Process Optimisation & Improvement PDF

Process Optimisation & Improvement 1 Process Optimisation & Improvement 2  Process Optimisation & Improvement Process Control is to evaluate the VARIATION of a process ove...

Process Optimisation & Improvement 1 Process Optimisation & Improvement 2  Process Optimisation & Improvement Process Control is to evaluate the VARIATION of a process over a period of time. It monitors the STABILITY of a process. The Goal of SPC (Statistical Process Control) is to reduce or eliminate the variation in the process. Control Charts (which is the main topic for SPC) are useful for monitoring the STABILITY of process, to IDENTIFY the assignable VARIATION. With the technical capability to remove the assignable causes, the quality of the process will be improved. 3  Process Optimisation & Improvement Defect & Defective A product may have many defects – imperfections. But a product is not defective unless the defects prevent the product from functioning. If a product is not usable, it is considered defective. Defects may be many on a shippable and acceptable product. An example is typo-errors in a book. A typo is a defect, but the book ships to satisfied customers. A defective book would probably fall apart. Ex. An undercooked hamburger cannot be used (consumed) by the customer, it is defective product. Other items (unevenly browned fries, underweight hamburger, too much ice in a drink) have flaws or defects, but you can still sell them and customers can still consume them. They do not need to be scrapped, so they are not truly defective. 4  Process Optimisation & Improvement Law of Nature, there is no TWO objects are exactly alike or identical. If we measure them with high precision instruments, the differences will be shown. These differences is termed as variation. Chance or Random variation is: the usual historical variations in a system that are random in nature. an inherent part of a process. Specific actions cannot be taken to prevent this variation from occurring. ongoing, consistent, predictable and small. This variation usually lies within three standard deviations from the mean where 99.73% of values are expected to be found. Assignable Variation, also refers to unexpected glitches that affect a process. Is sporadic, not random in nature. is not usually part of your normal process and occurs out of the blue, therefore it can be identified and eliminated. is usually much greater than the random variation, i.e. more than 3 standard deviation from the mean. They are a result of assignable cause that is brought about in a process resulting in a chaotic problem, (defects in the system or method) which is out of control in the process. On a control chart, the points lie beyond the preferred control limit or even as random points within the control limit. 5 Process Optimisation & Improvement 6 Process Optimisation & Improvement 7  Process Optimisation & Improvement Assignable causes of variation are present in most production processes. The sources of assignable variation can usually be identified (assigned to a specific cause) leading to their elimination. 1. Man - knowledge, training, experience, etc. 2. Materials - strength, thickness, weight, etc. 3. Machine - wear & tear, vibration, parameters, etc. 4. Method - production method, sequence, material handling, etc. 5. Measurement - precision, specifications, calibration, etc. 6. Environment – humidity, temperature, lighting, etc. If assignable causes are present in the process, the process cannot operate at its best. A process that is operating in the presence of assignable causes is said to be “out of statistical control (OOC).” The assignable causes must be eliminated before managerial innovations leading to improved productivity can be achieved. Assignable causes of variability can be detected leading to their correction through the use of control charts. 8  Process Optimisation & Improvement Normal Distribution: A normal distribution is the proper term for a probability bell curve. Normal distributions o are symmetrical , but not all symmetrical distributions are normal. o has a single peak, o mean= = median = mode, at the peak 9  Process Optimisation & Improvement In a standard normal distribution the mean is zero and the standard deviation is 1. It has zero skew and a kurtosis of 3. The normal distribution is the most common type of distribution. The standard normal distribution has two parameters: the mean and the standard deviation. For a normal distribution,  68.27% of the observations are within +/- one standard deviation of the mean,  95.45% are within +/- two standard deviations, and  99.73% are within +- three standard deviations. 10  Process Optimisation & Improvement An X-bar/R chart is actually two control charts in one: a chart of the average (X-bar) over time, plus a chart of the range (R) over time. The data for the control chart is obtained using subgroup sampling, which involves grouping together data collected under nearly identical conditions (produced about the same time), example 3 or 5 pieces of products are collected each time as a subgroup. This is often the case in manufacturing settings, where the conditions on an assembly line may vary over time (across hours or days) but are generally constant within a short time period (within minutes or hours). Each data point (X-Bar, R) on the control chart then represents one subgroup, and the data is said to be grouped into "rational subgroups.