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Introduction to Operations Management  Quality Assurance (Quality Control)

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Presentation on theme: "Introduction to Operations Management  Quality Assurance (Quality Control)"— Presentation transcript:

1 Introduction to Operations Management  Quality Assurance (Quality Control)

2 Introduction to Operations Management  Phases of Quality Assurance Acceptance sampling Process control Continuous improvement Inspection before/after production Corrective action during production Quality built into the process The least progressive The most progressive

3 Introduction to Operations Management  Inspection §How Much/How Often §Where/When §Centralized vs. On-site InputsTransformationOutputs Acceptance sampling Process control Acceptance sampling

4 Introduction to Operations Management  Inspection Costs Optimal Cost Amount of Inspection Cost of inspection Cost of passing defectives Total Cost

5 Introduction to Operations Management  Where to Inspect in the Process §Raw materials and purchased parts §Finished products §Before a costly operation §Before an irreversible process §Before a covering process

6 Introduction to Operations Management  Examples of Inspection Points

7 Introduction to Operations Management  Statistical Process Control §The Control Process l Define l Measure l Compare to a standard l Evaluate l Take corrective action l Evaluate corrective action

8 Introduction to Operations Management  Statistical Process Control §Variations and Control l Random variation: Natural variations in the output of process, created by countless minor factors l Assignable variation: A variation whose source can be identified

9 Introduction to Operations Management  Sampling Distribution Sampling distribution Process distribution Mean

10 Introduction to Operations Management  Normal Distribution Mean  95.5% 99.7%  Standard deviation

11 Introduction to Operations Management  Control Limits (Type I Error) Mean LCLUCL  /2  Probability of Type I error

12 Introduction to Operations Management  Control Limits Sampling distribution Process distribution Mean Lower control limit Upper control limit

13 Introduction to Operations Management  Mean Charts §Two approaches: If the process standard deviation  is available (x l If the process standard deviation is not available (use sample range to approximate the process variability)

14 Introduction to Operations Management  Mean charts ( SD of process available ) §Upper control limit (UCL) = average sample mean + z (S.D. of sample mean) §Lower control limit (LCL) = average sample mean - z (S.D. of sample mean)

15 Introduction to Operations Management  Mean charts ( SD of process not available ) §UCL = average of sample mean + A 2 (average of sample range) §LCL = average of sample mean - A 2 (average of sample range) §A 2 is a parameter depending on the sample size and is obtainable from table.

16 Introduction to Operations Management  Example §Means of sample taken from a process for making aluminum rods is 2 cm and the SD of the process is 0.1cm (assuming a normal distribution). Find the 3-sigma (99.7%) control limits assuming sample size of 16 are taken.

17 Introduction to Operations Management  Example (solution) §  x = SD of sample mean distribution l = SD of process /  (sample size) l = 0.1 /  (16) = §z = 3 §UCL = 2 + 3(0.025) = §LCL = = 1.925

18 Introduction to Operations Management  Example(p.427) §Twenty samples of size 8 have been taken from a process. The average sample range of the 20 samples is 0.016cm and the average mean is 3cm. Determine the 3- sigma control limits.

19 Introduction to Operations Management  Example §Average sample mean = 3cm §Average sample range = 0.016cm §Sample size = 8 §A 2 = 0.37 (From Table 9-2) §UCL = (0.016) = §LCL = (0.016) = 2.994

20 Introduction to Operations Management  Control Chart UCL LCL Sample number Mean Out of control Normal variation due to chance Abnormal variation due to assignable sources

21 Introduction to Operations Management  Observations from Sample Distribution Sample number UCL LCL 1234

22 Introduction to Operations Management  Mean and Range Charts UCL LCL UCL LCL R-chart x-Chart Detects shift Does not detect shift

23 Introduction to Operations Management  Mean and Range Charts UCL LCL UCL LCL x-Chart UCL LCL R-chart Detects shift Does not detect shift

24 Introduction to Operations Management  Control Chart for Attributes §p-Chart - Control chart used to monitor the proportion of defectives in a process §c-Chart - Control chart used to monitor the number of defects per unit

25 Introduction to Operations Management  Use of p-Charts §When observations can be placed into two categories. l Good or bad l Pass or fail l Operate or do not operate §When the data consists of multiple samples of several observations each

26 Introduction to Operations Management  p-chart §The center line is the average fraction (defective) p in the population if p is known, or it can be estimated from samples is it is unknown. §  p = SD of sample distribution =  {p(1-p)/n} §UCL p = p + z  p §LCL p = p - z  p

27 Introduction to Operations Management  Example (p.431) §The following table indicates the defective items in 20 samples, each of size 100. Construct a control chart that will describe 95.5% of the chance variations of the process

28 Introduction to Operations Management  Example §The following table indicates the defective items in 20 samples, each of size 100. Construct a control chart that will describe 95.5% of the chance variations of the process §No. of defective items

29 Introduction to Operations Management  Example (solution) §Population mean not available, to be estimated from sample mean §Total No. of defective items = 220 §Estimate sample mean = 220/{20(100)}=.11 §SD of sample =  {.11(1-.11)/100}= 0.03 §z = 2 (2-sigma) §UCL p = (.03) = 0.17 §LCL p = (.03) = 0.05 §Thus a control chart can be plotted (p.431)

30 Introduction to Operations Management  Use of c-Charts §Use only when the number of occurrences per unit of measure can be counted; nonoccurrences cannot be counted. l Scratches, chips, dents, or errors per item l Cracks or faults per unit of distance l Calls, complaints, failures per unit of time

31 Introduction to Operations Management  Process Capability Lower Specification Upper Specification Process variability matches specifications Lower Specification Upper Specification Process variability well within specifications Lower Specification Upper Specification Process variability exceeds specifications


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