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Process improvements can lead to changes in specification limits, but this is not an absolute set rule. In some cases, process improvement may be initiated to achieve better results or adapt to changing requirements, especially to extend or change specification limits. Here are some cases where process improvements can lead to changes in specification limits: Example: If we are running any process with the As- is methodology and we find that the the data points during inspection shows that the process are lying beyond the limits. So the plant team decides to improve the running process by means of improving the machine condition and also with some addition of Low cost automation, thereafter taking data shows that The process are now with better tolerances and best quality, resulting in revised specification limits to reflect improved performance.

Process Capability and performance (Pp, Ppk, Cp, Cpk) basically these are indicators of a process relating to process dispersion and process centering. Process capability is a statistical measurement of a process’s ability to produce parts within specified limits consistently. In other way we can say that it is the ability of the process to meet the design specification for a service or a product. Cp is basically also called as process capability Pp is basically also called as process performance In the Measure phase the focus is on evaluating the current state of the process and understanding its ability to meet customer needs. In this step, it is recommended to use process capability indices (Cp, Cpk) to determine the basic capability and identify areas for improvement. In the Control phase the focus shifts to implementing and maintaining process improvements. Process performance indices (Pp, Ppk) are more important at this stage to monitor ongoing performance and ensure that the process can still meet customer requirements.

If an "Caution" results comes out as a inference in attribute agreement analysis, this is a signal to investigate the source of the incompatibility and make the necessary corrections. These improvements may include 1. Providing clearer instructions to raters 2. Additional training, or improving the rating process to achieve better agreement and reliability in rating characteristics. The ultimate goal is a reliable measurement system to ensure consistent and accurate property evaluation, which is critical for quality control and decision-making processes. • Kappa value = the degree of agreement made by multiple appraisers when assessing the same samples/parts • How much better is your assessment compared to guessing – If you flipped a coin and you guessed heads or tails, you would be right about 50% of the time by chance • Kappa >= 0.9 means that you can accept the result or there is good agreement • Kappa value between 0.7 and 0.9 means that you can accept the result but with a caution • Kappa <=0.7 is not at all acceptable

Z-score : It basically is the most commonly used measure of process capability in six sigma. It usually indicates the number of standard deviation fitting between the mean and the specification limit Z within : Z within measures the ability of a process in a specific subgroup or sample. It evaluates how well a process performs against its sample data. Formulae used : z= (X-Xbar)/s Where : X represents the value which needs to be evaluated X bar represents the sample mean S represents the sample one standard deviation Z overall : Z overall measures the overall process capability, its basically gives us an idea that how a particular process is performing irrespective of subgroups. Formulae used : z = (x – μ) / σ Where : X represents the value which needs to be evaluated μ represents the overall process mean σ represents the overall process one standard deviation The option of selecting the right Z score in a DMAIC project depends on the focus, data structure, and goals of the project. Both metrics are valuable for process improvement, but provide different perspectives on process capability and efficiency. It is important to choose the one that meets your project goals and provides the most relevant insights for your improvement efforts. However we give better preference to Z overall As it provides a complete picture of the ability of the process to meet customer requirements in all subgroups or categories. This can be valuable if your primary goal is to evaluate the overall performance of the entire process and determine whether it meets your organization's standards or customer expectations.

The pooled standard deviation is considered especially in the case - if we have two or more than two groups and we also have the condition that the standard deviations of both groups are approximately the same, then we try to take the standard weighted average deviations. of them. groups Now if we consider the two groups as group1 and group2, where Group 1 Group 2 Sample size (n1): 15 Sample size (n2): 19 Standard deviation (s1) : 6.4 Standard deviation (s2) : 8.2 Now that we know the above formulas to calculate the PSD of these two groups Sum standard deviation = √ (15-1) 6.42 (19-1) 8.22 / (15 19-2) = 7.466 Note how the pooled standard deviation (7.466) is between the Group 1 (6.4) and Group 2 (8.2) values. This indicates that the population standard deviation is specifically the weighted average between the two groups. Steps to calculate the pooled standard deviation 1.Calculate the difference between each value and the means of that group. 2. Square those differences. 3. Add them all together (for all groups). 4.Divide by the number of degrees of freedom (total sample size minus the number of groups). 5. Take the square root of the last number.