“ Each chart consist of: A center line is drawn at the value of the mean; i.e. “X-Bar-Bar” and “R-Bar”. Upper and lower control limits that indicate the threshold at which the process output is considered statistically 'unlikely' and are drawn typically at 3 standard deviations from the center line 11 Process Optimisation & Improvement 12 Process Optimisation & Improvement 13 Process Optimisation & Improvement 14  Process Optimisation & Improvement The process (POPULATION of process data) distribution on the left shown if the data for every individual piece of product is measured and plotted. If a subgroup (i.e. sample) of 5 pieces of product is collected everyday, i.e. n=5. Suppose the weight of each 5 pieces is measured, so each subgroup has 5 readings. The average of the 5 readings is calculated and plotted on the control chart. In 15 days, there will be 15 subgroup averages plotted on the control chart, which is shown on the right. If these 15 subgroup averages are plotted as histogram (i.e. without considering the day the subgroups are collected), then the distribution of the subgroup averages (x-Bar) is shown in the centre of the slide. Notice: The process spread (6x STANDARD DEVIATION) of distribution for the population and subgroup are different. However, the MEAN of both distributions are the same. 15 Process Optimisation & Improvement 16  Process Optimisation & Improvement 1st. Given the readings collected for every product in each subgroup of n=4. 2nd. Calculate the average for each subgroup. This is the X-Bar (sum 4 readings then divide by 4) for each subgroup. 3rd. Calculate the range of each subgroup. This is the R (largest minus smallest value in the subgroup) for each subgroup. 4th. Calculate the Average (X-Bar-Bar) of the 25 averages (X-Bars). This is the centerline of the X-Bar Control Chart. 5th. Calculate the Average (R-Bar) of the R values. This is the centerline of the R Control Chart. 17  Process Optimisation & Improvement 6th. Calculate Control Limits for average-chart (X-Bar Chart) using the formula given. A2 is obtained from the Table for Control Chart Constant with n=4. 7th. Calculate Control Limits for range-chart (R chart) using the formula given. D3 and D4 are obtained from the Table for Control Chart Constant with n=4. 18  Process Optimisation & Improvement Finally, to complete the TRIAL control charts, with the trial control limits calculated, draw the 6 limit lines on the two charts: Trial Upper Control Limt (UCL), Trial Lower Control Limit (LCL) and Tria Central Line (X-Bar-Bar) for Average Control Chart; Trial Upper Control Limt (UCL), Trial Lower Control Limit (LCL) and Trial Central Line (R-Bar) for Range Control Chart; Evaluate the STABILITY of the process by identify the assignable variations in the process. With the technical capability to remove the assignable causes, the data of the affected subgroup(s) are removed. Then the REVISED control charts are plotted, and the process maintain a stable and in control process. 19 Process Optimisation & Improvement 20  Process Optimisation & Improvement Corrected: Rbnew = (0.08+0.10+0.06+...+0.06)/22 = 0.076 In this example, assume the assignable causes at subgroup 4, 18 & 20 were solved and removed, therefore, the data in these subgroups were removed. However, the assignable cause at subgroup 16 was either not known or not able to solve, therefore, the data in subgroup 16 shall remain. In the revised chart, calculate the revised limits again with only 22 subgroups because 3 subgroups (#4, 18 & 20) were removed. 21  Process Optimisation & Improvement Finally, to complete the Revised control charts, with the revised control limits calculated, draw the 6 limit lines on the two charts: Revised Upper Control Limt (UCL), Revised Lower Control Limit (LCL) and Revised Central Line (X-Bar-Bar) for Average Control Chart; Revised Upper Control Limt (UCL), Revised Lower Control Limit (LCL) and Revised Central Line (R-Bar) for Range Control Chart; Evaluate the STABILITY of the revised process most of the times this new process is likely to be stable and in control process. 22 Process Optimisation & Improvement 23  Process Optimisation & Improvement How do you determine the constants of A2, D3, D4 & d2 for Xb-R control charts? 1. Refer to Math Table issued by TP-ENG, flip to Pg 30; 2. Select the column with Xb-R charts; 3. Since the size of subgroup is 4, then select the row of n=4; 4. Then identify the constants for the control charts from this row under the Xb-R control charts 24  Process Optimisation & Improvement The process is in statistical control, i.e. no assignable cause, as shown in the control charts. This control chart has subgroup size, n = 6, with Xbb = 54.3mm & Rb = 17.73mm. The mean & standard deviation of the population PROCESS can be calculated. Using the mean & standard deviation of the PROCESS, the control limits of control charts for subgroup size n=5 can be calculated. Therefore, the control limits can be calculated with the n = 5. 