process control

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Introduction2/11/2017Ronald Morgan Shewchuk1Now that you have implemented process mapping, value stream mapping and 5S+Safety within your organization you have effectively leaned-out your operations. You are left with the core processes that add value to your products and/or services in the eyes of your customer. The degree of control that these processes exhibit is directly related to your companys profitability. The higher the degree of control, the more money your company makes its as simple as that. Process control implies reducing variation. Variation, as you will recall, is the enemy of Six Sigma. Jack Welch, the CEO of General Electric from 1981 through 2001, was keenly aware of the effect variation had on his business, and consequently was a leading proponent of driving Six Sigma throughout General Electrics operations. In this presentation we will review the fundamentals of process control.

Operational Excellence


Process ControlStandard Deviation and Variance2/11/2017Ronald Morgan Shewchuk2The DNA of statistics is the standard deviation, which may be visualized as the average distance of each data point to the mean of all the data points in the sample set. The equation for the standard deviation of a sample extracted from a larger population is provided in Eqn 6.1. This is the same equation used by MS Excel in the STDEV function to calculate the standard deviation of a data set.s =(xi x)2i = 1n

n - 1

wheres = sample standard deviationn = number of data points in samplexi = value of the ith element of xx = mean of all elements of x sample

Eqn 6.1



Process ControlStandard Deviation and Variance2/11/2017Ronald Morgan Shewchuk3The units of the standard deviation are the same as the data points. Variance is simply the square of the standard deviation, s2. Variances are additive whereas standard deviations are not. For example, if you wanted to calculate the standard deviation of a machined part consisting of multiple assemblies you must first add all the variances of each assembly and then take the square root of the total variance. The equation for variance is defined in Eqn 6.2.s2 =(xi x)2

i = 1n

n - 1

wheres2 = sample variancen = number of data points in samplexi = value of the ith element of xx = mean of all elements of x sample

Eqn 6.2



Process ControlStandard Deviation and Variance2/11/2017Ronald Morgan Shewchuk4If your sample size has the same number of elements as your population, that is, you have performed 100% inspection, then the standard deviation and variance of the population are denoted by and 2 respectively and may be calculated by Eqn 6.3 and 6.4 below. =(xi )2i = 1n

n

where = population standard deviationn = number of data points in populationxi = value of the ith element of x = mean of all elements of x populationEqn 6.32 =(xi )2i = 1n

nwhere2 = population variancen = number of data points in populationxi = value of the ith element of x = mean of all elements of x populationEqn 6.4



Process ControlNormal Distribution2/11/2017Ronald Morgan Shewchuk5 is the Greek letter sigma, thus we can see that six sigma implies six standard deviations. This implication is best illustrated by considering the normal distribution.If you measured the height of every adult male in the United States and plotted a graph with measured height on the x-axis and the number of occurrences of the measured height on the y-axis you would find that the data follows a bell-shaped curve. Scientists have found that many aspects of nature follow a bell-shaped curve and hence, have applied the name normal distribution to this type of curve, an example of which is shown in Figure 6.1. The probability density function that describes the normal distribution is given in Eqn 6.5.



Process Control2/11/2017Ronald Morgan Shewchuk6Figure 6.1 Normal Distribution



Process ControlNormal Distribution2/11/2017Ronald Morgan Shewchuk7An important property of the normal distribution is its relationship to the standard deviation. You will note from Figure 6.1 that 68.26% of the data fall within plus or minus one standard deviation of the mean. Similarly, 95.46% and 99.73% of the data points fall within +/- 2 and 3 standard deviations of the mean respectively. If we extrapolate the graph out to +/- 6 standard deviations of the mean we will include 99.9997% of the data. This is the formal definition of a six sigma capable process, that is, a process that can consistently manufacture product within specifications 99.9997% of the time allowing for a maximum of 3.4 defects per million opportunities (DPMO).f(x) =1

Eqn 6.5

ex

2-1

2



Process ControlNormal Distribution2/11/2017Ronald Morgan Shewchuk8Let us consider an industrial example to drive home the importance of the standard deviation to process control. Suppose your company was manufacturing a machined part with target length of 100 mm. The measured standard deviation is 3 mm resulting in the part distribution depicted in Figure 6.2A. If you could cut the standard deviation in half through process improvements the distribution of part sizes would be narrowed to that of Figure 6.2B. Clearly, this improvement will not only benefit your manufacturing operations but also those of your customer since the outbound variation in part length is dramatically reduced.



