© Anita Lee-Post Quality Control Part 2 By Anita Lee-Post By

© Anita Lee-Post Statistical process control methods Control charts for variables: process characteristics are measured on a continuous scale, e.g., weight, volume, widthControl charts for variables: process characteristics are measured on a continuous scale, e.g., weight, volume, width Mean (X-bar) chart Mean (X-bar) chart Range (R) chart Range (R) chart Control charts for attributes: process characteristics are counted on a discrete scale, e.g., number of defects, number of scratchesControl charts for attributes: process characteristics are counted on a discrete scale, e.g., number of defects, number of scratches Proportion (P) chart Proportion (P) chart Count (C) chart Count (C) chart Process capability ratio and indexProcess capability ratio and index Control charts for variables: process characteristics are measured on a continuous scale, e.g., weight, volume, widthControl charts for variables: process characteristics are measured on a continuous scale, e.g., weight, volume, width Mean (X-bar) chart Mean (X-bar) chart Range (R) chart Range (R) chart Control charts for attributes: process characteristics are counted on a discrete scale, e.g., number of defects, number of scratchesControl charts for attributes: process characteristics are counted on a discrete scale, e.g., number of defects, number of scratches Proportion (P) chart Proportion (P) chart Count (C) chart Count (C) chart Process capability ratio and indexProcess capability ratio and index

© Anita Lee-Post Control charts Use statistical limits to identify whether a sample of data falls within a normal range of variation or notUse statistical limits to identify whether a sample of data falls within a normal range of variation or not

© Anita Lee-Post Setting Limits Requires Balancing Risks Control limits are based on a willingness to think that something is wrong when it’s actually not (Type I or alpha error), balanced against the sensitivity of the tool - the ability to quickly reveal a problem (failure is Type II or beta error)Control limits are based on a willingness to think that something is wrong when it’s actually not (Type I or alpha error), balanced against the sensitivity of the tool - the ability to quickly reveal a problem (failure is Type II or beta error)

© Anita Lee-Post Control Charts for Variable Data Mean (x-bar) chartsMean (x-bar) charts Tracks the central tendency (the average value observed) over time Tracks the central tendency (the average value observed) over time Range (R) charts:Range (R) charts: Tracks the spread of the distribution over time (estimates the observed variation) Tracks the spread of the distribution over time (estimates the observed variation) Mean (x-bar) chartsMean (x-bar) charts Tracks the central tendency (the average value observed) over time Tracks the central tendency (the average value observed) over time Range (R) charts:Range (R) charts: Tracks the spread of the distribution over time (estimates the observed variation) Tracks the spread of the distribution over time (estimates the observed variation)

© Anita Lee-Post Mean (x-bar) charts

© Anita Lee-Post Mean (x-bar) charts continued Use the x-bar chart established to monitor sample averages as the process continues:Use the x-bar chart established to monitor sample averages as the process continues:

© Anita Lee-Post An example The diameters of five C&A bagels are sampled each hour during a 8-hour period. The data collected are shown as follows:

© Anita Lee-Post An example continued a)Develop an x-bar chart with the control limits set to include 99.74% of the sample means and the standard deviation of the production process (  ) is known to be 0.2 Inches. Step 1. Compute the sample mean x-bar: a)Develop an x-bar chart with the control limits set to include 99.74% of the sample means and the standard deviation of the production process (  ) is known to be 0.2 Inches. Step 1. Compute the sample mean x-bar:

© Anita Lee-Post An example continued Step 2. Compute the process mean or center line of the control chart:

© Anita Lee-Post An example continued Step 3. Compute the upper and lower control limits: To include 99.74% of the sample means implies that the number of normal standard deviations is 3. i.e., z=3 Step 3. Compute the upper and lower control limits: To include 99.74% of the sample means implies that the number of normal standard deviations is 3. i.e., z=3

© Anita Lee-Post An example continued b.C&A collects the process characteristics (i.e., diameter) of their bagels in days 2 through 10. Is the process in control? The process is not in control because the means of recent sample averages fall outside the upper and lower control limits LCL = 3.83 UCL = 4.25

