Process Optimisation & Improvement PDF

Process Optimisation & Improvement 1  Process Optimisation & Improvement Process Control is to evaluate the variation of the process over a period of time, with the goal to reduce or eliminate the variation in...

Process Optimisation & Improvement 1  Process Optimisation & Improvement Process Control is to evaluate the variation of the process over a period of time, with the goal to reduce or eliminate the variation in the process. Process Capability is to evaluate the variation of the process with respect to process specifications. Generally Process Capability is used when a process is under statistical control. Process capability uses the process sigma value determined from either the Average, Range ot Sigma control charts 2 Process Optimisation & Improvement 3  Process Optimisation & Improvement We are often required to compare the output of a stable process to the specifications limits by using Process Capability indices to make a statement about how well the process meets specification. To do this we compare the natural variability (process spread = 6) of a stable process to the product specification limits (USL, LSL). A process where almost all the measurements fall inside the specification limits is a capable process. In this comparison of the output of a stable process to the specification limits, is based on “individual-basis” of measurement for its output. It is shown on the right side of the slide. However, the control limits used in the control charts are usually computed, using “subgroups’ averages and range or standard deviation, not “individual” data, shown on the left side of the slides, 4  Process Optimisation & Improvement Process capability index (Cpk) is a statistical tool, to measure the ABILITY of a process to produce output within customer’s specification limits. In simple words, it measures producer’s capability to produce a product within customer’s tolerance range. Cpk is used to estimate how close your product is to a given target (Specification Limits), assuming performance is consistent (in statistical control) over time. Cpk statistics assume that the population of data values is normally distributed. Assuming a two-sided specification, if μ and σ are the population mean and standard deviation, respectively, of the normal data, and USL, LSL, and T are the upper and lower specification limits and the target value, respectively, then the population capability indices are defined as shown in the slide. 5  Process Optimisation & Improvement From these conversion formula for subgroup results of Rb or Sb to Process Standard Deviation, we can convert the variations of the stable process (in statistical control) to the standard deviation of the process, sigma. This sigma can be used to calculate the process capability index of the STABLE process, to determine the ABILITY of the process in meeting the specification limits. 6  Process Optimisation & Improvement Therefore, out-of-control refers to process is not in statistical control, therefore the process is not stable. At this condition, the process capability cannot be calculated. Process Capability ca only be calculated when the process is stable, i.e. the process is in statistical control. Therefore, the process data (which is “individual” data) isin NORMAL distribution (bell-shape). Under this condition, the Process Capability Index formula become valid to use. Of course, all the data collected for the control charts (to achieve stable process) shall be accurate and reliable, i.e. no significant error or mistakes in the data collection. (calibration is doen). 7 Process Optimisation & Improvement 8 Process Optimisation & Improvement 9 Process Optimisation & Improvement 10  Process Optimisation & Improvement A process where almost all the measurements fall inside the specification limits is a capable process. Process spread (6σ) is < (USL-LSL) Case 1-L (see Left curve): Upper specification limit (USL) =16 Lower Specification limit (LSL) = 0 Mean  = 8; Standard deviation (σ)= 2 Cpk = min [(USL−μ)/3σ, (μ−LSL)/3σ] = min[(16-8)/6, (8-0)/6] = min [1.33, 1.33] = 1.33  % of Rejects is 0.0064% (fall out of specification limits. Case 1-R (see Right curve) if Process shifted higher by 2 units (1σ) Mean = 10, Standard deviation (σ)= 2 Cpk = min [(USL−μ)/3σ, (μ−LSL)/3σ] = min[(16-10)/6, (10-0)/6] = min [1.0, 1.67] = 1.0  % of Rejects is 0.27%/2 (fall out of specification limits. In both situations, Cp = (USL-LSL)/6 = (18-2)/(12) = 1.33 11  Process Optimisation & Improvement Process spread (6σ) is = (USL-LSL) Case 2-L: if USL =18 & LSL = 0, Mean (μ)= 9 & Standard deviation (σ)= 3 Cpk = min [(USL−μ)/3σ, (μ−LSL)/3σ] = min[18-9/9, 9-0/9] = min [1 , 1] = 1  % of Rejects is 0.27% (fall out of specification limits. Case 2-R; if Process shifted higher by 3 units (1σ) Mean (μ)= 12 & Standard deviation (σ)= 3 Cpk = min [(USL−μ)/3σ, (μ−LSL)/3σ] = min [18-12/9, 12-0/9] = min [0.67 , 1.33] = 0.67  % of Rejects is 2.28% (fall out of specification limits. In both situations, Cp = (USL-LSL)/6 = (18-0)/(18) = 1.0 12  Process Optimisation & Improvement Process spread (6σ) is > (USL-LSL) Case 3-L: if USL =16 & LSL = 0, Mean (μ)= 8 & SD (σ)= 4 Cpk = min [(USL−μ)/3σ, (μ−LSL)/3σ] = min[(16-8)/12, (8-0)/12] = min [0.67 , 0.67] = 0.67  % of Rejects is 4.56% (fall out of specification limits. Case 2-R; if Process shifted higher by 4 units (1σ) Mean (μ)= 12 & SD (σ)= 4 Cpk = min [(USL−μ)/3σ, (μ−LSL)/3σ] = min [(16-12)/12, (12-0)/12] = min [0.33 , 1.0] = 0.33  % of Rejects is 15.87% (fall out of specification limits. In both situations, Cp = (USL-LSL)/6 = (16-0)/(24) = 0.67 13  Process Optimisation & Improvement Cpk is a Process Capability Index measures the capability of the process in producing products compared to its specification limits. The higher the Cpk value the better the process is. For instance, Machine 1 has a Cpk of 1.7 and machine 2 has a Cpk of 1.1. From the Cpk value, we can derive that Machine 1 is more capable than Machine 2. Cpk = Cp indicates that the process is centered at the center of the specifications limits. Cpk = Cp = 1 indicate a process is perfectly centered, and the mean (process average) is 3 standard deviations away from the upper limit and the lower limit. Cpk = or >1.33 indicates that the process is capable and meets specification limits. Any value less than this may mean variation is too wide compared to the specification or the process average is away from the target. 14  Process Optimisation & Improvement Cpk = 0, indicates that the process mean is equal to one of the specification limits values, i.e. the center line of the process is on either the USL or LSL lines. Cpk < 0, i.e. Cpk is negative, it means that the mean of the process is outside the customer specification limits; the process will produce output that is outside the customer specification limits. We generally want a Cpk of at least 1.33 [4 sigma] or higher to satisfy most customers. 15 Process Optimisation & Improvement 16 Process Optimisation & Improvement 17 Process Optimisation & Improvement 18