Process Control2/11/2017Ronald Morgan Shewchuk9Figure 6.2 Effect of Standard Deviation on Normal Distribution

ABx = 100 mms = 3 mm

x = 100 mms = 1.5 mm



Process ControlCentral Limit Theorem2/11/2017Ronald Morgan Shewchuk10Many statistical tests assume the data is normally distributed. It is common for the parent population from which the data is drawn to not be normal. Consider the case of the sales manager wanting to analyze the sales statistics from her territory recognizing that her customer base is far from being normal. Fortunately, this problem may be avoided through effective sampling design and an understanding of the central limit theorem.Population distributions come in all shapes and sizes. They may be skewed, uniform, exponential, parabolic, logarithmic, bimodal, etc. The central limit theorem states that, regardless of the shape of the parent population, the distribution of the means of sample subsets extracted from the parent population will be normal provided that a sufficient number of sample subsets are extracted. This theorem is best visualized in Figure 6.3.



Process Control2/11/2017Ronald Morgan Shewchuk11Figure 6.3 Effect of Sample Size on Mean Sample Distribution



Process ControlSampling Plan Design2/11/2017Ronald Morgan Shewchuk12It can be seen that a sample size of 30 or more subgroups will result in an approximately normal distribution of the means. Thus, you do not need to know the type of distribution the parent population exhibits as long as you extract a minimum of 30 subgroup samples from the parent population as part of your statistical analysis of the sample set. This illustrates the importance of sampling plan design to ensure that your samples are representative of the true population.Todays factories have a plethora of information due to Supervisory Control and Data Acquisition (SCADA) systems, Distributed Control Systems (DCS), data historians, etc. On the other hand, some measurements are time-consuming, expensive and sometimes destructive; resulting in yield losses. Consequently, a balance must be struck between extracting enough subgroups to manage the Producer Risk (also referred to as Type I Error or Alpha Risk - the risk of falsely rejecting good parts) and the Consumer Risk (also referred to as Type II Error or Beta Risk the risk of falsely accepting bad parts).



Process ControlSampling Plan Design2/11/2017Ronald Morgan Shewchuk13Deciding how many subgroups to sample at what periodicity is the essence of sampling plan design.The American Society for Quality has published national standards for sampling procedures for attribute data (count or classification) in ANSI/ASQC Z1.4 and sampling procedures for variable data (measurement) in ANSI/ASQC Z1.9. These standards are based upon military standards MIL-STD-105E and MIL-STD-414 respectively. The sampling plan tables and operating characteristic curves of these standards allow you to maintain the Acceptable Quality Level (AQL) of your process which is defined as the worst tolerable process defect average that you are willing to accept when a continuing series of lots is submitted for acceptance sampling.Sampling plans are designed to yield a high probability of accepting a lot at the AQL and a low probability of accepting a lot at the Rejectable Quality Level (RQL) also known as the Lot Tolerance Percent Defective (LTPD).Producer Risk is managed by the selection of AQL and . Consumer Risk is managed by the selection of RQL and .



Process ControlSampling Plan Design2/11/2017Ronald Morgan Shewchuk14Thus, our sampling plan will provide us with a 1- probability of accepting the lot at the AQL and a probability of accepting the lot at the RQL. A good starting point for is 0.05 and 0.10 for . The Quality Engineer will typically iterate selections of AQL and RQL to develop a sampling plan which minimizes the cost of quality while still protecting the customer from escaped detection. This sliding scale of risk management is best depicted as in Figure 6.4. The operating window between the AQL and RQL is the 95% to 10% portion of the Operating Characteristic (OC) Curve, a measure of the discriminating power of the sampling plan. The OC curve plots the probability of accepting the lot versus the lot fraction defective.



Process Control2/11/2017Ronald Morgan Shewchuk15Minitab can be used to generate the OC curve for a given AQL, RQL, lot size and historical standard deviation. It is a convenient way for the Quality Professional to compare sampling plans to manage risk. Lets consider the example where a candy manufacturer is dispensing 20 g of chocolate into individual serving bags that have a tolerance of 0.4 g. The historical standard deviation of fill weights is 0.1 g. How many bags of candy would have to be sampled out of a lot size of 5,000 bags to satisfy managements AQL and RQL agreement of 1% and 3% respectively with the candy distributor?Figure 6.4 Acceptance Sampling Plan Risk Management



Process Control2/11/2017Ronald Morgan Shewchuk16

Figure 6.5 Steps for Generating Acceptance Sampling Plan by VariablesOpen a new worksheet. Click on Stat Quality Tools Acceptance Sampling by Variables Create/Compare on the top menu.