© Anita Lee-Post Range (R) charts

© Anita Lee-Post An example The diameters of five C&A bagels are sampled each hour during a 8-hour period. The data collected are shown as follows:

© Anita Lee-Post An example continued a)Develop a range chart. Step 1. Compute the average range or CL: a)Develop a range chart. Step 1. Compute the average range or CL:

© Anita Lee-Post An example continued Step 2. Compute the upper and lower control limits: Control Limit Factors for Range Charts Sample size, nD3D

© Anita Lee-Post An example continued b.C&A collects the process characteristics (i.e., diameter) of their bagels in days 2 through 10. Is the process in control? The process is in control because the ranges of recent samples fall within the upper and lower control limits UCL = 0.57 LCL = 0 CL = 0.27

© Anita Lee-Post Using both mean & range charts Mean (x-bar) chart: measures the central tendency of a processMean (x-bar) chart: measures the central tendency of a process Range (R) chart: measures the variance of a processRange (R) chart: measures the variance of a process Case 1: a process showing a drift in its mean but not its variance  can be detected only by a mean (x-bar) chart  can be detected only by a mean (x-bar) chart Mean (x-bar) chart: measures the central tendency of a processMean (x-bar) chart: measures the central tendency of a process Range (R) chart: measures the variance of a processRange (R) chart: measures the variance of a process Case 1: a process showing a drift in its mean but not its variance  can be detected only by a mean (x-bar) chart  can be detected only by a mean (x-bar) chart

© Anita Lee-Post Using both mean & range charts continued Case 2: a process showing a change in its variance but not its mean  can be detected only by a range (R) chart  can be detected only by a range (R) chart Case 2: a process showing a change in its variance but not its mean  can be detected only by a range (R) chart  can be detected only by a range (R) chart

© Anita Lee-Post Construct x-bar chart from sample range

© Anita Lee-Post Control Charts for Attributes p-Charts:p-Charts: Track the proportion defective in a sample Track the proportion defective in a sample c-Charts:c-Charts: Track the average number of defects per unit of output Track the average number of defects per unit of output p-Charts:p-Charts: Track the proportion defective in a sample Track the proportion defective in a sample c-Charts:c-Charts: Track the average number of defects per unit of output Track the average number of defects per unit of output

© Anita Lee-Post Proportion (p) charts Data requirements:Data requirements: Sample size Sample size Number of defects Number of defects Sample size is large enough so that the attributes will be counted twice in each sample, e.g., a defect rate of 1% will require a sample size of 200 units. Sample size is large enough so that the attributes will be counted twice in each sample, e.g., a defect rate of 1% will require a sample size of 200 units. Data requirements:Data requirements: Sample size Sample size Number of defects Number of defects Sample size is large enough so that the attributes will be counted twice in each sample, e.g., a defect rate of 1% will require a sample size of 200 units. Sample size is large enough so that the attributes will be counted twice in each sample, e.g., a defect rate of 1% will require a sample size of 200 units.

© Anita Lee-Post Proportion (p) charts continued

© Anita Lee-Post Count (c) charts Data requirementsData requirements Number of defects Number of defects Monitoring processes in which the items of interest (in this case, defects) are infrequent and/or occur in time or space, e.g., errors in newspaper, bad circuits in a microchip, complaints from customers. Monitoring processes in which the items of interest (in this case, defects) are infrequent and/or occur in time or space, e.g., errors in newspaper, bad circuits in a microchip, complaints from customers. Data requirementsData requirements Number of defects Number of defects Monitoring processes in which the items of interest (in this case, defects) are infrequent and/or occur in time or space, e.g., errors in newspaper, bad circuits in a microchip, complaints from customers. Monitoring processes in which the items of interest (in this case, defects) are infrequent and/or occur in time or space, e.g., errors in newspaper, bad circuits in a microchip, complaints from customers.

© Anita Lee-Post Count (c) charts continued