part is almost 1. Normal Distribution, Cp and Cpk = 1.00 or greater. Specifications (Print Tolerance) at 6σ

Precontrol PRE-Control Rules: Start up Process 5 consecutive units in green zone –o.k. to run 1 yellow, restart counting 2 yellow in a row, adjust the process 1 red, adjust the process < 5 signifies: Process capability << 1 PRE-control is not appropriate

FIGURE 7-13 Precontrol Procedure

Precontrol Precontrol Rules cont’d: Sampling n = 2 units Sample six pairs between adjustments. See Table 7-2 stoppages 1 unit in red zone 2 consecutive units in opposite yellow zone 2 consecutive yellow zones , process adjusted and procedure goes back to start up

FIGURE 7-16 Precontrol Chart

Precontrol Precontrol can be used for single specifications Precontrol can be used for attributes Precontrol is also used for visual characteristics by assigning visual standards for the Precontrol lines For single spec, use ¾ of the tolerance Attributes are yes/no decisions Advantages Short or long productions No recording or plotting necessary Applicable to startup Works with tolerance vs control limits Applicable to attributes Simple to understand Monitoring only, not problem solving!!!!

% Tolerance Precontrol Chart Z Charts: Ability to accommodate more than one quality characteristic We can combine Z chart into one technique by the use of percent tolerance precontrol chart (PTPCC) Target or nominal X*= (X – nominal) / [(USL-LSL)/2] A negative value indicates that the observed value is below the nominal Percent tolerence precontrol chart vs target R

Out of control at 11:30

Gage Repeatability and Reproducibility Gage Repeatability and Reproducibility (GR&R) studies provide information on measurement system performance by analyzing measurement error from various sources. Typically the sources of variation are divided into three categories: part-to-part, operator or appraiser, and gage or equipment. In some instances another category, interaction between parts and operators, can provide additional information about the gaging process.

Gauge Control All data have measurement errors An observed value has two components Observed value = True value + Measurement error Total Variation = Production Variation (process) + Measurement Variation Measurement Variation = Repeatability (equipment variation) + Reproducibility (inspector or appraiser variation)

Gauge R&R METHODS: In instances such as automated measuring processes, the GR&R studies are not affected by operator influence. These data then are analyzed using a calculation method.

Gauge R&R Gage has to be calibrated using standards Data is collected 2 or 3 appraisers 2 or 3 trials 10 parts Part characteristic is measured in a random order These numbers are considered optimum Trials should be in random order

Gauge Control The preferred method is to use ANOVA, which is discussed in Chapter 13 A P/T is determined which compares the measurement variation (P) to the total variation (T)

Gage Control Guidelines for acceptance of GR&R using the P/T ratio: Under 0.10 (10%) error Gage system is satisfactory 0.10 to 0.30 (10% to 30%) error May be acceptable based upon importance of application, cost of gage, cost of repairs, etc. Over 0.30 (30%) error Gage system is not satisfactory. Identify the causes and take corrective action >0.3: May have bad parts that are declared good or good parts that are declared bad.

Evaluation If repeatability is large compared to reproducibility: The gage needs maintenance The gage should be redesigned to be more rigid The clamping or location for gaging needs to be improved There is excessive within-part variation

Evaluation If reproducibility is large compared to repeatability: The operator needs to be better trained in how to use and read the gage Calibrations on the gage are not legible A fixture may be needed to help the operator use the gage consistently HW 13,16

Homework Chapter 7 Problems 5, 6, 7, 13, 16, 17 HW 13,16

Computer Program EXCEL program files on the website solve for Zbar & W charts and PTPC chart. GR&R (Gauge Repeatable and Reproducibility) can be affected by environmental factors such as temp, humidity, air cleanliness, and should be controlled