Process Control2/11/2017Ronald Morgan Shewchuk17Figure 6.5 Steps for Generating Acceptance Sampling Plan by VariablesSelect Create a Sampling Plan from the drop down menu in the dialogue box. Select Percent defective for the units for quality levels. Enter 1 for AQL, 3 for RQL, 0.05 for Alpha, 0.10 for Beta, 19.6 for Lower spec, 20.4 for Upper spec, 0.1 Historical standard deviation, and 5000 for the lot size. Click OK.



Process Control2/11/2017Ronald Morgan Shewchuk18Figure 6.5 Steps for Generating Acceptance Sampling Plan by VariablesA graph is generated for the Operating Characteristic Curve, the Average Outgoing Quality Curve and the Average Total Inspection Curve. The required sample size is 44. If one of the bags of candy audited for fill weight is outside of the 20.0 0.4 g of chocolate, the entire lot must be rejected and 100% inspection performed. Click Window Session on the top menu.



Process Control2/11/2017Ronald Morgan Shewchuk19Figure 6.5 Steps for Generating Acceptance Sampling Plan by VariablesThe session window displays the descriptive statistics of the sampling plan. Lets say the Quality Engineer is concerned about escaped detection and wants to introduce some buffer into the RQL agreed upon with the candy distributor. Press CTRL-E to return to the last dialogue box.



Process Control2/11/2017Ronald Morgan Shewchuk20Figure 6.5 Steps for Generating Acceptance Sampling Plan by VariablesReduce the RQL level to 2% defective. Click OK.



Process Control2/11/2017Ronald Morgan Shewchuk21Figure 6.5 Steps for Generating Acceptance Sampling Plan by VariablesThe sample size is increased from 44 to 116 by reducing the RQL from 3% to 2%. The Quality Engineer decides to leave well enough alone and to remain with the sampling plan that represents the agreed upon terms with the distributor.



Process ControlSampling Plan Design2/11/2017Ronald Morgan Shewchuk22It is a common occurrence for manufacturers to struggle with the definition of lot size and lot number. If you conduct a supplier audit and the answer to your question how do you assign lot numbers to your finished product? results in the response well we use your P.O. number or we use the date of manufacture you know that it will be a lengthy audit. ANSI Z1.4 provides the following guidance for the formation of lots or batches: Each lot or batch shall, as far as is practicable, consist of units of product of a single type, grade, class, size, and composition, manufactured under essentially the same conditions, and at essentially the same time. This means that a part selected from the chronological front of the lot, the end of the lot or anywhere in between will have the same quality characteristics.A lot number should be a unique code assigned to a lot, used once, and then retired for life. The lot number must have traceability to raw material lot numbers, manufacturing location, manufacturing line and process conditions.



Process ControlSampling Plan Design2/11/2017Ronald Morgan Shewchuk23Typical reasons for a lot number change include a change in raw material lots, a change to a different production line, downtime exceeding x hours, a process upset, a process change to correct a defectives situation, or any other change that alters the quality characteristic of the process output. It is common for continuous process manufacturers to assign a maximum part count or maximum production time to a lot number to limit their exposure in the event of a quality nonconformance discovered after production.Samples should be collected in rational subgroups. For example, if your plant is running three shifts per day you will want to collect your samples to identify shift-to-shift differences. Thus, it is logical to collect five subgroup samples from each shift per day and track the trends of the means via Statistical Process Control. But before we venture into statistical process control we need to test the data set to confirm that it follows a normal distribution.



Process ControlNormality Testing2/11/2017Ronald Morgan Shewchuk24Normality testing compares the values of the data set to the probability density function of Eqn 6.5. Lets look at the measurement data compiled in Figure 6.6 representing a continuous process where assay wt % is a key process output variable. We will use Minitab to quickly assess if the data follow a normal distribution, the steps for which are captured in Figure 6.7.



Process Control2/11/2017Ronald Morgan Shewchuk25Figure 6.6 Assay Weight % Measurements Continuous Process



Process Control2/11/2017Ronald Morgan Shewchuk26Figure 6.7 Normality Testing StepsCopy and paste the assay weight % measurements into a Minitab worksheet.



Process Control2/11/2017Ronald Morgan Shewchuk27Figure 6.7 Normality Testing StepsClick Stat Basic Statistics Normality Test on the top menu.



