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OPSM 301 Operations Management Class 22: Quality: Statistical process control Koç University Zeynep Aksin

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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

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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

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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

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MBPF Process Control and Capability5 Process Control Chart 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: Type I - False alarm (unnecessary investigation) Type II - Missed signal (to identify and correct)

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X-bar – Chart Shows sample means over time Means of the values in a sample Monitors process mean

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7 X Bar Chart Average X bar = 82.5 kg Standard Deviation of X bar = 1.6 kg Control Limits= Average X bar + 3 Std of X bar = (3)(1,6) = [77.7, 87.3] Process is “In Control” (i.e., the mean is stable) UCL LCL

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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

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MBPF Process Control and Capability 9 Range (R) Chart Average Range R = 10.1 kg Standard Deviation of Range = 3.5 kg Control Limits: (3)(3.5) = [0, 20.6] Process Is “In Control” (i.e., variation is stable) UCL LCL

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17 = UCL 15 = LCL 16 = Mean Setting Control Limits Control Chart for sample of 9 boxes Sample number |||||||||||| Variation due to assignable causes Variation due to natural causes Out of control

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Mean and Range Charts (a) These sampling distributions result in the charts below (Sampling mean is shifting upward but range is consistent) R-chart (R-chart does not detect change in mean) UCLLCL x-chart (x-chart detects shift in central tendency) UCLLCL

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Mean and Range Charts R-chart (R-chart detects increase in dispersion) UCLLCL (b) These sampling distributions result in the charts below (Sampling mean is constant but dispersion is increasing) x-chart (x-chart does not detect the increase in dispersion) UCLLCL

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Process Control and Improvement LCL UCL Out of ControlIn ControlImproved

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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

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