OEE efficiency takes into account performance loss, which takes into account everything that makes the production process work at the highest possible speed while it is running (including both slow cycles and small stops). The decrease in working capacity is caused by, for example, machine wear, poor quality materials, feed failures and blockages. Efficiency is calculated by dividing the total by the driving time and comparing it to the ideal driving speed or performance = (total / driving time) / ideal driving speed. For example, If you produced 30,000 pieces (total) in 400 minutes and your ideal operating speed is 80 parts per minute, your throughput is calculated by dividing 30,000 pieces by 400 minutes and dividing that number by 80 parts per minute, which equals 0.9375 or . 93.75% throughput. In other words: (30,000 counts / 400 min runtime) / 80 parts per minute = 93.75% throughput. It is important to note that performance should never exceed 100%. If the performance exceeds this threshold, it may mean that the ideal driving speed is too low. Common methods used to miscalculate performance : Ignoring Downtime: One common mistake is to ignore downtime when calculating performance. Failure to properly account for downtime can lead to overestimation of equipment performance. Example: Suppose a machine produces 100 units per hour, but experiences an unexpected downtime of 30 minutes during that hour. If you calculate performance based only on units produced during an operation, you would mistakenly assume that the machine is operating at 100 degrees of capacity. Avoid: Efficiency should consider both operational time and ideal cycle time. In this example, the throughput calculation should consider that the machine only worked 30 minutes per hour, resulting in 50% throughput (actual production rate / maximum potential rate). Omitting set-up and change times: Another mistake is to omit set-up and change times from the calculation. These times are important to determine the efficiency of the machine. Example If you only consider the time the machine is actively producing and don't consider the time it takes to set up, it can artificially inflate the performance meter. Avoid: Allow for setup and changeover times when calculating total time available for production. The performance should reflect the actual production time of the machine.

Overall Equipment Effectiveness (OEE) is a critical metric used in manufacturing to evaluate the effectiveness and efficiency of manufacturing processes. It is calculated as the product of three main parameters: availability, performance and quality. In particular, quality is an integral part of OEE and measures the ratio of good parts produced to the total number of parts produced. Miscalculation of OEE quality can occur in a number of ways, resulting in artificially inflated OEE numbers. Here are some common pitfalls and ways to avoid them, along with relevant examples. Inadequate waste data: One common mistake is not accurately counting all defective or discarded products. If only a few defects are recorded, the quality indicator is imprecisely high. Example: Imagine a production line that produces 1000 devices per day. During quality control, 100 devices are discovered to be defective and are removed. However, only 50 of these failures are recorded. If you use the errors recorded in your quality calculation, you would mistakenly assume 95% quality (950 good widgets out of 1000), resulting in an artificially high OEE value. Avoidance: Ensure that all defects and waste are accurately recorded and included in the quality calculation. Exclusion of reproduced parts: Some organizations may not consider reproduced parts in their quality calculations. If reworked parts are not counted as defects, this can increase the quality gauge. Example In the production process, 50 devices out of 1000 are initially found to be defective and sent for repair. After being rewritten, 40 of them are kept and are considered "good". If these reworked parts are not considered as defects, the quality calculation would erroneously give a high quality percentage. Avoidance: Include repaired parts in total defects when calculating quality. Overly generous tolerance thresholds: Setting too high tolerance thresholds for what is considered a "good" product can artificially inflate quality. If too many truly defective products are considered accepted, this leads to a false indication of quality. Example: If a manufacturing process allows for a 20 percent deviation from ideal product specifications, many subproducts can still be classified as "good," resulting in a high quality score. Avoidance: Define clear and realistic tolerance limits that closely match product quality standards. Accounting for process variability: Sometimes manufacturing process variances are not considered in the quality calculation. Failure to account for changes can lead to overestimation of quality. Example: In a continuous production process, if some products are produced above the standard quality and others below, but the quality indicator is calculated only on average, this can artificially increase the quality percentage. Avoidance: Consider variability in product quality by calculating quality from individual product quality data or within control limits. Calculate the quality exactly by following the following formula: Quality = (total number of parts produced / total number of parts produced) × 100 Accurate data collection and a clear understanding of the defective part are critical to avoid OEE inflation due to incorrect quality calculations. It is important to continuously monitor and improve both product quality and the accuracy of data used in OEE calculations to achieve significant improvements in production operations.

Mann Whitney Test T- test Assumptions There is no requirement of 1. Random data 2.Depend data need not to be normal 3. Variance need not to be equal as prerequisite 1. Data needs to be continuous 2.Data variance in each group should be similar 3.Dependent data should be normally distributed an whitney test is most suitable in the case when Our dependent data i.e (Y) is continuous but non normally distributed and we have two groups of X factors and we want to test the significance level of X / find that wether X is having impact on Y or not i.e the medians of X are similar of different.

1-sample Sign test 1-sample Wilcoxon test Assumptions In any 1sample sign T test all dependent variables (Y) should be continuous, normaly distributed In any 1 sample wilcoxon test all dependend variables should be continuos,but non normal Advantages As the data required is less for conducting the test, so data can be collected easily Ex. If we want to see that the mean of length of shaft manufactured matched the standard. As this test can be performed on datas which are non parametric also,so the range of this test is more comparing to 1 sample sign test. Limitations In case the sample size is ver less then using this test is not useful If many measurments have same values then this test will mislead in inference Application If the data is collected from a single group and we want to know that the mean of this data are different from that specified by standard Where the data's have failed the nomality test , and we want to compare the before and after condition of the score of the same individual