Process Control2/11/2017Ronald Morgan Shewchuk28Figure 6.7 Normality Testing StepsSelect C7 Avg Assay wt% for the Variable field in the dialogue box. Click OK.



Process Control2/11/2017Ronald Morgan Shewchuk29Figure 6.7 Normality Testing StepsA normal probability plot is created in the Minitab project file.



Process ControlData Transformation for Normality2/11/2017Ronald Morgan Shewchuk30The measured data do not closely follow the blue line representing a normal distribution. The P-value is less than 0.05 which allows us to conclude at the 95% confidence level that the data set does not follow a normal distribution (we will learn more about P-values and confidence levels under the section entitled hypothesis testing). Although we have practiced good sampling design, averaged rational subgroups, and taken thirty samples from the parent population the data set is still not normal. What can we do? We can transform the data set.In 1964 George Box and David Cox derived a power transformation to convert non-normal data to normal data. In 1993 Norman Johnson developed an alternative transformation approach. In practice, it does not matter which transformation you use. Typically, analysts will select the approach which provides the best normalization of the data set. Figure 6.8 captures the steps required to transform data to conform to a normal distribution.



Process Control2/11/2017Ronald Morgan Shewchuk31Figure 6.8 Data Transformation Steps for NormalizationReturn to the active worksheet.



Process Control2/11/2017Ronald Morgan Shewchuk32Figure 6.8 Data Transformation Steps for NormalizationClick Stat Quality Tools Johnson Transformation on the top menu.



Process Control2/11/2017Ronald Morgan Shewchuk33Figure 6.8 Data Transformation Steps for NormalizationSelect C7 Avg Assay wt% for the Single column field in the dialogue box. Enter C8 to store the transformed data in column 8. Click OK.



Process Control2/11/2017Ronald Morgan Shewchuk34Figure 6.8 Data Transformation Steps for NormalizationThe Johnson Transformation probability plot is created in the Minitab project file. The transformation was successful to normalize the data set. The transformed data has a P-value which is well above 0.05. The derived transformation function is given as 1.35408 + 1.07249 * ln[(X - 92.2172)/(93.9892 - X)] where X is the original average assay wt% variable.



Process Control2/11/2017Ronald Morgan Shewchuk35Figure 6.8 Data Transformation Steps for NormalizationReturn to the active worksheet. Notice that the transformed data has been entered in column 8. Label the column as Johnson Transf Avg Assay.



Process ControlDistribution Identification2/11/2017Ronald Morgan Shewchuk36The transformed data set would subsequently be used as the source data to perform analyses such as Statistical Process Control and process capability.Periodically, data sets will prove to be particularly resilient to normal distribution transformation. You can do everything including standing on your head, but fail to normalize the data. In this case, it will be necessary to identify the distribution type which most closely matches the data in order to select the appropriate statistical analysis tool. Lets say we have the active ingredient concentration measurements as captured in the Minitab worksheet of Figure 6.9.The raw data does not follow a normal distribution (P-value less than 0.05) as shown in Figure 6.10. Johnson transformation and Box-Cox transformation fail to normalize the data as shown in Figures 6.11 and 6.12 respectively. Our next option is to identify the distribution type which most closely models the data set the screen shots for which are captured in Figure 6.13.



Process Control2/11/2017Ronald Morgan Shewchuk37Figure 6.9 Active Ingredient Concentration Worksheet



Process Control2/11/2017Ronald Morgan Shewchuk38Figure 6.10 Active Ingredient Normality Test Raw Data



Process Control2/11/2017Ronald Morgan Shewchuk39Figure 6.11 Active Ingredient Normality Test Johnson Transformation



Process Control2/11/2017Ronald Morgan Shewchuk40Figure 6.12 Active Ingredient Normality Test Box-Cox Transformation



Process Control2/11/2017Ronald Morgan Shewchuk41Figure 6.13 Steps for Distribution Identification

Return to the active worksheet. Click Stat Quality Tools Individual Distribution Identification on the top menu.



Process Control2/11/2017Ronald Morgan Shewchuk42Figure 6.13 Steps for Distribution IdentificationSelect C1 Active Ingredient (ppm) for the Single column field in the dialogue box. Enter 1 for the subgroup size. Ensure that the radio toggle button to use all distributions and transformations is checked. Click OK. Fifteen probability plots are generated for the distributions and transformations.















