Assignment-3

I Monalisa 130186

A control chart is a graphical display which measures quality characteristic. The quantity that has to be plotted is measured on vertical axis and samples are taken on the horizontal axis. All quality control charts have a midpoint (or centerline) which corresponds to the process average which is the mean of the normal distribution. A horizontal line is plotted as dotted line but can be reversed and plotted as a central dotted line. Upper control limit and lower control limit lines are present above and below to this dotted line which represent three standard deviations above and three standard deviations below the process mean . Data is provided about the X Bar and Range control charts , it shows the information about the improvements made on metal casting process after the completion of initial study on its capability. In this considered sample size is n=5, and the specified quality specification is 3.5 ± 0.10mm. As well Xbar and Range graphs are plotted regarding the data collected. The information is passed to the manager about the data collected on the new improvements made in metal casting. As an informed manager, I check the data depending on the requirements and make sure that every reading is within the quality specification or not from the graphs it was clear that everything is within the specified quality specifications i.e., from X Bar chart. As every reading is within the tolerances or quality specifications, that the process is capable at present. The approach is perfect till now as everything goes normal and no case of excluding the limits aspect. Different steps are followed by the employees to study the improvement in the process Step 1 : Selection of the Quality Characteristic ●

Inspect after operations that are likely to produce defective items to ensure that no more work will be performed on faulty items. Inspect before costly operations so that costly work will not be performed on defective Inspect prior to those operations where faulty items are likely to cause production problems (such as breaking or jamming a machine).

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Inspect before operations that might cover up a defect (such as painting, assembly,etc.).

Step 2: Developing the Quality Plan · The purpose of quality planning should be to establish an economic balance between the cost of measurement and the value of the measurement. The general rule is to inspect as little as possible while ensuring product quality. Quality plans along with production plans are primarily documented on the work order. The work order lists all production steps, inspection points, references the drawings, specifications, procedures, instructions and standards that contain information required for production and inspection. Quality plans should contain as many of the following elements as possible (usually on the work order).

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Step 3: Choosing the type of Control Chart This step is divided into two sub steps (of course it couldn’t be simple). First is determining which category of chart to use – variables or attributes. The second step is choosing which type of variable or attribute chart to use (there are at least 27 options to choose from). Step 4: Choosing the Rational Proper Sample Size. · Actually there are two sample sizes involved in control charts: the total sample size needed to start –up the chart, and the subgroup size. The total start-up sample size normally used is 25 subgroups. Thus if the subgroup size is 4, the total start-up sample size is 100. In order to be statistically viable the start-up sample size should consist of 100 or more measurements or observations. Some special charts do use less, which is one reason they should be used with a degree of caution. Step 5: Collection of the Data Any sample in order to properly represent the population characteristics, must be unbiased (random, independent and homogeneous). In meeting these criteria, subgroups can be selected at one time or

over a period of time. The instant time method is usually preferred because it provides a time reference for pinpointing assignable causes. If the instant time method is used, the inspector measures several subgroups of parts at random times during the day. That is each subgroup is randomly chosen but the subgroup itself consists of consecutive units produced at the random time chosen. If the purpose is to gather enough data for the construction of the control chart, the measurements are recorded until enough observations are made, after which the chart is made and the subgroup averages recorded. Data are usually gathered by the inspection function as a normal part of their regular duties or by the operator themselves if a complete SPC program is in effect.

Step 6: Determining the Trial Control Limits and the Chart Midpoint. · Control limits are values that are plus or minus three sigmas (s’s) from the central value, or midpoint. Therefore if the midpoints and limits have been properly determined and the process is properly operating, 99.73% of all subgroup averages will fall between these control limits. Any one average has only a .027% chance of being outside these limits. All statistical quality control charts have a midpoint or centerline which corresponds to process average (the m) and an upper and lower control limit which corresponds to the ± three standard deviations from this midpoint or centerline. Step 7: Determining the Revised Control Limits and Chart Midpoint. · Trial control limits are calculated first for the entire sample, after which the out-of-control subgroup means (those that are either above the upper limit or below the lower limit) are discarded and the limits recalculated. Before any values can be discarded, they must first be proved to be out of control (have assignable causes). If not they should not be discarded for revised limit calculation. Please note that only 27 subgroup means out of 10,000 can be outside of the control limits. If several subgroup means are outside the limits and no assignable causes can, at first, be found, it is far more likely that the search for assignable causes had been flawed. Under these conditions, the search should probably be expanded and continued.

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Step 8: Constructing the Revised Control Chart. · Control charts are just graphs of the subgroup means (averages) with the central value shown as a

solid line and each limit shown as a dotted line. ● All control charts are constructed from the basic normal curve model. Control charts for variables use the normal curve model direct, while attributes charts use the normal curve approximation to the binomial. Control charts are normally only constructed for revised limits only. Step 9: Continue to Use the Charts. · Once the revised control chart is constructed, all subgroup means (even out-of-control values) are entered on the chart, and the chart is displayed conspicuously at the job site. Samples of the same size (subgroup size) are measured periodically and charting is continued. The chart represents a continuous picture of the process improvement. (b) Initially it looks clear, appropriate and better results or solution there is a case of having problem in future. In case unexpected problem suddenly it take time to gather the data and analyse to previous solution its more complicated and time taking to solve a problem in the middle or after some time. As, the improved process is working nice and extracting the good results at present and have to confirm either the improvements are sufficient and effective enough for the long run, have to make a test for statistical control 1st step of the test is done by plotting the X bar and R charts we can observe the graph and say that the result is satisfying the requirements, as it was satisfying all the initial ten steps. Operational Control is used to detect the out of control conditions.

A) Cp =1.25 σ =? for X bar= 0.3010 cm USL=X bar + R USL=0.3010+0.015=0.316 LSL=Xbar-R LSL=0.3010-0.015=0.286 Cp= USL-LSL/6 σ

1.25= 0.316-0.286/6 σ σ = 0.004 for X bar = 0.3010 cm For X bar= 0.2980 USL=X bar + R USL=0.2980+0.015=0.313 LSL=Xbar-R LSL=0.2980-0.015=0.283 Cp= USL-LSL/6 σ 1.25= 0.313-0.283/6 σ σ = 0.004 for X bar = 0.2980 cm B) Cpm=1.25 for X bar = 0.3010 Cp= USL- μ/3σ 1.25=0.316- μ/ 3 * 0.004 μ = 0.301 Cpm= USL-LSL/6 √σ2 + (μ − t)2 1.25=0.03/6 √σ2 + (0.301)2 σ2 =− 0.548 Here, Cpm = 1.25 and variance σ2 =− 0.548 By this we can state that the process is capable by decrease in variance.