25  Process Optimisation & Improvement 1. The population PROCESS standard deviation is calculated using sigma = Rb/d2 ; (Rb & d2 are when subgroup size n=6). 2. The Rb for subgroup size n=5 is calculated using PROCESS standard deviation, sigma = Rb/d2 ; d2 are when subgroup size n=5). 3. For subgroup size n = 5, the Xbb is the same (unchanged), the Rb is calculated in step #2. 4. Go to math table, pg 30 to find the constants of A2, D3, D4 & d2 for Xb-R control charts when n = 5 5. Using the formula for Xb-R control charts, the control limits for subgroup size n=5 can be calculated. 26 Process Optimisation & Improvement 27 Process Optimisation & Improvement 28  Process Optimisation & Improvement Rule 1: If any 1 point is completely out of the control limits, then the process is out of control. Rule 2: if any 2 of 3 consecutive points fall outside warning 2-sigma limits, but within control (3-sigma) limits. (on the same side of the mean) (on the same side of the mean). Rule 2 is not applicable for R or S chart. 29  Process Optimisation & Improvement Rule 3: If any 4 of 5 consecutive points fall beyond 1-sigma limits, but within control limits. (on the same side of the mean). This rule 3 is not applicable for R or S chart. Rule 4: If any 6 consecutive points run either upward or downwards. 30  Process Optimisation & Improvement Rule 5: If any 7 consecutive points fall on one side of the centerline. 31  Process Optimisation & Improvement The sampling procedure is same for each sample and is carried out consistently. When the data is assumed to be normally distributed. Note: The S value in each subgroup is calculated using the Sn-1 in the calculator or excel statistical function. 32  Process Optimisation & Improvement 1. R chart more commonly used, because it is easy to use. 2. R charts uses only max. and min. values, while S chart uses all the data. 3. S chart is more accurate than R chart. 4. X-Bar R chart is to be considered if the subgroup size is between two and 10 observations. 5. The X-bar S chart to be used when rationally collect measurements in subgroup size is more than 10. 33 Process Optimisation & Improvement 34  Process Optimisation & Improvement Continuous data is essentially a measurement such as length, amount of time, temperature, or amount of money. Variable Control Charts (Xb-R or Xb-S) are used to monitor the process with this data Discrete data, also sometimes called attribute data, provides a count of how many times something specific occurred, or of how many times something fit in a certain category. For example, the number of complaints received from customers is one type of discrete data. The proportion of technical support calls due to installation problems is another type of discrete data. Attribute Control Charts are used to monitor the process with attribute data. 35 Process Optimisation & Improvement 36  Process Optimisation & Improvement np chart: is used for discrete attribute data. When each data point is based on the same sample size, it actually plots the number of defective in a category over time rather than the proportion in the category. The name “np” (n x p) refer to number of defective 37  Process Optimisation & Improvement p chart: is used to plot the data for proportion of defective in the subgroups, which have different subgroup size (or sample size). For example, you might track defective and non-defective components in a manufacturing process. 38 Process Optimisation & Improvement 39  Process Optimisation & Improvement The c chart is similar to the np chart, in that it requires equal sample sizes for each data point. The c chart plots count data, such as number of errors. For example, in evaluating errors on loan applications, if you sampled the same number of applications each week. 40  Process Optimisation & Improvement The u chart is a more general version of the c chart for use when the data points do not come from equal-sized samples. For instance, if you review all loan applications each week, and the number submitted differs on a weekly basis, you could still count errors and plot the number of errors by week over time. 41  Process Optimisation & Improvement This table summarized the main differences in using the different typs of attribute control charts. 42  Process Optimisation & Improvement This flow chart provides a selection guidelines for the control charts that we have learnt. First, determine the type of data collected, i.e. variables or attribute data. For Variable data, if the sample size (or subgroup size) is less than 10, use Xb-R charts, otherwise, use Xb-S charts. For Attribute data, if the data is on Defect (nonconformity), and if sample size is constant, then use c-chart, otherwise use u-chart; If the data is on defective (nonconforming product) and if sample size is constant, then use np-chart, otherwise, use p-chart. 43