Process ControlDistribution Identification2/11/2017Ronald Morgan Shewchuk47Notice that all the distribution and transformation P-values are less than 0.05. None of the distributions are a good match for the data. The best of the worst is the Weibull distribution with the lowest Anderson Darling test statistic, AD = 4.435. The Anderson Darling test statistic measures the goodness of fit of the data set to each distribution probability density function. The lower the AD test statistic, the more closely the data set follows the distribution in question. We will utilize this information when we explore process capability analysis of non-normal distributions.



Process ControlStatistical Process Control2/11/2017Ronald Morgan Shewchuk48In the mid 1920s Walter A. Shewhart of Bell Laboratories developed the first control charting procedures. Dr. Shewhart recognized that control charts are a powerful tool to determine if a process is operating in a state of statistical control or if there are special causes of variation present which require root cause investigation. Statistical Process Control (SPC) charts are useful to establish a benchmark for the current process variation, detect special causes of variation, ensure process stability, enable predictability, and to confirm the impact of process improvement activities. The data must be plotted in time-series order and it is recommended to plot a minimum of thirty (30) data points before establishing control limits. Control limits are calculated from the data set according to the formulas shown in Figure 6.14 and utilize the coefficients of Figure 6.15 which are a function of the subgroup size within the data set.



Process Control2/11/2017Ronald Morgan Shewchuk49Figure 6.14 Control Limit Formulas - Continuous Data



Process Control2/11/2017Ronald Morgan Shewchuk50Figure 6.15 Coefficients for Control Limit Formulas - Continuous Data



Process ControlStatistical Process Control2/11/2017Ronald Morgan Shewchuk51The tests developed by Dr. Shewhart to check for special causes of variation assume the data are normally distributed and independent (i.e. a measured value is not influenced by its past values). There are eight generally accepted rules to check for special causes of variation. These rules are summarized in Figures 6.16 through 6.23 for the example process of milk ultra pasteurization to prolong its shelf life. Notice that the control limits are separated from the overall mean by three zones labeled C, B and A respectively. These zones correspond to three standard deviations from the centerline where the standard deviation is not derived from equation 6.1 but from the control limit definitions of Figure 6.14. For example, the standard deviation for an individuals chart would be calculated as in Eqn 6.6.



Process ControlStatistical Process Control2/11/2017Ronald Morgan Shewchuk52s =|xi+1 xi|i = 1n - 1

n - 1wheres = short term process standard deviationn = number of data points in samplexi = value of the ith element of xmR = moving range average

Eqn 6.62.663

2.663

mR =

Equation 6.6 Individuals Chart - Short Term Process Standard Deviation



Process Control2/11/2017Ronald Morgan Shewchuk53Figure 6.16 SPC Rule 1: One or More Points are Outside the Control Limits



Process Control2/11/2017Ronald Morgan Shewchuk54Figure 6.17 SPC Rule 2: Seven Consecutive Points are on the Same Side of the Centerline



Process Control2/11/2017Ronald Morgan Shewchuk55Figure 6.18 SPC Rule 3: Seven Consecutive Intervals are Entirely Increasing or Entirely Decreasing



Process Control2/11/2017Ronald Morgan Shewchuk56Figure 6.19 SPC Rule 4: Fourteen Consecutive Points Alternate Up and Down Repeatedly



Process Control2/11/2017Ronald Morgan Shewchuk57Figure 6.20 SPC Rule 5: Two out of Three Consecutive Points are in the Same Zone A or Beyond



Process Control2/11/2017Ronald Morgan Shewchuk58Figure 6.21 SPC Rule 6: Four out of Five Consecutive Points are in the Same Zone B or Beyond



Process Control2/11/2017Ronald Morgan Shewchuk59Figure 6.22 SPC Rule 7: Fourteen Consecutive Points are in Either Zone C



Process Control2/11/2017Ronald Morgan Shewchuk60Figure 6.23 SPC Rule 8: Eight Consecutive Points are Outside Either Zone C



Process ControlStatistical Process Control2/11/2017Ronald Morgan Shewchuk61Rule 1 detects a shift in the mean, an increase in the standard deviation or a single anomaly in the process. Check the associated range chart to see if increases in variation are the source of the special cause. Rule 2 detects a shift in the process mean. Rule 3 detects an increasing or decreasing trend in the process mean. Rule 4 detects systematic effects such as two alternately used machines, vendors or operators. Rule 5 detects a shift in the process mean or increase in the standard deviation. Rule 6 detects a shift in the process mean. Rule 7 illustrates the symptom of hugging the centerline. If the special cause of this out-of-control symptom was a process change designed to reduce variation the result is understandable. If this phenomenon occurred on its own the measurement system may have lost resolution. Rule 8 violations can occur when the measurement system develops a blind spot at the process centerline or when operator interventions result in over-steering the process.



