Chapter 7 -Control Charts for Variables. Lecturer : Asst. Prof. Dr. Emine ATASOYLU

Transcription

1 Chapter 7 -Control Charts for Variables Lecturer : Asst. Prof. Dr. Emine ATASOYLU

2 Control Charts for Variables Chapter 6 Introduced the fundamentals of control charts. Chapter 7: details of control charts for variables will be covered. Charts for: Mean and Range (X and R) Mean and standard deviation (X and S) Moving Range (MR) will be covered.. Control charts for attributes (p-chart, np-chart, c- chart, u-chart, U-chart) will be covered in chapter 8

3 Variables are quality characteristics that are measurable on a numerical scale (like length, thickness, diameter, breaking strength, temperature, acidity, and viscosity). We must be able to control the mean value of a quality characteristic as well as its variability. The mean gives an indication of the central tendency of a process, and the variability provides an idea of the process dispersion.

4 Effect of the change in process mean and sd was covered before A change in the process mean of a quality characteristic may change the proportion p of parts that do not meet specifications. (remember that when the process mean increases the normal distribution shifts to the right). A change in the process standard deviation (dispersion) will change the proportion of output that does not meet the specifications (remember that t the spread increases as the sd increases, increasing the proportion not conforming). Control charts aid in detecting such changes in process parameters (mean and standard deviation).

5 Variables provide more information than attributes do. Remember that attributes deal with qualitative information such as whether an item is nonconforming or what the number of nonconformities in an item is. Attributes do not show the degree to which a quality characteristic is nonconforming. Ex: Specifications on the length of a part 40±0.5 Part with length 40.6 is nonconforming Part with length 42 is nonconforming BUT the degree to which two lengths deviate from the specifications is lost in attribute information. However variables which are measurable on a numerical scale show the degree to which the quality characteristic deviates from specifications (or control limits)

6 Cost of obtaining variable data is usually higher than attribute data. Attribute data is collected by means such as go/no-go gauge, which are easier to use and therefore less costly! Total cost of data collection=fixed cost + variable cost Fixed cost: cost of inspection equipment Variable cost: Cost of inspected units (the more units inspected the higher the variable cost)

7 Selection of characteristics ti for investigation 1) Select a few vital quality characteristics from the many candidates. A paretoanalysis helps clarify which hquality characteristics are the important quality characteristics; the ones that have higher priority. Priority=those characteristics that cause more nonconforming items and increase cost.. 2) Set up a scheme for obtaining data: for monitoring cutting speed, depth of cut, and coolant temperature (process characteristics that has relationship or has an impact on product characteristics) Monitoring process variables through control charts implicitly l controls product characteristics. Read section preliminary decisions

8 74C 7.4 Control lcharts for Mean and dr Range (X and dr)

9 Steps to develop control charts continued..

10 Steps to develop control charts continued.. Step 4: Draw the center line and the estimated control limits. Plot the values of the range on the control chart for the range. Determine whether the points are in statistical control. Investigate the special causes associated with the out of control points (if any). Take remedial action to eliminate i special causes. Repeat the same for the X-chart.. R-chart is usually analyzed before the X-chart to determine out of control situations. R-chart reflects process variability and should be brought into statistical control first. If R-chart shows an out of control situation ti the limits it on the X-chart may not be meaningful.

11 Steps to develop control charts continued.. Step 5: Delete the out of control point(s) for which remedial actions have been taken to remove special causes and use the remaining i samples to determine the revised center line and control limits for X- and R-charts. These are known as revised control limits. Cycle of obtaining information determining trial limits finding out of control points identifying and correcting special causes determining revised control limits.. Continues! This ongoing process is a critical component of continuous improvement

12 Steps to develop control charts continued.. Step 6: Implement the control charts The X- and R- charts should be implemented for future observations using revised center line and revised control limits. The charts should be displayed in a place where they will be visible to operators, supervisors, and managers. Statistical i process control will illbe effective only if everyone is committed to it (from the operator to the CEO)

13 Example 7.1 consider a process by which coils are manufactured. Samples of size 5 are randomly selected from the process, and the resistance values (in ohms) of the coils are measured. The data values are given in the following table. Coil resistance data Sample Observations (ohms) X R Comments 1 20, 22, 21, 23, , 18, 22, 20, , 18, 20, 17, New Vendor 4 20, 21, 22, 21, , 24, 23, 22, , 20, 18, 18, , 20, 19, 18, , 18, 23, 20, , 20, 24, 23, , 19, 20, 20, , 20, 23, 22, , 21, 20, 22, , 22, 19, 18, , 21, 22, 21, , 24, 24, 23, , 20, 24, 20, , 18, 18, 20, , 24, 22, 23, , 19, 23, 20, , 21, 21, 24, , 22, 22, 20, , 18, 18, 17, high temperature 23 21, 24, 24, wrong die 24 20,22, 21, 21, , 20, 21, 21, sum:

14 Eqns to calculate l Mean and Range ( X and R) of each sample

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16 Find revised control limits after remedial actions were taken for causes of plots 3, 22 and 23 Delete samples 3, 22, 23 and find revised control limits and center line for the X and R charts: Revised center line R=72/22=3.273 UCL R =D 4 R=(2.114)(3.273)=6.919 LCL R = D 3R=(0)(3.273)=0 Revised center line: X=459/22= UCL X= X + A 2 R= (0.577)(3.273)= ) 753 LCL X = X - A 2 R= (0.577)(3.273)= Sample 15=22.80 slightly above the revised UCL.. Further investigation, no special causes found (identified) for this.