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Question 1: a. A control chart can indicate an out-of-control condition even though no single point plots outside the control limits. Comment. Illustrate your answer using suitable sketches. b. Compare between assignable cause variation and chance cause variation. In your opinion what are the reasons behind each one?
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I write answer for part a and upload a photo for part b also please consider it. the tide the ntral Oits stitetrom equipn oc et LC七 aihtly outaida e com near the Centex 0ine as-ahesyig_tu2_ mox atterne 2 process Jeve i j madhime ,a e in the ims pectiom method on aond the aperalo Covlituous movemen im one disc hon is hoon onIn any production process, regardless of how well designed or careiully maintained it is, a cer- tain amount of inherent or natural variability will always exist. This natural variability or background noise is the cumulative effect of many small, essentially unavoidable causes. In the framework of statistical quality control, this natural variability is often called a stable system of chance causes. A process that is operating with only chance causes of variation resent is said to be in statistical control In other words. the chance causes are an inherent part of the process Other kinds of variability may occasionally be present in the output of a process. This variability in key quality characteristics usually arises from three sources: improperly adjusted or controlled machines operator errors, or defective raw material Such variability is generally large when compared to the background noise, and it usually represents an unac- ceptable level of process performance. We refer to these sources of variability that are not part of the chance cause pattern as assignable causes of variation. A process that is operating in the presence of assignable causes is said to be an out-of-control processA major objective of statistical process control is to quickly detect the occurrence of assignable causes of process shifts so that investigation of the process and corrective action may be undertaken before many nonconforming units are manufactured. The control chart is an on-line process-monitoring technique widely used for this purpose. Control charts may also be used to estimate the parameters of a production process, and. through this informa- tion, to determine process capability. The control chart may also provide information useful in improving the process. Finally, remember that the e trol is the elimination of variability in the process. It may not he possible to completely eliminate variability. but the control chart is an effective tool in reducing variability as much as possíble ventual goal of statistical process con-

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