Process ControlStatistical Process Control2/11/2017Ronald Morgan Shewchuk62The type of control chart selected will depend upon your data type and subgrouping. Attribute data where you can count the number of occurrences but not the number of non-occurrences (eg the number of defects in a plate of glass) follow the poisson distribution and are analyzed by c-charts or u-charts depending on whether the sample size is fixed or not respectively. Attribute data of the pass/fail type (eg the number of dropped calls per day at a call center) follow the binomial distribution and are analyzed by np-charts or p-charts depending on whether the sample size is fixed or not respectively. Variables data which are measured are sampled such that the sample means follow the normal distribution. A subgroup sample size of one derived from continuous data such as the pasteurization process temperature example we reviewed earlier is analyzed by individuals, moving range chartsA subgroup sample size of two to nine is best analyzed by an Xbar-R chart which plots averages of subgroups and the range within subgroups.



Process ControlStatistical Process Control2/11/2017Ronald Morgan Shewchuk63A subgroup sample size equal to or larger than ten is best analyzed by an Xbar-S chart which plots averages of subgroups and the standard deviation within subgroups. Figure 6.24 summarizes the logical decision process for selecting a control chart type.

Figure 6.24 Control Chart Type Decision Tree



Process ControlStatistical Process Control2/11/2017Ronald Morgan Shewchuk64In general, it is best to convert attribute data into continuous data and conduct SPC analysis via Xbar-R or IMR charts since the zone rules of Figures 6.16 through 6.23 do not apply to attribute data. For example, the number of defects in a plate of glass could be divided by the weight of the plate glass. The resulting measure of defects/lb of glass could be analyzed via an IMR chart. For data that occurs infrequently (such as the occurrence of a safety incident) consider monitoring the time between incidents rather than the binomial attribute data of yes/no a safety incident has occurred. Also, consider to track leading continuous indicators such as days between near misses. Minitab makes creating SPC charts easy. We will consider a sample data set each from manufacturing and the service sector to illustrate the process of generating SPC charts and the implications that can be derived from the analysis of these charts. Let us first consider a data set from our previous example process of the ultra pasteurization of milk. Figure 6.25 captures the screen shots of the SPC chart generation steps.



Process Control2/11/2017Ronald Morgan Shewchuk65Figure 6.25 SPC Chart Generation Steps Manufacturing ExampleMake sure that your data is entered into the worksheet in the correct format and in chronological order. Click on Stat Control Charts Variables Charts for Individuals I-MR on the top menu.



Process Control2/11/2017Ronald Morgan Shewchuk66Figure 6.25 SPC Chart Generation Steps Manufacturing ExampleHighlight C2 Temp_F in the dialogue box and click Select. Click Scale.



Process Control2/11/2017Ronald Morgan Shewchuk67Figure 6.25 SPC Chart Generation Steps Manufacturing ExampleClick the radio toggle button for Stamp under the X Scale in the dialogue box. Place your cursor in the Stamp columns box, highlight C1 Time and click Select. Click OK.



Process Control2/11/2017Ronald Morgan Shewchuk68Figure 6.25 SPC Chart Generation Steps Manufacturing ExampleClick I-MR Options.



Process Control2/11/2017Ronald Morgan Shewchuk69Figure 6.25 SPC Chart Generation Steps Manufacturing ExampleClick on the tab for Tests. Check the boxes to perform special cause analysis for test numbers 1, 2, 5 and 6. Click OK.



Process Control2/11/2017Ronald Morgan Shewchuk70Figure 6.25 SPC Chart Generation Steps Manufacturing ExampleClick OK.



Process Control2/11/2017Ronald Morgan Shewchuk71Figure 6.25 SPC Chart Generation Steps Manufacturing ExampleA graph is created in the Minitab project file with the stacked Individuals Moving Range SPC Charts. Out of control data points are highlighted in red and include a superscript number indicating which special cause test has been violated. In this case, test number 6 (4 out of 5 points greater than 1 standard deviation from the center line) is indicative of special causes which have resulted in a mean shift.



