Quality Control Essay ⋆ Business Essay Examples ⋆ EssayEmpire

The systematic approach to quality control was developed in industrial manufacturing in the interwar years. With the impact of mass production required during World War II, it became necessary to introduce a more rigorous form of quality control. Some of the initial work is credited to Walter Shewhart of Bell Labs, starting with his famous one-page memorandum of 1924.

Control charts are often employed to detect changes in a process mean over time. In the traditional approach, a sample is drawn, and the sample mean ( x) is calculated and plotted on a Shewhart X chart having control limits, which depict the extremes of pure chance fluctuations. A point outside the limits suggests that the process is off target. While a Shewhart X chart is relatively easy to use and interpret, according to W. H. Woodall, a cumulative sum (CUSUM) chart is more capable of detecting small changes in the process mean, as well as pinpointing the exact time when the process goes “out of control.” Faster detection of significant changes means tighter control, which is necessary if corrective action is to be taken promptly.

Like Shewhart and CUSUM control schemes, an exponentially weighted moving average (EWMA), as discussed by J. M. Lucas and M. S. Saccucci, control scheme is easy to implement and interpret. The ability of the EWMA chart to detect small shifts in the process mean is on a par with the CUSUM chart and superior to the Shewhart X chart. Lucas and Saccucci argued that the EWMA chart is simpler to explain to the lay user than the CUSUM chart, by noting its similarity to the classical Shewhart X chart. Both the CUSUM and EWMA charts are more suitable for single sampling schemes.

A control chart procedure has been proposed for which the Shewhart X chart, the cumulative sum chart, and the exponentially weighted moving average chart are special cases. The procedure for constructing these charts has been described by C. W. Champ and colleagues.

A typical statistical test examines the validity of a null hypothesis, H0 (the process is on target), against an alternative, HA (the process has changed). A Type on target, but, by chance, lies outside the control limits. A Type II error is said to occur if H0 is accepted when HA is true and occurs with a probability β. That is, the process has deviated, but lies within the control limits. The power of a test is defined to be the probability of correctly rejecting a false null hypothesis, and is equal to 1-β. For a given α, one test is more powerful than another if 1-β for the former is greater than for the latter for all possible changes in the process mean.

Referring to the process under consideration, assume a batch has a true mean μ. Let τ be an acceptable target value for μ; therefore a batch is acceptable if μ=τ. In this case H0 is μ=τ and HA is μ≠τ. If a batch is rejected when, in fact, the mean is μ=τ, this is unfair to the producer. This is called the producer’s risk or Type I error, and occurs with a probability α. Conversely, if a batch is accepted when, in fact, the mean is μ≠τ, this is unfair to the consumer. This is called the consumer’s risk or Type II error, and occurs with a probability β.

The consumer’s risk (β) depends on the absolute difference between μ and τ. This is the drift Δ, where Δ=τμ. The sample size and control limits may be selected to obtain acceptable values of α and β for a specified Δ.

The Average Run Length (ARL) for a given Δ gives the average number of batches sampled till one is rejected. The ARL is dependent on both α and β and is an important factor in selecting a control chart. The plan (the sample size and control limits) is usually chosen so that the ARL is large (500 to 1,000) when the process is on target, and small (1.1 to 10) when the process changes by Δ. The criteria are acceptable risks of incorrect actions, expected average quality levels reaching the customer and expected average inspection loads.

All the charts described so far examine the sample mean. In a process the mean might appear acceptable, but there could be a change in the inherent process variation. To monitor this variability, a range chart should also be used.

Bibliography:

Ron Basu, Implementing Six Sigma and Lean: A Practical Guide to Tools and Techniques (Butterworth-Heinemann, 2008);
Dale H. Besterfield, Quality Control (Pearson Prentice Hall, 2009);
Charles W. Champ, William H. Woodall, and Hassan A. Mohsen, “A Generalised Quality Control Procedure,” Statistics & Probability Letters (v.11/3, 1991);
Mark L. Crossley, The Desk Reference of Statistical Quality Methods (ASQ Quality Press, 2008);
Acheson J. Duncan, Quality Control and Industrial Statistics (Richard D. Irwin Press, 1986);
James M. Lucas et al., “Exponentially Weighted Moving Average Control Schemes: Properties and Enhancements,” Technometrics (v.32/1, 1990);
Douglas C. Montgomery, Statistical Quality Control: A Modern Introduction (John Wiley & Sons, 2009);
Walter A. Shewhart, Economic Control of Quality of Manufactured Products (Macmillan, 1931);
William H. Woodall, “The Design of CUSUM Quality Control Charts,” Journal of Quality Technology (v.18/2, 1986).

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