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# Class 22 - AGENDA • FINISH UP X-BAR AND R CHART •...

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Unformatted text preview: AGENDA • FINISH UP X-BAR AND R CHART • PROCESS CAPABILITY Mean and Range Charts (a) (Sampling mean is (Sampling shifting upward but range is consistent) range These These sampling distributions result in the charts below charts UCL x-chart LCL UCL R-chart LCL Figure S6.5 (x-chart detects (x-chart shift in central tendency) tendency) (R-chart does not (R-chart detect change in mean) mean) Mean and Range Charts (b) These These sampling distributions result in the charts below charts (Sampling mean (Sampling is constant but dispersion is increasing) increasing) UCL x-chart LCL UCL R-chart LCL Figure S6.5 (x-chart does not (x-chart detect the increase in dispersion) in (R-chart detects (R-chart increase in dispersion) dispersion) Control Charts for Attributes For variables that are categorical Good/bad, yes/no, Good/bad, acceptable/unacceptable acceptable/unacceptable Measurement is typically counting Measurement defectives defectives Charts may measure Percent defective (p-chart) Number of defects (c-chart) Control Limits for p-Charts Population will be a binomial distribution, Population but applying the Central Limit Theorem allows us to assume a normal distribution for the sample statistics for ^ UCLp = p + zσ p σp = ^ ^ LCLp = p - zσ p p = = = = p(1 - p) n mean fraction defective in the sample number of standard deviations ^ standard deviation of the sampling distribution sample size Control Limits for c-Charts Population will be a Poisson distribution, Population but applying the Central Limit Theorem allows us to assume a normal distribution for the sample statistics for UCLc = c + 3 c c = LCLc = c - 3 c mean number defective in the sample Which Control Chart to Use Variables Data Using an x-chart and R-chart: Observations are variables Collect 20 - 25 samples of n = 4, or n = Collect 20 or 5, or more, each from a stable process or and compute the mean for the x-chart and range for the R-chart and Track samples of n observations each Which Control Chart to Use Attribute Data Using the p-chart: Observations are attributes that can Observations be categorized in two states We deal with fraction, proportion, or We percent defectives percent Have several samples, each with Have many observations many Which Control Chart to Use Attribute Data Using a c-Chart: Observations are attributes whose Observations defects per unit of output can be counted counted The number counted is a small part of The the possible occurrences the Defects such as number of blemishes Defects on a desk, number of typos in a page of text, flaws in a bolt of cloth of Patterns in Control Charts Upper control limit Target Lower control limit Figure S6.7 Normal behavior. Normal Process is “in control.” Process Patterns in Control Charts Upper control limit Upper Target Lower control limit Figure S6.7 One plot out above (or One below). Investigate for cause. Process is “out of control.” of Patterns in Control Charts Upper control limit Upper Target Lower control limit Figure S6.7 Trends in either Trends direction, 5 plots. Investigate for cause of progressive change. progressive Patterns in Control Charts Upper control limit Upper Target Lower control limit Figure S6.7 Two plots very near Two lower (or upper) control. Investigate for cause. cause. Patterns in Control Charts Upper control limit Upper Target Lower control limit Figure S6.7 Figure Run of 5 above (or Run below) central line. Investigate for cause. Patterns in Control Charts Upper control limit Upper Target Lower control limit Erratic behavior. Erratic Investigate. Investigate. Figure S6.7 Process Capability The natural variation of a process The should be small enough to produce products that meet the standards required required A process in statistical control does not process necessarily meet the design specifications specifications Process capability is a measure of the Process relationship between the natural variation of the process and the design specifications specifications Process Capability Ratio Upper Specification - Lower Specification Upper Cp = 6σ A capable process must have a Cp of at capable least 1.0 1.0 Does not look at how well the process Does is centered in the specification range Often a target value of Cp = 1.33 is used Often to allow for off-center processes to Six Sigma quality requires a Cp = 2.0 Process Capability Ratio Insurance claims process Process mean x = 210.0 minutes Process 210.0 Process standard deviation σ = .516 minutes Process Design specification = 210 ± 3 minutes Design 210 Upper Specification - Lower Specification Upper Cp = 6σ Process Capability Ratio Insurance claims process Process mean x = 210.0 minutes Process 210.0 Process standard deviation σ = .516 minutes Process Design specification = 210 ± 3 minutes Design 210 Upper Specification - Lower Specification Upper Cp = 6σ 213 - 207 = = 1.938 6(.516) Process Capability Ratio Insurance claims process Process mean x = 210.0 minutes Process 210.0 Process standard deviation σ = .516 minutes Process Design specification = 210 ± 3 minutes Design 210 Upper Specification - Lower Specification Upper Cp = 6σ 213 - 207 Process is = = 1.938 6(.516) capable Process Capability Index Upper Lower Cpk = minimum of Specification - x , x - Specification Limit Limit 3σ 3σ A capable process must have a Cpk of at capable least 1.0 1.0 A capable process is not necessarily in the capable center of the specification, but it falls within the specification limit at both extremes the Process Capability Index New Cutting Machine New process mean x = .250 inches New .250 Process standard deviation σ = .0005 inches Process Upper Specification Limit = .251 inches Upper .251 Lower Specification Limit = .249 inches Process Capability Index New Cutting Machine New process mean x = .250 inches New .250 Process standard deviation σ = .0005 inches Process Upper Specification Limit = .251 inches Upper .251 Lower Specification Limit = .249 inches Cpk = minimum of (.251) - .250 , (3).0005 Process Capability Index New Cutting Machine New process mean x = .250 inches New .250 Process standard deviation σ = .0005 inches Process Upper Specification Limit = .251 inches Upper .251 Lower Specification Limit = .249 inches Cpk = minimum of (.251) - .250 .250 - (.249) , (3).0005 (3).0005 Both calculations result in Cpk = .001 = 0.67 .0015 New machine is NOT capable Interpreting Cpk Cpk = negative number Cpk = zero Cpk = between 0 and 1 Cpk = 1 Cpk > 1 Figure S6.8 SPC and Process Variability Lower Lower specification limit limit Upper Upper specification limit limit (a) Acceptance Acceptance sampling (Some bad units accepted) bad (b) Statistical process Statistical control (Keep the process in control) process (c) Cpk >1 (Design a process that is in control) is Process mean, µ Process Figure S6.10 ...
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