Process ControlStatistical Process Control2/11/2017Ronald Morgan Shewchuk72In this example the data points are all within the temperature specification of 285 5F but the process has shifted high beginning at point number 18 (15:30 hrs) indicating the occurrence of a special cause which requires investigation. It could be that a heater control module has failed or a heat exchanger valve has stuck open. This might result in the product developing a cooked aftertaste, which is objectionable to customers. Without seeing this shift in a control chart format, this special cause could be overlooked.In our second example, we will analyze the process control condition of dropped calls at a 24/7 customer service call center. Please refer to Figure 6.26.



Process Control2/11/2017Ronald Morgan Shewchuk73Figure 6.26 SPC Chart Generation Steps Service ExampleMake sure that your data is entered into the worksheet in the correct format and in chronological order. Click on Stat Control Charts Variables Charts for Individuals I-MR on the top menu.



Process Control2/11/2017Ronald Morgan Shewchuk74Figure 6.26 SPC Chart Generation Steps Service ExampleHighlight C2 % Dropped Calls in the dialogue box and click Select. Click Scale.



Process Control2/11/2017Ronald Morgan Shewchuk75Figure 6.26 SPC Chart Generation Steps Service ExampleClick the radio toggle button for Stamp under the X Scale in the dialogue box. Place your cursor in the Stamp columns box, highlight C1 Time and click Select. Click OK.



Process Control2/11/2017Ronald Morgan Shewchuk76Figure 6.26 SPC Chart Generation Steps Service ExampleClick I-MR Options.



Process Control2/11/2017Ronald Morgan Shewchuk77Figure 6.26 SPC Chart Generation Steps Service ExampleClick on the tab for Tests. Select the drop down menu to perform all tests for special causes. Click OK.



Process Control2/11/2017Ronald Morgan Shewchuk78Figure 6.26 SPC Chart Generation Steps Service ExampleClick OK.



Process Control2/11/2017Ronald Morgan Shewchuk79Figure 6.26 SPC Chart Generation Steps Service ExampleA graph is created in the Minitab project file with the stacked Individuals Moving Range SPC Charts. Out of control data points are highlighted in red and include a superscript number indicating which special cause test has been violated. In this case, test number 1 (one point greater than three standard deviations from the center line) is indicative of special cause variation.



Process ControlStatistical Process Control2/11/2017Ronald Morgan Shewchuk80In this case a spike in dropped calls has occurred at 13:00 hrs indicating a special cause. As it turns out, this data point records the percentage of dropped calls which occurred between the hours of 12:00 pm and 1:00 pm. This corresponds to the lunch hour where the number of customer calls increase while the number of call center associates decrease resulting in a spike of dropped calls because customers get tired of waiting in the incoming call queue. This indicates the need for a staffing schedule change to split the call center associates lunch hour and to provide additional support staffing during the lunch hour rush.



Process ControlProcess Capability2/11/2017Ronald Morgan Shewchuk81Analysis of your data may indicate that your process is in control but is it capable of meeting your customer requirements? Capability implies comparison of your process mean and standard deviation to the specification limits, the upper and lower bounds for which you and your customer have mutually agreed upon. This could be an external customer, in the case of a measured quality characteristic that is reported on your Certificate of Analysis (C of A) or it could be an internal customer, the next downstream process. A commonly used measure of process capability is the short term process capability index Cpk as defined by Eqn 6.7 and the long term process capability index Ppk as defined by Eqn 6.8. The difference between these two indices lies in the calculation of the standard deviation. Short term process capability utilizes the standard deviation as derived from control limits (remember X-bar 3s) whereas long term process capability utilizes the standard deviation as calculated from the overall data set (eg the STDEV function of Excel).



Process ControlProcess Capability2/11/2017Ronald Morgan Shewchuk82

Equation 6.7 Short Term Process Capability IndexEquation 6.8 Long Term Process Capability Index



Process ControlProcess Capability2/11/2017Ronald Morgan Shewchuk83Let us consider the example SPC chart of Figure 6.27 to understand the implications of process capability. The process appears to be in control with individual data points randomly distributed about the mean. If we add upper and lower spec limits to the control chart we notice that the process is operating in the upper half of the spec range as shown in Fig 6.28.The mean for this process is 287.58 F with an overall standard deviation of 1.212 F. Thus, we may calculate the Ppk as follows.



