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

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

 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)

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

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

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

 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

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

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

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

Process Control and Improvement LCL  UCL Out of ControlIn ControlImproved

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