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Koç University OPSM 301 Operations Management Class 22: Quality: Statistical process control Zeynep Aksin [email protected] Statistical Process Control Detect and eliminate assignable variation (statistical process control) – If there is no assignable variation, Process is in control – We use Process Control charts to maintain this Natural Variations Also called common causes Affect virtually all production processes Expected amount of variation, inherent due to: - the nature of the system - the way the system is managed - the way the process is organised and operated can only be removed by - making modifications to the process - changing the process Output measures follow a probability distribution For any distribution there is a measure of central tendency and dispersion Assignable Variations Also called special causes of variation Exceptions to the system Generally this is some change in the process Variations that can be traced to a specific reason considered abnormalities often specific to a certain operator certain machine certain batch of material, etc. The objective is to discover when assignable causes are present Eliminate the bad causes Incorporate the good causes Process Measure Process Control Chart Time Information: Monitor process variability over time Control Limits: Average + z Normal Variability Decision Rule: Ignore variability within limits as “normal” Investigate variation outside “abnormal” Errors: MBPF Type I - False alarm (unnecessary investigation) Control and Capability TypeProcess II - Missed signal (to identify and correct) 5 X-bar – Chart Shows sample means over time Means of the values in a sample Monitors process mean X Bar Chart UCL Average 86 84 82 80 LCL 78 19 17 15 13 9 11 7 5 3 1 76 Day Average X bar = 82.5 kg Standard Deviation of X bar = 1.6 kg Control Limits = Average X bar + 3 Std of X bar = 82.5 + (3)(1,6) = [77.7, 87.3] Process is “In Control” (i.e., the mean is stable) 7 R – Chart Type of variables control chart Shows sample ranges over time Difference between smallest and largest values in sample Monitors process variability Independent from process mean Range Range (R) Chart UCL 20 15 10 5 0 LCL 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Day Average Range R = 10.1 kg Standard Deviation of Range = 3.5 kg Control Limits: 10.1 + (3)(3.5) = [0, 20.6] Process Is “In Control” (i.e., variation is stable) MBPF Process Control and Capability 9 Setting Control Limits Control Chart for sample of 9 boxes Variation due to assignable causes Out of control 17 = UCL Variation due to natural causes 16 = Mean 15 = LCL | | | | | | | | | | | | 1 2 3 4 5 6 7 8 9 10 11 12 Sample number Out of control Variation due to assignable causes Mean and Range Charts (a) (Sampling mean is shifting upward but range is consistent) These sampling distributions result in the charts below UCL (x-chart detects shift in central tendency) x-chart LCL UCL (R-chart does not detect change in mean) R-chart LCL Mean and Range Charts (b) These sampling distributions result in the charts below (Sampling mean is constant but dispersion is increasing) UCL (x-chart does not detect the increase in dispersion) x-chart LCL UCL (R-chart detects increase in dispersion) R-chart LCL Process Control and Improvement Out of Control UCL LCL In Control Improved Important points to remember Control charts are used to differentiate normal variability from assignable/abnormal variability X-bar chart monitors control of process mean R-chart monitors control of process variability An improvement in the process implies lower normal variability