Process Control2/11/2017Ronald Morgan Shewchuk84Figure 6.27 Process Capability Implications SPC Chart



Process Control2/11/2017Ronald Morgan Shewchuk85Figure 6.28 Process Capability Implications SPC Chart with USL and LSL



Process ControlProcess Capability2/11/2017Ronald Morgan Shewchuk86A Ppk value below one indicates poor process capability. The typical goal for long term process capability is 1.33 or above. This corresponds to a sigma level of 4. Avoid the temptation to widen the spec limits to improve the Ppk. Centering the process mean over the process target while simultaneously reducing the standard deviation maximizes process capability.Minitab can be used to perform process capability analysis on your data and generate tiled charts which provide information on process control, data set normality and process capability. Figure 6.29 captures the screen shots of the process capability analysis steps.



Process Control2/11/2017Ronald Morgan Shewchuk87Figure 6.29 Process Capability Analysis Steps Manufacturing ExampleMake sure that your data is entered into the worksheet in the correct format and in chronological order. Click on Stat Quality Tools Capability Analysis Normal on the top menu.



Process Control2/11/2017Ronald Morgan Shewchuk88Figure 6.29 Process Capability Analysis Steps Manufacturing ExampleClick on Single column in the dialogue box and highlight C2 Temp_F. Click Select. Enter a Subgroup size of 1. Enter the lower spec and upper spec in the appropriate fields. Click OK.



Process Control2/11/2017Ronald Morgan Shewchuk89Figure 6.29 Process Capability Analysis Steps Manufacturing ExampleA graph is created in the Minitab project file with the process capability analysis results. The graph indicates that the process is biased toward the upper specification limit. The short term process capability index, Cpk is 0.60 and the long term process capability index, Ppk is 0.66.



Process Control2/11/2017Ronald Morgan Shewchuk90Figure 6.29 Process Capability Analysis Steps Manufacturing ExampleReturn to the active worksheet. Click on Stat Quality Tools Capability Sixpack Normal on the top menu.



Process Control2/11/2017Ronald Morgan Shewchuk91Figure 6.29 Process Capability Analysis Steps Manufacturing ExampleClick on Single column in the dialogue box and highlight C2 Temp_F. Click Select. Enter a Subgroup size of 1. Enter the lower spec and upper spec in the appropriate fields. Click OK.



Process Control2/11/2017Ronald Morgan Shewchuk92Figure 6.29 Process Capability Analysis Steps Manufacturing ExampleA new graph is created in the Minitab project file with the process capability sixpack analysis results.



Process ControlProcess Capability2/11/2017Ronald Morgan Shewchuk93The Individuals Chart and Moving Range Chart indicate no special causes of variation. The Last 25 Observations chart indicates randomly distributed points about the mean (a desirable result). The Capability Histogram indicates a bias of the process toward the upper spec limit. The Normal Probability Plot indicates that the source data is normally distributed since the P-value is greater than 0.05. The Capability Plot stacks the short term and long term process capability over the spec range. This is a powerful collection of charts enabling the analyst to understand the current state of process control and capability.But what should we do if the data set is not normally distributed as we experienced with the active ingredient concentration data of Figure 6.9? We can conduct a non-normal process capability analysis as shown in Figure 6.30 provided that we have identified the distribution type which most closely matches the data set as shown in Figure 6.13.



Process Control2/11/2017Ronald Morgan Shewchuk94Figure 6.30 Process Capability Analysis Steps Non-normal DistributionOpen the worksheet with the non-normal data you want to conduct process capability analysis on. Click on Stat Quality Tools Capability Analysis Nonnormal on the top menu.



Process Control2/11/2017Ronald Morgan Shewchuk95Figure 6.30 Process Capability Analysis Steps Non-normal Distribution

Click on Single column in the dialogue box and highlight C1 Active Ingredient (ppm). Click Select. Enter a Subgroup size of 1. Select Weibull from the Fit distribution drop down menu. Enter the lower spec and upper spec in the appropriate fields. In this case we have no lower spec, so the process capability analysis will be one-tailed. Click OK.



Process Control2/11/2017Ronald Morgan Shewchuk96Figure 6.30 Process Capability Analysis Steps Non-normal DistributionA new graph is created in the Minitab project file with the process capability sixpack analysis results.



Process ControlSummary2/11/2017Ronald Morgan Shewchuk97We now have tools for evaluating the degree of control a process exhibits and the capability of that process to meet customer requirements. Standard DeviationVarianceNormality TestingDistribution IdentificationSampling Plan DesignData Transformation for NormalityStatistical Process Control ChartsProcess Capability AnalysisRemember that variation has many sources. Before we pass judgment on the health of the process we must first understand the variation contribution caused by the measurement system.



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